MASTER NEGATIVE NO. 95-82432 COPYRIGHT STATEMENT The copyright law of the United States (Title 17, United States Code) governs the making of photocopies or other reproductions of copyrighted materials Including foreign works under certain conditions. In addition, the United States extends protection to foreign works by means of various International conventions, bilateral agreements, and proclamations. Under certain conditions specified In the law, libraries and archives are authorized to furnish a photocopy or other reproduction. One of these specified conditions Is that the photocopy or reproduction Is not to be "used for any purpose other than private study, scholarship, or research." If a user makes a request for, or ater uses, a photocopy or reproduction for purposes In excess of "fair use," that user may be liable for copyright infringement. The Columbia University Libraries reserve the right to refuse to accept a copying order If, in its judgement, fulfillment of the order would Involve violation of the copyright law. Author: Inwood, William Title: Inwood's tables of interest and mortality for the... Place: London Date: 1920 ^5-^2.431-1 MASTER NEGATIVE # COLUMBIA UNIVERSITY LIBRARIES PRESERVATION DIVISION BIBLIOGRAPHIC MICROFORM TARGET ORIGINAL MATERIAL AS FILMED - EXISTING BIBLIOGRAPHIC RECORD D481 In8 Inwood, William Inwood* s tables of interest and mortality for the purchasing of estates and valuation of properties... rev. and extended by William Schooling. . . with logarithms of natural numbers and Thoman' s logarithmic interest and annuity tables... London, Lockwood, 1920. xl, 320 p. tables. 22 cm. \^^^/ RESTRICTIONS ON USE: TECHNICAL MICROFORM DATA FILM SIZE: i5<»i«>i REDUCTION RATIO: Ik IMAGE PLACEMENT: lA @) IB MB DATE FILMED: TRACKING # : ^1% INITIALS: .1 ^^ OSSU^ FILMED BY PRESERVATION RESOURCES. BETHLEHEM. PA. (Jj CJI 3 3 Q) CT O > %^ ?Q a -.m io |o en OOM o '•<« cN C7I 3 3 > o m CD O OQ ^ o O CO X < N X o- ^: ^V .»^ A^' ^, A^^ n^-^ "j;^ ^ ^^^^. ^.< Ol ^r-? jj: *^: •m :^^' ^ .>** *»' i 3 3 Ul o 3 3 <^ > j^/ >« %5^ O o 3 3 O «rpi!|=p|?|;|;|- bo o 00 K3 b to cn 1.0 mm 1.5 mm 2.0 mm ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghi|klmnopqrstuvwxy2l234667890 ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyzl234567890 ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz 1234567890 2.5 mm ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz 1234567890 % .«« ** fo V ^ Ik \? ^^ ^o ip f^ '■is- '>, '/!'. '?' ■#. r^ •/^ *^ 4^ V ** r^ fo ^CP 'f* ^^^ '^ m o •o m -o OL,"0 > C c*> z ^ ^ s Ooo OC/) 5 m 30 o m .*♦*. •#. «•. € ^%. ^/^> '^^ 4 'l^ 3 3 3 3 Is 3i 3rr 13 3»>C ^o ^^^. ^^^J ^ * ^ in ttie Cttp of ^to l^orb LIBRARY ^t&ool of iBus(inefi(K dTb^ iKontgometp Hiibratp of 9ttotintamp INWOOD'S TABLES OF INTEREST AND MORTALITY FOR THE PURCHASING OF ESTATES AND VALUAirON OF "PROPERTIES INCLUDING ADVOWSONS ASSURANCE POLICIES COPYHOLDS DEFERRED ANNUITIES FREEHOLDS GROUND RENTS IMMEDIATE ANNUITIES ETC. LEASEHOLDS LIFE INTERESTS MORTGAGES PERPETUITIES RENEWALS OF LEASES REVERSIONS SINKING FUNDS Era BY WILLIAM SCHOOLING, F.R.A.S. WITH LOCJARITHMS OF NATURAL NUMBERS AMD THOMAN'S LOGARITHMIC INTEREST AND ANNUITY TABLES tTbirt^sfiret 5mprcggion ^ol]^ LONDON CROSBY LOCKWOOD AND SON 7 STATIONERS' HALL COURT. LUDGATE HILL 1920 ^^»^» I I ■ ■ ^8 1 o NOTE TO THB THIRTIETH EDITION. The present edition, besides retaining the additions to the preceding issue, has been carefully revised, and in it, thanks to the courtesy of correspondents, a few errors of the press will be found corrected. Should any user of the book discover a mistake in even a single figure, the Publishers will be greatly obliged by having their attention called to it. William Schooling. I? Old Queen Street, Westminster, S.W. (iii) PREFACE TO THE TWENTY-SIXTH EDITION In response to requests received since the issue of the Twenty-fifth Edition of this work, Tables I. and XVII. of the Twenty-fourth and earlier editions are now given here, in similar form to that in which they there appeared. They have, however, been extended to many more rates of interest, and Table XVII. has been extended to longer terms of years than formerly. The old Table I. will be found in the present edition on pp. xx to xxxi, and the old Table XVII. on pp. xxxii to xxxix. The former of these two Tables, it may be pointed out, appears also for integral years to a larger number of decimal places in the Tables showing the present value of £i per annum (pp. 50 to 85, and 92 and 93). The present value of the reversion of a perpetuity appears to a larger number of decimal places on pp. 95 to 98. The values in the Table for purchasing of leases, estates, or annuities (pp. xx to xxxi) do not agree, so far as half- years are concerned, with the Twenty-fourth edition. The method formerly adopted assumed interest to be convertible momently or continuously. This supposition, however, is not usually employed, but in practice the value of a lease or annuity certain, say for 22^ years at 6 per cent, per annum, would be considered to be equivalen\t to the value of a lease or annuity certain for double the term (or 45 years), at half the rate of interest (or 3 per cent per annum;. This value would be equal to 12*259, whilst the value given in old editions of * Inwood' is 121 74 only, thelatter representing the value of an annuity of i for 22 i years, computed at such a rate of interest convertible momently as would be equivalent to an PREFACE TO THE TWENTY-SIXTH EDITION actual or-e-ffective rate of 6 per cent, per annum. The value assigned in practice of 12*259 i^ based upon a rate of interest at 3 per cent, per half-year, which is equal to an effective annual rate of 6*09, or £6 is. lod. per cent, per annum (see pp. 18 and 122). It will be recognised therefore that in conformity with the usual practice the values now given for integral years assume interest to be convertible annually, and the values for the half-years assume it to be convertible half- yearly. In response to a suggestion that the present value of ;^i and of £1 per annum at 15 per cent, per annum would be found convenient by mining engineers and others, a table giving these values has been computed, and is given on p. xl. The method adopted was as follows. The present value * of ^i per annum due at the end of 100 years was calculated by the aid of Gray's 24 figure logarithms, true to fifteen places of decimals ; multiplying this amount by the rate of interest gives the arithmetical complement of the present value of £\ due at the end of 100 years ; adding these two items together and deducting unity gives the amount of ^i per annum at the end of 99 years, and this process was continued to the end of the Table. In multiplying by the rate of interest it was convenient to employ Tate's Arithmo- meter, by means of which the necessary multiplications and additions were performed with the greatest ease. The results were checked every ten years, and the number of decimal places was reduced from time to time, the result being brought true to nine places when, at the end, of the calculations, the first year was reached. In the present edition a few errors, which have been discovered since the publication of the last edition, have been corrected. William Schooling. iv) PREFACE TO THE TWENTY-FIFTH EDITION PREFACE TO THE TWENTY-FIFTH EDITION In the present edition of this work, many extensive additions have been made, and the book has been entirely reset ; the size of the page has been enlarged, to allow of a more convenient arrangement of the Tables ; the whole of it has been carefully revised ; and the Tables have been placed in logical sequence. The volume now contains 336 pages demy 8vo, as compared with 308 pages crown Svo in the last edition. The principal alterations and additions may be briefly recorded. The Interest Tables, which were formerly scattered throughout the book, are now all brought together. The amount and present value of £1 and of £1 per annum at the same rate of interest all appear on the same page, instead of each of these items at varying rates of interest being tabu- lated separately. For most purposes this is more convenient, but on pp. 86-93 abbreviated Tables appear in the old form. Throughout the book any Table that occupies two pages is arranged so that the whole of it may be seen at one opening — a detail that adds much to the convenience of using the Table. The Rates of Interest for which Tables were previously given were 2, 2^, 3, 3J, 4, 41, 5, 6, 7, 8, 9, 10. These are all retained, and six other rates— i, i^, i^, ij, 2J, 2|— have^ been added. (vi) Five places of decimals are given instead of four, as was the case for some of the rates in previous editions. The abbreviated Tables in the old form are given at 3J, 3l, 44 » 4h and 5^ per cent, in addition to the 18 rates mentioned above. The present value of Perpetuities and of the Reversion to a Perpetuity are given in very much greater detail than before, both as regards the rates of interest and the number of decimal places. The Tables dealing with the Renewals of Leases are given at more rates of interest, while the Miscellaneous Tables, such as those on pp. 104, 105, 124, etc., are extended. The Sinking Fund Table is now given for 20 different rates of interest to 6 places of decimals for every year from I to 100, as compared with 10 rates of interest to (mostly) 4 places. The Tables showing the Value of an Annuity yielding interest at one rate, and providing for replacing capital at another rate, now occupy six pages instead of less than two, and are given to 5 places of decimals instead of 2, as well as at many more rates of interest. On pp. 122 and 123 some important Tables appear dealing with Interest payable half-yearly, quarterly, and monthly, together with a Table of constant factors for finding the values of Annuities payable half-yearly, quarterly, and monthly from the values of yearly annuities. These are quite new to the book. The decimals of ^i are given for every farthing instead of for every penny, and the decimals of a year are given in more detail. In the Mortality Tables and the combined Mortality and Interest Tables, very many additions of much importance have been made. Apart from more numerous Tables and lower rates of interest, the values of the benefits according to the Healthy Males Table of the Institute of Actuaries and the Govern- (vii) \\ PREFACE TO THE TWENTY-FIFTH EDITION ment Experience Table of 1883 are introduced. These Tables are of the greatest value, and many of the items deduced from them are tabulated in considerable detail. Among the Mortality Tables the English No. 3 also appears; while here, as throughout the book, all kindred tables appear on consecutive pages. Users of the book will find reference to it facilitated, if by a glance at the Table of Contents they grasp the order in which the contents are arranged. It will be seen to be— 1. Interest apart from lives. 2. Lives apart from interest. 3. Interest in connection with single lives. 4. Interest in connection with two lives. 5. Interest in connection with three lives. 6. Logarithmic tables. In each of the divisions 3, 4, 5, the same order is main- tained. The additions in the parts of the book dealing with Interest and Mortality combined are too numerous for detailed record. Everything of any value in former editions is retained, while additions have been made that bring the whole thoroughly up to date as regards both the Mortality Tables and the rates of Interest employed. In addition to this, care has been taken to supply such data in the Tables, and such explanations and examples in the Introduction, as to make it a perfectly simple matter to calculate the values of benefits for other ages or at other rates of interest than are contained in the Tables. If any required information is not found in the Tables, a reference to the part of the Introduction dealing with the subject in question will probably show how the information may readily be arrived at. Special attention may perhaps be called to the Premium Conversion Tables on pp. 185 and 186, and to the explana- tion of them given in the Introduction. The Annual Premium Table is given ia a novel form, which, it is believed, (viii) PREFACE TO THE TWENTV-FIFTH EDITION offers considerable advantages. Both the Conversion Tables will be found very convenient for many purposes, and readers unfamiliar with such tables would do well to spend a few minutes in grasping their nature, which is quite simple. The Post Office Annuities are given in less detail than before, and the average rates of Insurance Companies for annuities and assurances are added. A Table of Logarithms of Natural Numbers has been introduced in order to facilitate calculation, and especially to enable use to be made of the extremely valuable Logarithmic Tables of Interest by M. Fedor Thoman without reference to any other book. Logarithms are very easy to use, and every one engaged in calculations should avail himself of the enormous advantages they offer. ^ M. Thoman's Tables have been printed from stereotype plates, in which any errors that have been noticed have beeti corrected, but they have not been re-checked for this edition. The difficulty of ensuring accuracy in so vast a number of figures will be well understood, and it can scarcely be hoped that no errors exist. Very great care has been taken in calcu- lating and checking the Tables, and in reading and re-reading the proofs, but as there are considerably more than a quarter of a million figures in the book, the entire absence of errors IS improbable. Any users of the book who come across even a single mistake would confer a benefit by reporting it to the Publishers for correction in future editions. The great majority of the calculations have been made by Tate's Arithmometer. Even with this powerful aid the preparation of the book, involving the formation of many fresh Tables and the checking of many existing ones, has been an arduous task ; without an efficient calculating machine it would have been scarcely practicable. In former editions the headings of the Tables rather suggested the limitation of their use to one specific purpose, whereas most of the Tables are available for many purposes. (u4 PREFACE TO THE TWENTY-FIFTH EDITION The headings of the Tables are now stated in a more general form, and in the Introduction examples are given of some of the various uses to which they may be put. In consequence, some habitual users of * In wood ' may, perhaps, miss the familiar heading, and at first fail to recognise a well-known • Table in its new garb. To obviate any inconvenience of this kind, and to increase the facility with which the book can be consulted, a full and specially arranged Table of Contents (pp. xi-xvi) has been prefixed, by reference to which any information needed may at once be found. An extensive collection of Examples has also been supplied (pp. 42-48), in which the actual working of every Table is illustrated. The book, as it now stands, serves innumerable purposes, but any suggestions (to be addressed to the PUBLISHERS) tending to increase its usefulness and convenience will be greatly appreciated and carefully considered, with a view to their adoption in future issues. In regard to such of the Tables in the book as are based on the Healthy Males Tables of Mortality, I am greatly indebted to the Council of the Institute of Actuaries, who have kindly given permission for the use in this volume of their valuable copyrights. William Schooling. >x) CONTENTS Tilles Introduction and Examples interest tables- Table FOR THE Purchasing of Leases, Estates, &c. Present Value of Reversion ] OF A Perpetuity Rates of Interest I Present Value of £1 Present Value of £1 per Annum Amount of £i Present Value of £1 Amount of £1 per Annum Present Value of £1 per Annum Amount of £i, io-yr. Intervals Present Value of £i, do. . Amount of £1 per Annum, do. . Present Value of £1 per Annum, do Value of a Perpetuity Value of Reversion to a Per- petuity Value of Perpetual Fines for Renewing Leases . Renewal of any Number of Years in a io-yrs.' Lease xi t2 2 2I 2|, 2f , 3, 3§, 4> Ah 5. 6, 7, 8, 9, 10 25, 2^, 3» 32> 4. 45. 5. 6, 7, 8, 9, 10 1 li ll tS *> •4» *2» *4» 2 2— 2A ^S Ay ^4, ^2> •^4> 3. 3l. 4. 4^, 5. 6, 7, 8, 9. 10 I to 10 I to 10 I to 10 I to 10 I to 10 I to 6 3 to 10 2 to 17-95 Table Pages xx-xl,49-i24 xx-xxiv xxi-xxv xxvi-xxx xxvii-xxxi xxxii-xxxiv xxxiii-xxxv xxxvi-xxxviii xxxvii-xxxix xl 49-57 58-65 66-73 74-81 82-85 86,87 88, 89 90,91 ' 92,93 94 95-98 99 99 Text Pages 1-48 8-21 xvm r >2, 13 XVlll 13 [ XIX i 10,12 8-10 ID, II II, 12 12,13 8-10 10,11 II, 12 12,13 13 13 14 14-16 (Xi) r" CONTENTS Titles INTEREST TABLES-<:<7«/. Renewal of any Number of Years in a 20-yrs.' Lease Do. 2I-YRS.' Lease Do. 40-YRS.' Lease Interest Yielded by Numbers of ♦ Years' Purchase ' . Interest, Amount, and Dis-\ count of £1 in a Year, 9f Months, 6 Months, and 3 [ Months Sinking Fund . . . . Value of Annuity Yielding 1 Interest on Capital at [ Replacing Capital when In- vesied at Nominal and Effective Rates OF Interest when Convertible Half - Yearly, Quarterly, Monthly Constant Factors for Convert- ing Values and Amounts of Yearly Annuities into those of Annuities for One Year Payable Half-Yearly, Quar- terly, and Monthly Value of Annuity for 25 Yrs. Payable,and Interest Conver- tible, Yearly, Half-Yearly, Quarterly, and Monthly Present Value of One Due a Year hence .... Discount on One for i Year . Time in which an Amount Doubles at Simple and Com- pound Interest Decimals of i Year Rates of Interest 2 to 12-304 2 to II -564 2 to 8 Table Pages 2^> 22, 2^, 3> 32» 4» 42> 5 I to 10 3. 3i 4. 5» 6, 7. 1h 8, 9. 10 2> 2i, 3, 3I, 4 J 100 ID! 102, 103 104 105 IO6-II5 Il6-I2lf Text Pages I to 10 Decimals of £1 I to 10 I to 10 I to 10 I to 10 122 123 123 123 123 14-16 14-16 14-16 16 16 16,17 18 18,19 19,20 20 20 20 21 124 124 I I 125-128 j 21-23 21 CONTENTS Titles Rates of Interest Table Pages Text Pages MORTALITY TABLES- • • • 129-136 23-25 Expectation of Life according TO the Northampton, Car- lisle, Equitable, 17 Offices, English No. 3, and Hm Tables • ■■ 130, 131 23,24 English Life Table, No. 3 • •• 132, 133 23,24 Institute of Actuaries Healthy Males (Hm) Table . • •• 134, 135 23,24 Carlisle Table . . . - • •• 136 23,24 SINGLE LIVES & INTEREST— • •• 137-154 25-28 Value of an Annuity : • • • 138-145 25-27 Northampton Table 3» 4, 5. 6 138, 139 25-27 Carlisle Table 3, 4, 5, 6, 7, 8 140, 141 25-27 Healthy Males ... 2a. 3>32j4>42»5 142, 143 25-27 Government Exp. (1883), Males 2|, 3. 35, 4, 5 144 25-27 Do., Females .... 2^, 3. Zh 4, 5 145 25-27 Single Payment to Secure £1 AT Death : • •• 146-149 27,28 Carlisle Table ... 3, 4, 5, 6, 7, 8 146, 147 27,28 Healthy Males 2^,3,3^,4,4^,5 -148, 149 27.28 Annual Payment to Secure £'i AT Death : • • • 150,151 28 Healthy Males Table . 2i,3,3i4,4i5 150, 15I' 28 Value of Reversion to a Per- petuity AT Death : • • • • 152-154 28 Government {1883) Table, Males 2i. 3, 35. 4, 5 152 ?8 Do., Females .... 2h 3, Zh 4, 5 153 28 Northampton Table 3, 4, 5, 6 154 28 Carlisle Table 3, 4, 5, 6 154 28 (xii) (xiii) CONTENTS Titles TWO LIVES & interest- Joint Life Annuity : Northampton . Carlisle . Government (1883) Two Males Two Females Male and Female Healthy Males Joint Life Assurance, Single Payments : Northampton . . . . Carlisle ..... Healthy Males Joint Life Assurance, Annual Payments : Healthy Males Last Survivor Annuity : Northampton .... Carlisle ..... Healthy Males Assurance at Death of Last Survivor, Single Payment : Northampton .... Carlisle Healthy Males Rates of Interest 3, 4, 5 Table Pages 155-181 156-165 156 158-163 158-160 158-160 161-I63 164, 165 166-169 166 167 3, 3^, 4 168, 169 ^h 3> 3h 2h 3, 3l ^2» 3j 35 2i, 3» 3h 3. 3l. 4 3, 3i 4 3. 4, 5» 6 3» 32» 4 3 3 3» 3^, 4 Text Pages 170 170 17I-I73 31,32 29-34 29-31 29-31 29-31 29-31 29-31 29-31 29-31 29-31 29-31 29-31 29-31 29-31 29-31 29-31 171 172 173 174-6 174 175 31,32 31,32 31,32 31,32 31,32 31,32 176 31, 32 CONTENTS Titles TWO LIVES & INTEREST- if more places of decimals were used , in the calculation. (xviii) Seep. xxiu xxiii xxiii xxiii XXX XXX 71 f EX«AMPLES (3) Find the present value of a perpetual income of £2^ per annum to comTnence 30 years hence so that the investment may yield 5 per cent. Value of reversion to a perpetuity oi £\^ ^^4-628 " M •> ;;^25=4-628x 25= 115-700 or 25X4J=^ ii8 i5.f. The difference between the answers is explained under example (i). The nature of reversions is explained on pp. 13, 14. XXXVl xxxvi (4) Find the present value of ^1,000,000 due at the end of 100 years at i^ %. The present value of i in 100 years =;^ -0000009 M J) 1,000,000 „ ) _ =•0000009x1,000,000 f~ ^ This example is principally given to show the startling fact tha a modest 18^. would at 15 % compound interest accu- mulate in 100 years to the vast amount of ^1,000,000. xl (5) Find the present value of £^0 per annum to be received for 20 years certain so that the purchaser would obtain 15 %. £^ per annum for 20 years=^6-25933i5 ^40 „ =6-2593315 X 40= 250-3732600 Other examples of the working of the tables in this book are given on pp. 42-48. ^ xl (XiX) a 1 INTEREST TABLES TABLE for the PUBCHASING of Leases, Estates, or Annaities, for terms of years certain at Bates from 1^ to 10 per cent. Interest which the FoTchaser may thereby make of his money Years I a I I| 2 2i 3 3h 4 4^ 5 5^ 6 6h 7 1\ 8 8| 9 9^ 10 II 11^ 12 I2| 13 131 14 14 i 16 i6t i7i 18 19 I9I 20 20h 21 2I\ 22 22i 23 23I 24 24^ 25 Yews' 1 1 0/ Purcha»e ±5^ /O •496 •98s 1-478 I 956 2-445 2-912 3*397 3854 4-336 4-783 5-260 5-697 6-171 6-598 7-069 7-486 7-953 8-361 8-823 9-222 9-681 10-071 10-527 10-908 1 1 -359 11-732 12-180 12-543 12-988 13-343 13-784 14-131 14-569 14-908 15-341 15673 16-103 16-426 16-853 17-169 17-592 17-900 18-319 18-621 19-037 19-331 19-743 20-030 20-439 20-720 5? 5f 6i 6i 7 7i 8 8i 8l 9I 9| 10 lO^ II II 12; 12; 13 i3k i3f I4i I4i 15 i5i I5| 16 i6i i6| 171 i7h 18 i8i i8i 19 19*^ I9f 20 20^ 20f Tears' 1 3. 0/ Purchase ±4 /O •496 •983 1-474 1-949 2-436 2-898 3-381 3831 4-309 4-748 5-222 5-649 6-119 6-535 7-000 7405 7-866 8-260 8717 9101 9-554 9.927 10-376 10-740 1 1 -184 1 1 -538 1 1 -977 12 322 12-758 13-093 13-524 13-851 14-278 14-595 15-018 15-327 15-746 16-046 16-461 16-753 17-163 17-448 17-854 18-130 18-533 18-801 19-200 19-461 19-855 20-109 Years' O 0/ Purchase £t /o i •495 I •980 i^ 1-470 2 1-942 2h 2-427 3 2-884 3i 3-364 3-808 1* 44 4-283 4-713 5,^ 5-184 5f 5-601 6 6-067 6| 6-472 7 6-933 7h 7-325 7i 7-781 H 8-162 8| 8-613 9 8-983 9^ 9-428 10 9-787 io.| 10-228 I of 10-575 II; 11-012 11^ 11-348 12 11-780 I2i i2-io6 i 12,^ 12-533 ' 13 12-849 I3h 13-271 I3I 13-578 i4i 13-995 I4i 14-292 15 14-704 154^ 14-992 i5f 15-400 ; 16 15-678 i6.i 16-082 i6f 16-351 i7i 16-750 '7? 17011 17^ 17-405 i8i 17-658 18^ 18-047 i82 18-292 I9t 18-677 19! 18-914 19-294 20 19-523 ^ 3 3i 31 4i 4| Sk 5i 6 6^ 7 7i 7| H 9 9h 9| io| loi- II H^ III 12 12^ I2f i3i I3I 14 144^ i4f 15 15^ i5f 16 i6i i6f 17 17^ I7f 18 i8f 19 194^ 19^ piXse 21% Years •494 -978 1-467 1-934 2-418 2-870 3-348 3-785 4-257 4-679 5-J46 5-554 6-016 6-410 6-866 7-247 7-697 8-066 8-510 8-866 9-306 9-649 10-083 10-415 10-843 II -164 1 1 -587 11-896 12-314 12-612 13-025 13-313 13-720 13-998 14-400 14-668 15-064 15-323 15-715 15-964 16-350 16-590 16-972 1 7 -203 17-580 17-803 18-174 18-389 18-755 18-962 h ih 2h 2f 3i 3l 4| 5i Sh 6 6^ 6| 7} I* 8f 94^ 9f o o| of 2i ■^4 2i 3 3^ 31 4 4^ 4| 5 5^ 5i 6 6i 6^ 7 71 71 71 8| 8^ 8| 9 I i^ 2 3 3^ 4 4^ 5 5^ 6 6h 7 7k 8 8^ 9 9^ o oh I I^ 2 2h 3 3i 4 4^ 5 S§ 6 6| 7 71 8 8^ 9 91 20 20| 21 24 22 22^ 23 23i 24 245 25 Examples. — A lease or annuity for 14 years to make 2 per cent, and to get back the principal is worth 12- 106, or 12 years' purchase of the dear annual rent. At 3 per cent, it is worth 11-296, or 11^ years' purchase. (XX) INTEREST TABLES TABLE for the PTTBCHASIiro of Leases, Estates, or Annuities, for terms of years certain at Bates from 1^ to 10 per cent. Interest which the Purchaser may thereby make of his money Tears a I^ 2-1 ^2 3 31 4 4i 5 el 32 6h 72 8 10 io| II "^ 12 12^ 13 13I 14 14^ 15 151 16 i6| 17^ 18 18^ 19 I9f 20 20| 21" 21^ 22 22i 23 231 24 24§ 25 Years' Purchase 2* O/ ^O •494 •976 1-463 1-927 2-409 2-856 3-331 3-762 4-231 4-646 5-109 5-508 5-965 6-349 6-800 7-170 7-615 7-971 8-410 8-752 9185 9-514 9-941 10-258 10-679 10-983 1 1 -398 11-691 I2-IOO 12-381 12-785 13-055 13-452 13-712 14-104 H-353 H-739 14-979 15-359 15-589 15-964 16-185 16-554 16-765 17-129 17-332 17-690 17-885 18-238 18-424 J ih -^2 3i 3f 4^ 4f 5 5^ 6 64^ 6| 7i 7h 8 8f 94^ 9^ 10 lol I of II Hi iif 12 12^ I2f 13 13^ I3f 14 I4i I4f 15 I5i 15^ 16 161 161 i6f i7i i7i I7f 18 181 i8i Years' O 3. 0/ Purchase ^4 /O •493 •973 1-460 1-920 2-400 2-842 3-315 3-739 4-206 4-613 5-072 5-462 5-915 6-289 6-736 7-094 7-534 7-878 8-311 8-640 9-066 9-382 9-802 10-104 10-518 10-807 II -214 1 1 -491 1 1 -891 12-157 12-551 12-805 13-192 13-435 13-817 14-049 14-424 14*646 15-015 15-227 15-591 15-793 16150 16-344 16-695 16-879 17-225 17-401 17-740 17-908 I Ih 2 2^ -^2 2| 3i 3f 4i 4^ 5 5h 6 6i 6f 7 7h 8 8^ SI 9 9h 91 ID I of Hi 12 I2i I2§ I2f 134^ 13^ I3f 14 14^ Hf 15 15^ 15^ 15I i6i i6i i6f 17 I7i 171 i7f 18 Years' Q 0/ Purchase O /O •493 -971 1-456 1-913 2-391 2-829 3 299 3-717 4-180 4-580 5-036 5-417 5-866 6-230 6-672 7-020 7-454 7-786 8-213 8-530 8-950 9253 9-665 9-954 10-360 10-635 1 1 034 1 1 -296 11-688 1 1 -938 12-323 12-561 12-939 13-166 13-538 13754 14-119 14-324 14-682 14-877 15-229 15-415 15-761 15-937 16-276 16-444 16-777 16-936 1 7 262 17-413 1 2 2i ■^2 2f 1 3k 3f ! 4| 5 i 5^ I 51 I 6i 6f : 7 7h 7J 8i S^ 9 9k 9| 10 loi lof II Hi III 12 I2i I2i 13 I3i i3i I3f 14 Ui 14^ 15 i5i 151 15I 16 i6i i6| i6f 17 i7i 171 Years' Qi Purchase O 2 Oy ^O I I 2' 2- 3' 3' 4' 4' 4- For Explanations and Examples see pp. xxii. to xxxi. (xxi) •491 •966 -449 -900 •374 -802 -267 •673 130 •515 -964 5329 5-769 6-115 6-546 6-874 7-298 7-608 8-023 8-317 8724 9-002 9-401 9-663 10-054 10-303 10-686 10-921 11*296 11-517 1 1 -885 12-094 12-454 12-651 13-004 13-190 13-535 13-710 14-047 14-212 14-543 14-698 15-021 15-167 15-483 15-620 15-929 16058 16-361 16-482 2 2i 2f 3i 3l 4i 4^ 5 54^ 51 6 6^ 6f 74^ 71 8 8} 8f 9 9h 9f 10 loi lof II .Hi la 12 12 I2i i I2f : i3h \ i3f 14 144^ 14^ 14^ 15 154^ i5h 16 16 Years 1 3 2i ' 3 3^ 4 41 5 161 2 24 , 24I _ >6i_2S pp. xviii., xix. Tables continued on 6^ 7^ 8 8^ 9 9^ 10 lOi ii "5 12 I2| 13 13^ M 15 it i6| 17 17^ 18 i8i 19 19^ 20 20h 21 2li 22 22i 23 23f INTEREST TABLES TABLE for the PUBCHA8ING of LeaaesTKstates, or AnnuitiesTfor terms of years certain at Bates from 1| to 10 per cent. Interest which the Purchaser may thereby make of his money Years Yean' 1 1 o/ Purchase A2 To Yeara' Purchase 21-125 21-399 21-800 22 -068 22-466 22-727 23-121 23-376 23767 24-016 24-404 24-646 25-031 25-267 25-648 25-879 26-257 26-482 26-856 27-076 27-446 27-661 28-028 28-237 28-601 28-805 29-166 29-365 29-722 29-916 30-270 30-459 30-810 30-994 31-342 31-521 31-866 32-041 32-382 32-552 32-891 33-056 33-392 33*553 33-885 34-043 34-371 34-525 34-850 I 35*000 , 21 21^ 2I| 22 22^ 22f 23 23i 23f 24 24^ 24f 25 25i 251 26 26| 26* 26f 27 27I 27f 28 28i 28I i 28f I 29i 294^ 29f I 30 I 30i 3oi 3o| 31 31^ 3i§ 3if 32 32| 32^ 32f 33 33^ 33^ 34 34 34^ 341 34f 35 lf% Years' Q Purchase ^ 20-499 20-746 21-132 21-372 21-754 2 1 -987 22-365 22-592 22-966 23-186 23-556 23-770 24-136 24-344 24-707 24-908 25-267 25-462 25-817 26-007 26-359 26-543 26-890 27-069 27-413 27-586 27-926 28-095 28-431 28-594 28-927 29-085 29-414 29-568 29-893 30-042 30-364 30-508 30-826 30-966 31-281 31-416 31-728 31-859 32-167 32-294 32-598 32-721 33-022 33-141 ExA^rPLEs.— A lease get back the principal annual rent. At 3^ per % iP^^wSLe 2i- % l^ears 19-894 20-121 20-492 20-707 21-074 21-281 2 1 -644 21-844 22 -202 22-396 22-750 22-938 23-287 23-468 23-813 23-989 24*329 24-499 24-835 24-999 25-331 25-489 25-817 25969 26-294 26-441 26-761 26-903 27-219 27355 27-667 27-799 28-107 28-235 28-5-39 28-662 28-962 29-080 29-376 29-490 29-783 29-892 30-181 30-287 30-571 30-673 30-954 31-052 31-330 31-424 19*324 19-523 19-880 20-072 20-423 20-608 20-955 21-132 21-474 21-645 21-983 22-147 22-480 22-638 22-966 23-118 23-441 23-587 23 905 24-046 24-360 24-495 24-804 24934 25239 25-363 25-664 25-783 26-079 26-194 26-486 26-595 26-883 26-988 27-272 27-372 27-652 27-748 28-023 28-115 28-386 28-474 28-742 ! 28826 29-089 29-170 29-429 29-506 29-761 ! 29-834 I 194^ 19^ 20 20 20| 2o| 21 21I 2U 2lf 22 22I 22| 22f 23 23 23i 23^ 24 24 24i 24I 24f 25 254^ 25} 25I 25f 26 26i 26^ 26I 27 27 27^ v\ 27I 27| 28 28 28^ 28A 28| 28f 29 29i 29I 29^ 29f 29I 25^ 26 27^ 28 28A 29 30 31 34 32 32§ 33 33^ 34 34^ 35 3Sh 36 37 37^ 38 •2 39 391 40 40^ 41 411 42 42^ 43 43^ 44 44^ 45 45^ 46 46^ 47 47^ 48i 49 49^ SO or annuity for 49 1 years to make 2\ per cent, and to IS worth 29-761 or 29I years' purchase of the clear cent. It 18 worth 23-443 or 23^ years' purchase, (xxii) INTEREST TABLES TABLE for the PUBCHASINO of Leases, Estates, or Annuities, for terms of years certain at Bates from 1§ to 10 per cent. Interest which the Purchaser may thereby make of his money Years Yean' Qi o/ Purchase £i 2 7X) 18-772 18-951 19-293 19-464 19-801 19-965 20-297 20-454 20-780 20-930 21-252 21-395 21-712 21-849 22-160 22-292 22-598 22-724 23025 23-145 23-442 23-556 23-848 23-957 24-244 24-349 24-631 24-730 25-008 25-103 25-376 25-466 25-735 25821 26-085 26-166 26-426 26-504 26-760 26-833 27-084 27-154 27-401 27-467 27-711 27-773 28-012 28-071 28-306 28-362 i8f 19 19\ 19^ I9f 20 20|- 20^ 20f 21 2li 21,^ 2l| 2lf 22^ 22^ 22^ 22f 23 234- 235 23^ 23f 24 24r 24¥ 24f 24f 25 25 25i 25^ 251 25f 26 26\ 26^- 26| 26| 26f 27 27i 275 275 27f 271 28 28 28 1- Years' Pi rchase 18-242 18-402 18-730 18-883 19-206 19-351 19-668 19-806 20-118 20-249 20555 20-681 20-981 21-100 21-396 21-509 21-799 21-906 22-191 22-293 22-573 22-670 22-945 23 036 23-306 23-393 23-658 23-740 24-000 24-078 24-334 24-407 24658 24-727 24-973 25-038 25-280 25-341 25-579 25-636 25-869 25-924 26-152 26-203 26-427 26-475 26-695 26-740 26-955 26-997 2i % 184^ i8f 19 ^9\ i9i I9f 19I 20 20i 20i 20| 21 21 2li 21^ 2lf 22 22^ 22^ 22-| 22f 23 ' 23 23i 23^ 23f 23f 24 24 24i 24i 24f 24f 25 25 25i 25i 25^ 25I 25f 26 26i 26i 26i 26i 26f 26f 27 27 Years' q n/ Purchase O yo ^7'734 17-877 18-192 18-327 18-636 18-764 19-067 19-188 19485 19-600 19-892 20-000 20-286 20-389 20-669 20-766 2 1 -040 21-132 21-401 21-487 21-751 21-832 22-091 22-167 22-421 22-492 22*741 22 -808 23-052 23-115 23-353 23-412 23-646 23-701 23-930 23-982 24-206 24-254 24-474 24-519 24-734 24-775 24-986 25 025 25-231 25-267 25-469 25-502 25-700 25-730 For pp. XX., I7f 18 i8i 184^ i8| i8f 19 194^ 19^ 19I 20 20 20i 20| 20f 20| 21 2li 2li 2li 2lf 2l| 22 22i 22i 22§ 22f 22f 23 23 23i 235 23f 23f 24 24 24r 24k 24I 24^ 24I 24f 25 25 251^ 254^ 25^ 251 251 251 Years' Qj^ q. Purchase k 8^ 6| 9 H 9.^ 7k 10 7f 10.^ 8 II «i II* ^ 12 8| 12* 8| 13 9k 13.^ 9k 14 9k 142^ 9t 15 10 15^ 10 16 IO.| 16^ io.i 17 lOf i7§ io| 18 II m Ilk 19 I If 191 11^- 20 llf 20* Hi 21 12 211 12 22 I2i 22,^- I2i 23 12^ 23* 1 2k ^4. I2f 24I I2'i 25 13 years to make 4^ per cent, and to years' purchase of the clear annual k years' purchase. INTEREST TABLES TABLE for the PURCHASING of Leases, Estates, or Annuities, for terms of years certain at Rates firom 1^ to 10 per cent. Interest whioh the Purchaser may thereby make of his money Years k Years' n 0/ Purohaae 1 /O Pur^il!se. 8 % 1 Pu^hLe 9 % Purchase 10 %\ Years k -483 ! h •481 ! k -478 k -476 k I •935 I -926 , I 917 I -909 I I I* 1-401 ll 1-388 1 Ik 1-374 li 1-362 Ik li 2 I -808 If 1-783 n 1-759 i| 1-736 II 2 2k. 2-258 : 2i 2-226 2k 2*195 2k 2165 2k 2^ 3 2 624 2k 2-577 2k 2*531 2k 2-487 2k 3 3^ 3-057 3 3-001 3 2*946 3 2-893 3 zk 4 3-387 3* 3-312 3i 3*240 3i 3-170 3i 4 4* 3804 3i 3-718 3f 3634 3f 3-554 3^ 4^ 5 4100 4 3-993 4 3-890 4 3-791 3f 5 5* 4-501 4* 4-380 1 4^ 4*264 Ak 4-153 4i i^ 6 4-767 4f 4-623 4§ 4*486 Ak 4-355 4i 6^ 5-151 5i 4-993 5 4-841 \ 4f 4-697 i 4i 61 7 5-389 5* 5 -206 ! Sk 5-033 1 5 4-868 1 4| 7 7* 5*759 1 5f 5*559 i Sk 5-370 1 Sk 5-190 1 Sk 7i 8 5-971 6 5-747 Si 5-535 1 Sk 5-335 ; Sk 8 ^ 6-326 6i 6*083 6 5-854 1 5f 5-637 5f 8^ 9 6-515 6* 6*247 ; 6^ 5995 6 5*759 1^ 9 9^ 6-855 61 6-567 6\ 6 297 1 6^ 6043 6 9k 10 7-024 i 7 1 6-710 6| 6*418 ; 6i 6-145 6i 10 io| 7-349 7k \ 7-015 ■ 7 6-702 6! 6-411 6i I0| II 7-499 7k 1 7-139 I 7k 6*805 i 6| 6-495 6^ II 11^ 7-810 7f 1 7-428 ' 7k 7-074 7 6-744 61 11^ 12 7*943 8 7-536 i 7k 7*161 : ^\ 1 6814 6f 12 I2| 8-241 8i 7-8ii 71 7-414 7k 7-047 7 12^ 13 8-358 8i 7-904 8 7-487 7k 7*103 7 13 13^ 8-643 8| 8-165 84^ 7-726 - 7f 7*322 7k 134 14 8-745 8| 8-244 8i 7-786 7f 7-367 7k '^x 145 9-018 9 8-492 8^ 8-01 1 8 7-571 -7k I4i 15 9-108 9 8-559 8^ 8-o6i 8 7*606 7k 15 15^ 9-368 9k 8-794 8| 8-272 8i 7-796 71 '5* 16 9-447 9k 8-851 8-313 8i 7-824 7f 16 16^ 9-695 91 9-074 9 8-511 ^ 8-OOI 8 Itk 17 9-763 9\ 9*122 9 8-544 ^ 8-022 8 '7. 17* lo-ooo 10 9-332 9k 8-731 8| 8-187 8i 17* 18 10-059 i 10 9-372 9k 8-756 8| 8-20I H 18 18^ 10-285 loi 9-571 9k 8-931 9 8-356 8i 184 19 10-336 lot 9-604 9k 8-950 9 8-365 !^ '^r 19H 10-551 IO§ 9-792 ! 9\ 9-115 9 8-509 8^ 19J 20 10-594 10^ 9-818 1 9l 9-129 9k 8-514 8^ 20 20^ 10-800 lof 9.997 10 9-283 9\ 8-647 8| 20* 21 10-836 1 io| 10-017 10 9-292 9k 8-649 8| 21 21* 11-031 II 10-185 loi 9*437 9\ 8-773 8f 21* 22 II -061 II 10-201 lOj 9*442 9l 8*772 8f 22 22^ 1 1 -248 Hi 10-360 lOj 9-578 9k 8*887 9 22* 23 11-272 "i 10-371 lOj 9-580 9k 8*883 9 23 235 11-450 ! Hi 10-521 10^ 9-707 9l 8-991 9 23i 24 11-469 1 Hi 10-529 IO| 9-707 91 8-985 9 124 245! "-638 i Ilf 25 1 "-654 , II| 10-671 IO| 9*826 9f 9*084 9 1 24I 10*675 lOj 9-823 94 9-077 9 |25 (xxvi) For Explanations and Examples see pp. xviii. pp. XX. to XXV. and on pp. xxviii. to xxxi. (xxvii) xix. Tables .continued on INTEREST TABLES INTEREST TABLES TABLE for the PURCHASING of Leases, Estates, or Annnitiei, for terms of years certain at Kates from 1^ to 10 per cent. Interest which the Purchaser m ay thereby make of his money 6% Yea« Tears 25h 26 27 28 29 30 30^ 31 3i§ 32 32^ 33 33^ 34 34f 35 35t 36 36^ 37 37^ 38 2»h 39 395 40 4o| 41 41^ 42 42I 43 43^ 44 44^ 45 iSh 46 46I 47 47i 48 48^ 49 491 50 Yean' Purchase 4% 15-894 15-983 16-248 16-330 16-587 1 6 663 16-914 16-984 17-228 17-292 17-530 17-588 17-820 17-874 18-099 18-148 18-367 18-411 18-624 18-665 18-872 18-908 19-110 19-143 19-339 19-368 19-558 19-584 19-770 19793 19-973 19-993 20-168 2o-i86 20-356 20-371 20-536 20-549 20-709 20-720 20-876 20-885 21-036 21-043 21-190 21-195 21-338 21-341 21-480 21-482 16 16 16.^ i6i 16^ i6| 17 '7\ 174 I7t J7 I7f 18 i8[ i8i i8| i8f i8| 19 19 194^ i9i 19k I9h 19I 19I 19I 20 20 20J 20| 20^ 20 f 20| 20| 20f 20f 21 21 21 21 2li 21I 2li 2li 2I| 2I| Ye»s' A 10/ Purchase ^2 /<> 15-078 15-147 15-389 15-451 15-686 15-743 15-971 16-022 16-243 16-289 16503 16-544 16-752 16-789 16-990 17-023 17-218 17-247 17-436 17-461 17-644 17-666 17-843 17-862 18-034 18-050 18-216 18*230 18-391 18-402 18-557 18-566 18-717 18-724 18-869 18-874 19-015 19-018 19-155 19-156 19-288 19-288 19-416 19-415 19-538 19-536 19-655 19-651 19-767 19762 Tears' Purchase 5% 15 14-323 i5i 14-375 155 14-597 15^ 14-643 i5f 14-857 151 14-898 16 15-105 16 15-141 i6i 15-341 I6i 15-372 i6i 15-565 I6,i 15-593 i6f 15-779 i6| 15-803 17 15-982 17 16-003 i7i 16-176 17 k 16-193 i7k 16-360 i7k 16-374 I7f 16-536 m 16-547 i7i 16-702 I7f 16-711 18 i6-86i 18 16-868 i8i 17-013 m 17-017 1 81 17157 18^ 17-159 I$l 17-294 i8i 17-294 'St 17-424 i8| 17-423 i8| 17-548 i8f 17-546 19 17-666 19 17-663 I9i 17-779 19.^ 17-774 I9l 17-886 I9i 17-880 19.^ 17-988 19^ 17-981 19^ 18-085 19.^ 18-077 I9f 18-177 I9f 18-169 i9| 18-265 I9| 18-256 144^ 14^ 141 i4f I4f 15 15 i5i i5i i5i 15^ 15^ 151 1 51 16 16 i6| i6i 16} 16L i6i i6i i6| i6| i6f i6| 17 17 i7i i7i 171 i7i 17^ 17^ 17^ 17^ i7f i7f 171 i7f 18 18 18 18 18 18 181 i8| 18I 18I Years' Purchase 12-976 13-003 13-187 13-211 13-387 13-406 13-575 13-591 13-753 13-765 13-920 13-929 14-078 14-084 14-226 14-230 14-367 14-368 14-499 14-498 14-623 14-621 14-740 14-737 14-851 14-846 14-955 14-949 15-053 15-046 15-146 15-138 15-233 15-225 15-316 15-306 15-393 15-383 15-466 15456 15-535 15-524 15-600 15-589 15-661 I 15-650 I 15-719 15-708 i 15-773 ^ 15-762 i 391 h^of^tT^^^'~\ ^-^^'^ "il ^"''""y ^"""^ 40 years to make 4 per cent, and to get rent AtT2'^^ I" '7"^"'^ 'V^^ ^^'^f years' purchase of the cUar annua rent. At 6 per cent, it is worth 15-046 or 15 years' purchase. (xxviii) TABLE for the PUBCHA8ING of Leases, Estates , or Annuities, for terms of years certain at Bates from 1^ to 10 per cent. Interest which the Purchaser may thereby make of his money Years 25^ Years' 7 n, 1 Purchase 1 /o | Pu^^ue 8 % 1 Purc"ase 9 % \ FurX!MlO%| Yeais 251 11-814 iif 10-809 lof 9-934 10 9-169 91 1 1 -826 III io-8io lOf 9.929 10 9-161 91 26 26h 11-979 12 10-936 11 10-033 10 9-247 91 26| 27 11-987 12 10-935 11 10-027 10 9-237 91 27 27^ 12-132 12i 11-054 11 10-124 10 9-317 9l 271 28 12137 121 11-051 11 10-116 10 9-307 91 28 28,} 12-275 I2I 11-163 ''\ 10-207 lol 9-380 9l 284 29 12-278 I2I 11-158 III 10-198 lol 9-370 9l 29 292^ 12*409 12^ 1 1 -264 III 10-283 lol 9-438 9l 29I 30 12-409 12i 11-258 111 10-274 loi 9427 9l 30 301 12-534 12^ 11-357 111 10-353 lol 9-490 9| 30I 31 12-532 12| 11-350 111 10-343 lol 9 479 92 31 31^ 12 650 12f 1 1 444 11^ 10-417 io| 9538 9h 3II 32 12-647 12f 11-435 i Hi 10-406 io| 9-526 9h 32 32.^ 12-759 12| 11-523 11^ IO-475 io| 9-581 9h 32I 33 12-754 12f 11514 III 10-464 io| 9-569 9k 33 33l 1 2 860 I2f 11-597 i 111 10-529 10^ 9 620 9k 33l 34 12-854 12f 11-587 : III 10-518 io| 9-609 9h 34 34^ 12-955 13 11-665 iif 10578 io| 9-655 9f 341 35 12-948 13 11-655 iif 10-567 IO§ 9-644 9f 35 35^ 13-044 13 11-728 uf 10623 io| 9-687 9f 351 36 13-035 13 11-717 Iif 10612 10^ 9677 9f 36 362^ 13-126 13 11786 llf 10 664 I of 9-716 9f 36I 37, 13-117 13 11-775 llf 10-653 lOf 9-706 9f 37 37^ 13-203 1 31 1 1 -840 llf 10-702 lOf 9-742 9f 371 38 13-193 131 11 829 Iif 1 10-691 lOf 9-733 9f 38 38^ 13-275 131 11-890 12 10-736 lOf 9-766 9I 38I 39 13-265 131 11-879 12 10-726 I of 9-757 9f 39' 39^ 13-342 13I 1 1 936 12 10-768 I of 9-788 9f 391 40 13-332 13I 1 1 -925 12 10-757 I of 9-779 9f 40 40I 13-405 131 11-979 12 10-797 I of 9-808 9f 40! 41 13-394 13^ 11-967 12 10-787 lof 9-799 9f 41 4ii 13464 131 12-018 12 10-823 lof 9-826 9f 41I 42 13-452 i3i 12-007 12 10-813 I of 9-817 9f 42 421 13-518 13^ 12-054 12 10-848 lOf 9-842 9f 42i 43, 13-507 13^ 12-043 12 10-838 lof 9834 9i 43 AZk 13-569 13^ 12-088 12 10870 I of 9-857 .91 43l 44 13-558 131 12-077 12 10-861 lof 9-849 9f 44 445 13-617 13^ 12-119 12 10-890 II 9-870 9 44l 45 13 606 13^ 12-108 1 12 IO-88I II 9-863 9f 45 451 13-662 i3f 12-148 1 ^2l 10909 11 9-882 10 451 ^Jx 13650 I3f 12-137 12; 10-900 11 9-875 10 46 46^ 13-703 i3f 12-174 12- 10926 11 9893 10 46I 47 13-692 13? 12-164 12: 10-918 II 9-887 10 47 47^ 13-742 i3f I2I99 12; 10-941 II 9-903 10 471 4f. 13-730 13I 12-189 I21 10-934 II 9-897 10 48 48I 13-778 13I 12-222 I21 10-956 II 9-912 10 48I 49 13-767 131 12-212 121 10-948 11 9906 10 49 49l 13812 13I 12-243 121 10-969 11 9-920 10 49l 50 13-801 i3f 12-233 I2I 1 10-962 II 9-915 ID 1^0 For Explanations and Examples see pp. xviii., xix. Tables continued on pp. XX. to xxvii. and on pp. xxx., xxxi. (xxix) INTEREST TABLES INTEREST TABLES I TABLE for the PURCHASING of Leues, Estates, or Annuities, for temg of years certain at Rates from 1^ to 10 per cent. Interest which the Purchaser may thereby make of his money. i Tears |pTm!^!!M 4 % 51 52 53 54 55 56 57 58 00 6i 62 P 65 66 67 68 69 70 71 72 73 74 75 76 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 21-617 21748 21-873 21-993 22-109 22 -220 22-327 22 '430 22-528 22-623 22-715 22-803 22-887 22-969 23-047 23-122 23-194 23-264 23-330 23-395 23-456 23-516 23-573 23-628 23-680 23-731 23-780 23-827 23-872 23-915 23-957 23-997 24-036 24-073 24-109 24-143 24*176 24-207 24-238 24-267 24-295 24-323 24-349 24-374 24-398 24-421 24443 24-465 24-485 24-50 I 2li 2lf 22 22 22^ 22J 22i 22^ 22I 22| 22f 23- 23 23 23 23i 23i 234^ 23i 23I 23i 235 23f 23f 23f 23f 23f 23f 24 24 24 24 24 24 24^ 24f 24f 24i 24i 244^ 24^ 24i 24i 241 245 24^ 24.^ 241 24^ Yew.' A 10/ Purehase%2 /^ 19-868 19*969 20 -066 20*150 20-248 20 '333 20-414 20-492 20 567 20*638 20*706 20*772 20*834 20*894 20*951 21*006 21-058 2I'Io8 21-156 2 1 -202 2 1 -246 21*288 21-328 21*367 21*404 21*439 21-473 21-505. 21*536 21*565 21-594 21-621 21-647 21-671 21-695 21-718 21-740 21-760 21-780 21-799 21-817 21-835 21-852 21-868 21-883 21-897 21-911 21-925 21-938 21-950 I9f 20 20 20} 20|^ 2o| 20^ 20^ 20§ 20f 20f 20f 20| 21 21 21 21 21 2li 2li 2ll 2li 21A 2li 21A 2li 21^ 2li 21^ 21^ 21J 2lf 21.1 2I| 2I| 2I| 2I| 2lf 2lf 2lf 2I| 21I 4 22 22 22 22 22 22 Yean' |; 0/ Pnrohase U /O 18-339 18*418 18-493 18*565 18*633 18-699 18-761 18*820 18*876 18*929 18*980 19-029 19075 19*119 19*161 19-201 19*239 19-275 19-310 19-343 19-374 19-404 19*432 19-459 19-485 19*509 '9-533 19-555 19-576 19-596 19*616 19*634 19-651 19668 19-684 19-699 19-713 19-727 19-740 19-752 19764 19775 19*786 19*796 19-806 19*815 19-824 19*832 19-840 19-848 i8i 18^ 18.^ i8| 18^ i8f i8f i8f 19 19 I 19 19 I 19 19 I9i 194^ 194^ 19} 194^ 194^ 19^ I9i 19I ^9h 19I 19^ i9i 19^ 19^ I9i 19^ 19^^ 19I 19I 19I 19I 19I 19I i9| I9| 19? 19I I9l I9| i9f 19I I9f I9t Yean' £% q. Purchase U To 15-813 15-861 15*907 15-950 15-991 16-029 16*065 16-099 16*131 i6-i6i 16-190 16-217 16-242 16*266 16*289 16*310 16*331 16*350 16*368 16-385 16*401 16*412 16*430 16-443 16-456 16-468 16*479 16-490 16*500 16*509 16*518 16*526 16*534 16*542 16-549 16*556 16-562 16-568 16-573 16-579 16*584 16*588 16-593 16*597 16*601 16-605 1 6 608 16-611 16*615 16*618 Examples. — A lease or annuity for 70 back the principal is worth 23*395 or 23^ rent. At 6 per cent, it is worth 16*385 or (xxx) I5I 16 16 16 16 16 16 I6i i6|^ I6i 161 161 161 161 i6i 161 i6i 161 1 61 161 i6§ 161 16^ 16I 16^ 16^ 161 1 61 16^ 16^ 16 i6| 161 16^ 16^ 16^ .16^ 161 16^ 16^ 16^ 16^ 161 i6| 16^ 16I 16^ Years 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67J 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 TABLE for the PURCtfASING of leases, Estates, or Annuities, for years certain at Rates from li to 10 per cent. Interest which Purchaser may thereby make of his money. terms of the Years 51 52 53 54 55 56 5Z 58 59 Yean' fj Purohate I 61 62 63 64 65 66 57 68 69 70 71 72 73 74 75 76 77 78 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 99 zoo 13-832 13*862 13-890 13-916 13-940 13*963 1 3 '984 14*003 14*022 14*039 14-055 14*070 14-084^ 14-098 14-110 14-121 14-132 14-142 14*152 14-160 14-169 14-176 14*183 14-190 14-196 14*202 14-208 14-213 14-218 14-222 14-226 14 230 14-234 14-237 14-240 14-243 14-246 14-249 14-251 14253 14255 14-257 14-259 14-261 14-263 14-264 14-266 14-267 14-268 14-269 % i3f i3f 14 14 14 14 14 14 14 14 14 14 14 14 14 14 ^A\ 144^ ^A\ Hi Hi Hi Hl- Hi Hi Hi Hf Hi ^^\ ^^\ ^^\ Hi Hi Hi Hi IA\ Hi iA\ ^A\ Hi Hi H\ '^\ 141, HI Hi Hi Hi Hi Yean' Purohase 8% 12-253 12*272 12*288 12*304 12*319 12*332 12*344 12*356 12*367 12*377 12*386 12-394 12-402 12*409 12*416 12-422 12:428 12*433 12-438 12-443 12-447 12-451 12-455 12-458 12*461 12*464 12*467 12*469 12*471 12*474 12*475 12-477 12-479 12-481 12-482 12*483 12*485 12*486 12*487 12-488 12*489 12*489 12*490 12-491 12*492 12*492 12-493 12-493 12-494 12-494 Yean' Purohase 9 % Ul^SllO 0, o 121 I2i I2i I2i I2i 12i I2I I2i 12^ 12^ I2I 1 21 I2I I2I 121 I2| 121 12^ 12^ 121 1 21 121 12§ I2| I2| I2| 121 121 I2i 121 12^ 121 121 I2| 121 IH I2I I2I 12| 124- 121 121 121 121 12^ I2i 12^ I2I 10-974 10-985 10-996 11-005 11-014 1 1 *022 1 1 029 1 1 -036 1 1 042 1 1 -048 1 1 -053 1 1 -058 11*062 11*066 1 1 *o7o 1 1 -073 1 1 -077 1 1 -079 11-082 1 1 -084 11-087 11*089 11 091 11*092 11*094 11*095 1 1 -097. 11-098 II 099 11*100 11-101 II 102 11-102 11-103 11-104 11*104 11*105 11*105 ii*io6 II -106 11-107 11*107 11*107 11*108 11*108 11*108 11-109 11*109 11-109 11*109 11 11 li II II II II II II II II 11 II II II II 11 u II II 11 II II 11 II II II II II II II II II 11 II II II II II II II 11 II II 11 II II II II II 9-923 9-930 9-936 9-942 9-947 9-952 9-956 9-960 9-964 9-967 9-970 9-973 9-975 9-978 9-980 9-981 9983 9985 9986 9-987 9988 9-990 9-990 9-991 9992 9 993 9-994 9-994 9 995 '9 995 9-996 9-996 9.996 9-997 9 997 9-997 9997 9*998 9-998 9-998 9-998 9-998 9-999 9-999 9*999 9-999 9 999 9-999 9 999 9-999 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 Years 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 63 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 years to make 4 per cent, and to get years' purchase of the clear annual i6| years' purchase. For Explanations and Examples see pp. xviii., xix. Tables continued on pp. XX. to xxix. (xxxi) I INTEKEST TABLES INTEREST TABLES The Present Value of the EEVEESION OF A PEEPETUITY after any given Term not exceeding 100 Tears After Years' 1 11^.1 Years Purchase 12^ %| I 65-681 65f 2 6471 1 64I 3 63754 63^ 4 62 812 62f 5 61-884 62 6 60-969 61 7 60 -068 60 8 59-181 59i 9 58-306 58i 10 57-444 57h II 56-596 SH 12 55-759 551 13 54-935 55 14 54-123 54 15 53-323 53i 16 52-535 52^ 17 51-759 51^ 18 50-994 51 19 50-241 5oi 20 49-498 49| 21 48767 48I 22 48-046 48 23 47-336 47i 24 46-636 46^ 25 45-947 46 26 45-268 45i 27 44-599 44^ 28 43 940 44 29 43-291 43i 30 42-651 42f 31 42-021 42 32 41-400 41^ 33 40-788 401 34 40-185 4oi 35 39-591 39^ 36 39-006 39 37 38-430 ^H 38 37-862 37i 39 37-302 37} 40 36-751 36I 41 36-208 3Sl 42 35-673 43 35-145 35i 44 34-626 i 34^ 45 34-114 34 46 33-610 33^ 47 33-113 33 48 32-624 32i 49 32-142 3H 50 31-667 i 31? Years' 1 3. 0/ Purchase ±4. /O 56-160 55-194 54-245 53-312 52-395 51-494 50-608 49-738 48-882 48-042 47-215 46-403 45-605 44-821 44-050 43-292 42-548 41-816 41-097 40-390 39-695 39-013 38-342 37-682 37-034 36-397 35771 35-156 34-551 33 957 33-373 32-799 32-235 31-680 31-136 30-600 30-074 29557 29-048 28-549 28-058 27-575 27-101 26 635 26-177 25-726 25-284 24-849 24-422 24-002 49-020 48-058 47-116 46-192 45-287 44-399 43-528 42-675 41 838 41-017 40-213 39-425 38-652 37-894 37-151 36422 35-708 35-008 34-322 33-649 32-989 32-342 31-708 31 086 30477 29-879 29*293 28-719 28-156 27-604 27-062 26-532 26-011 25-501 25-001 24-511 24 03 1 23-559 23-097 22645 22-201 21-765 21-338 20-920 20-510 20-io8 19-713 19-327 18-948 '!J76 Examples.— The perpetuity of an annuity 0/ £1 is worth in present money : At 1^ per cent., £54- at 2 per cent., £'37 -894 or 38 years' purchase. ^ (zxxii) 56i 55i 54i 53? 52^ 51^ 50^ 49f 49 48 47k 4^ 45i 44f 44 43i 42^ 4if 41 40^ 39? 39 3H 37'i 37 36I 35? 35i 34^ 34 33i 32^ 32i 31^ 3ii 30A 30 29§ 29 28I 28" 27^ 27 26^ 26i 25f 25i 24f 24^ 24 Years' Q 0/ Purchase a /O 49 48 47 46i 45i 445 43h 42| 4if 41 4oi 39^ 38I 38 37i 36^ 351 35 33I 33 32i 3if 31 30I 30 29} 28f 28J 27^ 27 26| 26 25^ 25 24^ 24 23^ 23 22f 22^ 21} 2I,i 21 20| 20 I9I I9i 19 Years' Ql 0/ Purchase ^4/0 43466 42-510 41-575 40 660 39-765 38890 38034 37-197 36-379. 35-578 34-795 34-030 33281 32-549 31832 31-132 30-447 29-777 29-122 28-481 27-854 27-241 26-642 26-055 25-482 24-921 24-373 23-837 23-312 22*799 22-297 21-807 21*327 20858 20-399 19-950 19:511 19081 18-662 18-251 17-849 17-457 1 7 072 16-697 16-329 15-970 15-619 15-275 14-939 14-610 143^ 42§ 41^ 4o| 39| 39 38 37i 36k 35^ 34| 34 33r 3i| 31^ 30I 29I 29 28i 27f 27J 26f 26 25^ 25 24i 23f 234^ 22f 22| 2lf 2li 20| 20| 20 I ^9 i8| I 18^ I i7f ! 171 17 i i6f i6i 16 iSh i5i 15 After Years I 2 3 4 5 6 7 8 9 10 II 12 13 14 15 16 % 19 20 21 22 23 24 25 26 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 per annum after 14 years 123 or 54 years' purchase ; "iie P^es^^alie^he REVERSION OF A PEEPETUITY after any given The Preseni a ^^^ ^^^ exceeding 100 Years After Years I 2 3 4 5 6 7 8 9 10 II 12 13 M 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 Years' Olo/ Purchase ^2/0 39-024 38-073 37-144 36-238 35-354 34-492 33-651 32-830 32-029 31-248 30-486 29742 29-017 28-309 27619 26-945 26-288 25-647 25-021 24-411 23-815 23-235 22-668 22-115 21-576 2 1 -049 20-536 20-035 19-546 1 9 070 18-605 18-151 17-708 17-276 16-855 16-444 16 043 15-651 15-270 14-897 14-534 14-179 13-834 13-496 13-167 12-846 12-533 12-227 1 1 -929 11*638 Years' Purchase 219 o 39 38 371 36I 35i 34l 33f 32I 32 31I 301 29f 29 28i 275 27 26i 25f 25 24^ 23I 23i 22| 22 2li 21 20| 20 I9I 19 i8i I7f m i6f : 16" 151 i5i 15 1 I4I i4i i i3f I 13^ i3t I2f I2i I2i 12 III 35-390 34-443 33-521 32*624 3175I 30-901 30-074 29-269 28-486 27-724 26-982 26-259 25-557 24-873 24-207 23-559 22-929 22-315 21-718 21-136 20-571 20-020 19-484 18-963 18-455 17-961 17-481 17-013 16-557 16-II4 15-683 15263 14-855 14-457 14-070 13-694 13.327 12-971 12-623 12-286 1 1 -957 11-637 1 1 -325 1 1 -022 10-727 10*440 IO-161 9-889 9-624 9-366 34^ 335 32I 3i| 31 30 29f 28i 27f 27 26I 25I 24f 24t 235 23 22} 2lf 2li 20| 20 i9h 19 i8i 18 i7h 17 i6i 16" i5f 15} Hf 14^ 14 i3f 13.^ 13 I2i I2i 12 uf II lOf lOi loj 10 9h 9\ Years' Piirchase 32-362 31-420 30-505 29-616 28-754 27-916 27-103 26-314 25-547 24-803 24-081 23-379 22*697 22-037 21-395 20-772 20167 19-580 19*010 18-456 17-918 17-396 16-890 16-398 15-920 15-456 15-006 14-569 14-145 13733 13-333 12-945 12-568 12-201 1 1 -846 11-501 1 1 -166 10-841 10-525 10-219 9-921 9-632 9-351 9-079 8-815 8-558 8-309 8-067 7-832 7-604 3% Years' QIq/ Purchase O2 /«> ^2^ 3ih 305 295 28f 28 27 26} 25^ 24? 24 232 22f 22 21^ 20f 20| I9I 19 i8i 18 17^ 17 16^ 16*^ 151 15 145 ^4\ 13I i3i 13 I2i 12.^ Ilf III "1 I of 10^ lol 10 9|' 9\ 9 8f 8| 8i 8 71 71 27-605 26-672 25-770 24-898 24-056 23-243 22-457 21-697 20-964 20-255 19-570 18-908 18-269 17-65' 17-054 16-477 1 5 -920 15-382 14-862 14-359 13-873 13-404 12-951 12-513 12-090 11-681 1 1 -286 10-904 10-536 10-179 9-835 9-503 9181 8-871 8-571 8281 8-OOI 7730 7-469 7*216 6*972 6737 509 289 076 5-871 5-672 5-480 5-295 5116 27^ 26f 25? 25 24 23t 22| 2l| 21 20] 9| 9 8} 71 7 6i- 6 51 4| 4\ 3f 3^ 3 2h If 0% ol 9| 9^- 9.^ 8f 8i 8i 8 7f 71 7^ 7 6f 6| 6} 6 5f 5f 5^ 51 5 Aftei Year!> I 2 3 4 5 6 7 8 9 10 II 12 13 M 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 For Explanations and Examples, see pp. xviii. on pp. xxxiv.-xxxix. (xxxiii) and xix. Tables continued INTEREST TABLES I I The Present Value of the REVERSION OF A PERPETUITY after any given Term not exceeding 100 Tears SI 52 S3 , 54 I 55 56 57 I 58 I 59 ! 60 61 i 62 63 64 I 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 85 90 95 100 31199 30-738 30-284 29-836 29-395 28-961 28-533 28-111 27-696 27-286 26-883 26-486 26-094 25 709 25-329 24-955 24-586 24-222 23-864 23-512 23-164 22-822 22-485 22-152 21-825 21-503 21-185 20-872 20-563 20-259 18806 17-457 16-204 15-042 3ii 3of 3oi 29f 29h 29 28§ 28 271 27i 27 26i 26' 25.^ 25i 25 24| 24i 23f 235 23k 22f 22§ 22I 2lf 21^ 21I 20f 20| 2o| I8f i7t '>k 15 i6f Tears' T 3^ Purchase X4 O/ ^O 23-589 23-183 22-784 22-393 22-007 21-629 21-257 20-891 20-532 20-179 19-832 19-491 19-156 18-826 18-502 18-184 17-871 17-564 17-262 16-965 16-673 16-386 16-105 15-828 15-555 15-288 15-025 14-766 14-513 14-263 13-078 1 1 -991 1 0995 10-081 I 23A ! 23I 22f 22| 22 ! 2lf 2li 21 20i 20i I9| i9h 19 i8f i8i I7f 17^ i7i 17 i6f i6i 16' ^51 151 i5i 15 i4f 14^ 14] 13 12 II 10 Years' O 0/ Purchase a yo 18-212 17-855 17-505 17-162 16-825 16-495 16-172 15-855 15-544 15-239 14-940 14-647 14-360 14-079 13-803 13-532 13-267 13006 12-751 12-501 12-256 12-0X6 11-780 11-549 11-323 II-IOI 10-883 10-670 10-461 10-255 9-289 I 8-413 7-620 6 902 i8i i7f 17^ 17 k i6| i6i 1 51 15^ 15 I4f 14} 14 I3f I3§ ^3k 13 I2f I2i I2i 12 Hi Hi II II I of 10^ loi 9i 8| 71 Years' 1 «/ Purchase £14 7^ 14-289 13-974 13-667 13-366 13-072 12-784 12-503 12-228 11-959 11-695 11-438 1 1 186 10-940 10-700 10-464 10-234 10-009 9-788 9-573 9-362 9156 8-955 8-758 8-565 ^•377 8-192 8-012 . 7-836 j 7663 j 7*495 I 6-706 ; 6-000 5-368 4-803 14.^ 14 13I 13.^ 13 12f 12^ I2I 12 Ilf II I of io§ 10 9l 9h 9k 9k 9 8| 8| 8^ 8.^ 8 7f 7f 7h 6f 6 51 4f After, I Years SI 52 53 54 55 56 59 60 61 62 63 ^ 65 66 67 68 69 70 71 72 73 74 75 76 INTEREST TABLES 79 80 85 90 95 100 The Present Value of the REVERSION OF A PERPETUITY after any given Term not exceeding 100 Years f After Years Purchase Examples. -The perpetuity of an annuity of £1 per annum after 65 years IS worth m present money: at i^ per cent. £18502, or 18^ years' purchase: at 2k per cent. £10-464, or io| years' purchase. 51 52 53 54 55 56 57 58 59 60 61 62 65 66 $7 68 69 70 71 72 73 74 75 76 77 78 79 80 85 90 95 zoo Years' «2i% 11-354 Hi 1 1 -077 II 10-807 lOf 10-543 loh 10-286 loi 10-035 10 9-790 94^ 9-552 9k 9-319 9k 9-091 9 8-870 8f 8653 8| 8-442 Sh 8-236 ^ 8-035 8 7-839 71 7-648 7f 7-462 7^ 7-280 7k 7-102 7 6-929 6-760 6-595 6-434 6-277 6-124 5-975 5-829 5687 5-548 4904 4-334 3-831 3-386 7 6| 6| 6| 6^ 6 6 5f 5! 5^ 5 44^ 31 3k Years' Q^ 0/ Purchase C14. /o 9'ii6 8-872 8-634 8403 8-178 7-959 7-746 7-539 7-337 7-141 6-950 6-764 6-583 6-407 6-235 6-068 5-906 5-748 5-594 5-444 5-299 5-157 5-019 4-884 4-754 4-626 4-503 382 265 151 624 164 2-763 2-413 9 8f 8f ^ H 8 71 7k 7\ 7k 6| 6h 6k 6} 6 6 51 5^ 5k 5\ 5k 5 5 4? 4f 4| 4k 4k 4k 3k 3i 2| 2h Years' Purchase ae3 % 7-382 7-167 6-958 6756 6-559 6-368 6-182 6-002 5-828 5-658 5-493 5-333 5-178 5-027 4-880 4-738 4-600 4-466 4-336 4-210 4-087 3-968 3-853 3-740 3-632 3-526 3-423 3-233 3-227 3-133 2-702 2-331 2-01 1 1-734 7h 7k 7 6f 6| 6i 6| 6 51 5f 5k 5k 5k 5 5 4| 4k 4k 4k 4k 4 4 3f 3! 3l 3^ 3.^ 3i 3k 3k Years' Purchase :« 3i % 2i 2 If 4943 4-776 4-614 4-458 4-307 4-162 4-021 3-885 3-754 3-627 3-504 3-386 3-271 3-160 3-054 2-950 2-851 2-754 2-66i 2-571 2-484 2-400 2-319 2-241 2-165 2-092 2-021 1-952 1-886 1-823 1-535 1-292 I 088 •916 4^- 4^ 4k 4k 4k 4 4 31 3^- 3k 3\ 3k 3 2^ 23 ■^4 2i 2 2i 2i 2 2| 2| 2 I After Years 51 52 53 54 55 56 57 58 59 60 61 62 63 ^ 65 66 67 68 69 70 71 72 73 74 75 2 76 2 77 2 78 79 I'i 80 i| 85 14^ 90 I 95 I 100 PP xxxU ''xll'lfj*'^"^ *°'^ Examples, see pp. xviii. and xix. Tables continued on pp. &ZX11., xxxiii. and xxxvi.-xxxix. ^ fxxxiv) (xxxv) INTEREST TABLES INTEREST TABLES ) The Present Value of the REVERSION OF A PERPETUITY after any given Term not exceeding 100 Years After Years Years' JT 0/ 1 Purchase \t /<> Years' A\o/ Purchase Tt2 /<^ Years' Co/ Purchase i/ /o Years' fi 0/ Purchase U /O After Years I 24-038 24 21-265 2li 19-048 19 15-723 "151 I 2 23-114 23 20-350 20| 18-141 18] 14-833 i4l 2 3 22-225 22^ 19-473 I i9h 17-277 i7\ 13-994 14 3 4 21-370 2I| 18-635 i i8| 16-454 m 13-202 13I 4 5 20-548 20^- 17-832 I7f 15-671 151 12-454 I2h 5 6 19758 I9f 1 7 -064 1 7 14*924 15 11-749 III 6 7 18-998 19 16-330 16] 14-214 14^ 1 1 -084 II 7 8 18-267 18] 1 5 626 i5f 13*537 13^ 10-457 lOi 8 9 17-565 in. 14-953 15 12-892 13 9*865 91 9 10 16-889 17 14-310 j I4{ 12*278 12] 9*307 9\ 10 II 16-240 16; 13-693 ! I3f 1 1 -694 iif 8-780 H II 12 15-615 i5i 13-104 13 II-I37 III 8-283 8| 12 13 15-014 15 12-539 12^ 10 -606 IO| 7*814 71 13 14 14-437 . i4j 1 11-999 ' 12 lO'IOI 10 7*372 n 14 15 13-882 14 11-483 i 1I2 9-620 9l 6*954 7 15 i6 13-348 nk 10-988 II 9*162 9k 6-561 6i 16 17 12-834 I2| 10-515 loi 8-726 H 6-189 6i 17 i8 12-341 I2i 10-062 10 8-310 8i 5*839 51 18 19 1 1 -866 Ilf 9-629 9f 7*915 8 5*509 5* 19 20 11-410 in 9-214 9i 7*538 7h 5-197 S\ 20 21 10-971 II 8-8i8 8f 7-179 n 4-903 5 21 22 10-549 10^ 8-438 8^ 6-837 6f 4-625 4f 22 23 10-143 lol 8-074 8 6-511 6| 4*363 4i 23 24 9-753 9? 7-727 7f 6-20I 6i 4-116 4 24 25 9-378 9h 7-394 n 5-906 6 3-883 3f 25 26 9-017 9 7-076 7 5*625 51 3*663 3f 26 27 8-670 8f 6-771 6f 5*357 51 3-456 3i 27 28 8-337 84 6-479 eh 5-102 5 3-261 3i 28 29 8-oi6 8 6'200 6i 4-859 44 3-076 3 29 30 7-708 7l 5-933 6 4-628 4| 2-902 3 30 31 7-412 7h 5-678 51 4-407 4^ 2-738 2| 31 32 7-126 Ik 5-433 51 4-197 4| 2-583 2^- •^0 32 33 6-852 6| 5-199 5} 3*997 4 2-436 2I 33 34 6-589 ^ 4-975 5 3-807 3f 2 299 2\ 34 35 6-335 6] 4-761 4| 3-626 3f 2-168 2i 35 36 6-092 6 4-556 45 3*453 3^ 2-046 2 36 37 5-857 5f 4 360 4| 3-289 3i 1-930 2 38 5-632 5f 4-172 4| 3*132 : 3t I 821 I^ *4 38 39 5'4i6 5* 3-993 4 2-983 3 1-718 l2 *4 39 40 5-207 5i 3-821 3f 2-841 i 2f I 620 1 1 40 41 5-007 5 3-656 3f 2-706 2f 1-529 T 1 41 42 4-814 4f 3-499 J 2 2*577 2^ 1-442 » 1 42 43 4-629 4f 3-348 3] 2-454 2\ 1-360 1 T *4 43 44 4-451 4i 3-204 3i 2-337 2i 1-283 T 1 44 45 4-280 44^ 3-066 3 2-226 2[ I -21 1 T 1 *4 45 46 4-115 4 2-934 3 2 -120 2 I 142 1 1 *4 46 47 3*957 4 2-808 2^- 2-019 2 1-078 47 48 3-805 31 2-687 2f 1-923 2 I 017 48 49 3-659 31 2-571 2i 1-831 If -959 49 50 3-518 _3l 2 -460 2| 1-744 l'\ -905 50 Ex AMPLES.— ^ ['he pe ipetuity of an ar inuity of £1 per annum af ter 37 years is wor th in pres ent m oney : at 4 per cent., .€5-^ >57, 01 I- 5f years ' pure base; The Present Value of the REVERSION OF A PERPETUITY after any given ^ Term not exceeding 100 Years ! After Years Years' TJ 0/ Purchase 1 /O Years' Q q/ 1 Purchase O /o | Years' Q 0/ Purchase U /O 10-194 j 10} Years' "I Purchase X 9*091 0% After Years I 13*351 134 11*574 11^ 9 I 2 12-477 12^- 10-717 io| 9-352 94^ 8-264 81 2 3 II -661 Hi 9*923 10 8-580 , H 7513 7h 3 4 10-898 II 9-188 9\ 7-872 ^ 71 6-830 6f 4 1 5 10-185 io| 8-507 H 7*222 ; 7i 6-2IO ! 1 61 5 6 9-519 9h 7-877 7f 6-626 5^ 5-645 i 51 6 7 8-896 9 7-294 74^ 6-078 6 5-132 1 5i I 8 8-314 8^ 6-753 6f 5-577 51- 4-665 1 4f 9 7-770 7f 6-253 6| 5II6 5 4-241 4l 9 ID 7-262 7t 5-790 5^- 4-694 4f 3^855 ' 31 10 II 6-787 6f 5-361 51 4-306 4} 3505 3h II 12 6-343 6i^ 4-964 1 5 3*951 4 3-186 31 12 13 5-928 6 4-596 i Ah 3*625 31 2-897 3 13 14 5-540 5^ 4-256 4i- 3*325 3i 2633 2| 14 15 5178 ; 54^ 3-940 4 3*051 3 2-394 1 2h 15 16 4-839 , 4l 3-649 2-799 '>a -'4 2-176 21 16 17 4-522 Ah 3-378 ; 3i 2-568 2h 1-978 2 i^ 18 4-226 4t 3-128 -3i 2-356 n 1-799 *■ V 19 3-950 4 2 -896 3 2161 2{ 1*635 i f ^ * 4 19 20 3-691 3l 2-682 2f 1-983 2 1-486 20 21 3-450 3^ 2-483 2§ 1-819 T ^ *4 1*351 . 1 * 1 21 22 3-224 2>k 2299 ; 2\ I 669 T '•* *4 1-229 T I *4 22 23 3*013 3 2-129 2t I -531 T 1 *2 1-117 23 24 2-8l6 2f 1-971 2 1-405 » 1 *2 1-015 24 25 2-632 2i 1-825 If 1-289 T 1 •920 25 26 2-460 2\ 1-690 If 1-182 1 1 *4 •839 3 4 26 27 2-299 2| 1-565 I5 1-085 -763 3 4 27 28 2-148 2^ 1-449 ih 1-005 -693 a 4 28 29 2 -008 2 1*342 H •913 •630 3 4 29 30 1-876 2 1-242 1 III •838 3 4 •573 i «2 30 31 1-754 If I -150 n •769 f •521 1 2 31 32 I -639 I f I 065 I •705 4 ■474 1 2 32 33 1*532 i| •986 I 1 -647 3 4 •431 1 2 33 34 1-431 I'i 913 ; I 594 ^ -391 1 3 34 35 1*338 li *845 f •545 ^ •356 ± 3 35 36 1-250 i| *783 i f •500 2 323 * 36 37 I -168 i^ *725 ! f *458 2 -294 ^ 37 38 I 092 I *67i ; 1 -421 2 •267 - 1 4 38 39 I 021 i I -621 f •386 •243 1 4 39 40 •954 I *575 i ^ -354 ^ •221 i 5 40 41 -891 I •533 i ? -325 ^ -201 1 5 41 42 *833 f •493 2 -298 ^ •183 i. 5 42 43 -778 8 4 *457 ' h -273 4" -166 i 43 44 -728 f •423 h -251 - 1 4 •151 1 44 45 •680 f *392 1 2 •230 i 4 •137 1 7 1 I 45 46 -635 s 4 *363 1 • •211 j ' -125 i 46 ^2 *594 h *336 r -194 ' 1 •113 1 y 47 48 *555 h -311 i -178 -103 .1. 1 n I ' 48 49 519 1. 2 •288 1 ^ •163 I -094 1 11 49 50 *485 ^ •267 ! 1 4 •150 7 •085 1 12 50 at 5 per cent., ±'3-289, or 3J years' purchase (xxxvi) For Explanations and Examples, see pp. xviii. and xix. Tables continued on pp. xxxii.-xxxv. and xxxviii., xxxix. (xxxvii) INTEREST TABLES The Present Value of the BEVEESION OF A PEBPETUITY after any given Term not exceeding 100 Tears After Years 51 52 53 54 55 56 57 58 60 6c 62 63 65 66 67 68 69 70 71 72 73 74 75 76 77 7^ 79 Sol 85 90 95 100 Tears' A ^/ Purchase % to 3-383 3-253 3-128 3007 2-892 2781 2674 2-571 2-472 2-377 2-285 2-197 2-113 2-031 1-953 1-878 1-806 1-736 1-670 1-605 1-544 1-484 1-427 1-372 1-320 , I -269 I -220 1-173 I -128 1-085 -891 -733 -602 -495 3^ 34^ 3l- 3 3 2^ 2| 2| 2} 2 2 2 *4 If If u If tJ If li 2 4 a a Years' Purchase 2-354 2253 2-156 2-063 1-974 1-889 I -808 1-730 1-655 1-584 1-516 I -451 I 388 1-328 1-271 1-217 I -164 1-114 1-066 1-020 •976 •934 •894 -855 -819 -783 -750 -717 •686 -657 -527 -423 -339 -272 4i% ■'4 2^ •^4 2 2 i^r If If li- i| If *4 I I I I I 3 4 8 4 I 8 4 S. 4 8 4 3 4 Jw 2 A 2 ll Years' c ^z Purchase U 75 f h a k a a i 4 1 7. 'I Pu^^iLe 6 % '211 After Years Examples. -.u^ — "'^^® perpetuity of an annuity of £1 per annum after 65 years IS worth in present money: at 4 percent., £1-953, or 2 years' purchase: at 4A per cent., £1-271, or i| years' purchase. INTEREST TABLES The Present Value of the SEVESSIOIT OF A FEBPETITITT after any given Term not exceed:ng 100 Tears After Years Years' 17 q. Purchase f /o •453 -423 -396 •370 -346 -323 •302 •282 •264 •246 -230 -215 -201 •188 -176 •164 -154 -143 -134 -125 •117 •109 -102 -096 •089 •084 -078 •073 -068 -064 •045 -032 -023 •016 2 1 2 A 2 1 3 1 3 i 3 1 4 1 4 I 4 JL 4 1 1 6 f5 1 6 * 1 T l~ 5 1 9 1 » _L 10 JL 10 1 IX 1 12 _l. 13 JL 14 1 15 JL 16 L 22 J_ 31 JL 43 1 »2 Years' Q ^/ Purchase O % •247 •229 •212 •196 •182 •168 •156 -144 -134 •124 -114 •106 -098 -091 -084 •078 •072 -067 -062 -057 •053 •049 -045 •042 •039 •036 -033 -031 -029 •026 •018 •012 •008 •006 Years'" Purchase -078 •071 •064 -059 -053 1 13 1 14 1 IB 1 IT JL 19 After Years -049 * 56 044 1 23 SZ -040 1 25 5JB •037 1 27 59 -033 1 : 60 -030 1 33 61 •027 3V 62 -025 1 ] 40 63 -022 I 1 43 64 •020 1 j 1 50 65 •019 1 1 53 66 -017 ' 1 59 67 ■015 1 «7 68 -014 A 69 •0.3 1 70 -012 ^3 71 •010 1 100 72 •010 Too 73 •009 1 111 74 1 •008 1 125 75 1 •007 1 143 76 •006 1 T«7 77 -006 1 78 •005 1 200 79 -005 1 200 80 ' •003 _1_ 333 85 -002 1 500 yo 001 1 1000 95 •001 1 non 100 ' For Explanations and Examples, see pp. xviii. and xix. pp. xxxii.-xxxvii. Tables continued on (xxxviii) (xxxix) INTEBEST TABLES 15"/< Years PilESENT VALUE OF I 2 3 4 5 6 7 8 9 10 II 12 13 14 15 i6 17 i8 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 One Poand £X per Annum J Years •8695652 7561437 •6575162 •5717532 •4971767 •4323276 •3759370 •3269018 •2842624 •2471847 •2149432 •1869072 •1625280 •I413287 •1228945 •1068648 •0929259 •0808051 •0702653 •061 1003 •0531307 •0462006 •0401744 •0349343 •0303776 •0264153 •0229699 •0199738 •0173685 •OI51031 •0131331 ■01 1 420 1 •0099305 •0086352 •0075089 •0065295 •0056778 •0049372 •0042932 •0037332 •0032463 •0028229 •0024547 ■002 1 345 •OOI8561 •OOI6140 •0014035 •0012204 •OOI0612 0009228 •8695652 1 -6257089 2'283225I 2 •8549784 3-3521551 3^7844827 4^i6o4i97 4-4873215 4-7715839 5-0187686 5-2337118 5-4206190 5 •5831 470 5-7244756 5-8473701 5^9542349 6-0471608 6^1279659 6^i9823i2 6^2593315 6-3124622 6^3586627 6^3988372 6^4337714 6^464 1 49 1 6-4905644 6^5i35343 6^5335081 6-5508766 6^5659796 6^5791127 6^5905328 6 •6004633 6 ^6090985 6-6166074 6-6231369 6-6288147 6^6337519 6-6380451 6-6417784 6-6450247 6-6478475 6^6503022 6-6524367 6-6542928 6-6559068 6-6573102 6-6585306 6-6595919 6-6605147 51 52 53 54 55 56 57 58 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 PRESENT VALUE OF One Pound i £1 per Annum -0008024 •0006978 •0006068 •0005276 •0004588 •0003990 •0003469 -0003017 -0002623 •0002281 •0001983 •0001725 •0001500 •0001304 •0001 134 •0000986 •0000858 •0000746 •0000648 •0000564 •0000490 •0000426 •0000371 -0000322 -0000280 -0000244 -0000212 •0000184 •0000160 •0000139 -C000121 •0000105 •0000092 •0000080 •0000069 •0000060 0000052 •0000046 •0000040 •0000034 •0000030 •0000026 •0000023 -0000020 •0000017 •0000015 •0000013 •000001 1 •oooooio •0000009 6-66I3I7I 6-6620x49 6-6626216 6-6631492 6-6636080 6-6640070 6^6643539 6-6646556 6-6649179 6-6651460 6-6653443 6-6655168 6-6656668 6-6657972 6-6659106 6-6660092 6 -6660950 6-6661696 6-6662344 6-6662908 6-6663398 6-6663824 6-6664195 6-6664518 6-6664798 6 -6665042 6-6665254 6-6665438 6-6665598 6-6665738 6-6665859 6-6665964 6 -6666056 6-6666135 6-6666205 6-6666265 6 -66663 1 7 6-6666363 6 -6666403 6-6666437 6 -6666467 6 -6666493 ' 6-6666516 6-6666535 6-6666552 6 6666567 6-6666580 6-6666592 6-6666601 6 -66666 10 Tor explanation see pp. xviii, 10, 12 (xl) INTRODUCTION ■«o«- ON THE NATURE AND USE OF DECIMALS In order to render the following tables intelligible to persons onlv moderate y acquainted with common arithmetic it ma^^weU to fr,.?"' entire system of numbering (if for the moment we leave tas out of consideration) is. in fact, the a ^"""^ " '^" ''"^^ «=> ""^^h s.de and one tenth rmuc'f "a tS^alurof 1' °" '^^ '''''''"' ^'le value of the same figure placed IxNTRODUCTION next to it on the left-hand side. It is, therefore, just as simple to deal with decimals as it is to deal with whole numbers. If we see a number, such as 346, without any decimal dot we understand, as explained above, that the 6 stands for six ones, but if between the four and the six we place a decimal dot, 34-6, we then know that the four no longer stands for four tens, but for four ones, and the 6 no longer stands for six ones, but for six tenths of one. So if we write 3-46 the 3 no longer stands for three hundreds, but for three ones, the 4 iox four tenths of one, and the 6 for six hundredths of one. The decimal dot, therefore, is simply employed to tell us where the ones come, for the figure immediately to the left of the decimal dot always stands for so many ones. If these uniform grada- tions by tens and tenths are kept in mind no difficulty will arise in dealing with the decimals. Decimals and Fractions From this it will be seen that any decimal may be converted into its equivalent fraction at once :• we have only to write the decimal, removing the dot, for numerator, and to write for denominator i followed by as many cyphers as there are figures, or places, in the decimal. Thus : 06=1 ; -06= ^- ; 10 100 •006 = 1000 42 42 , 100 •423=^ -^ » 1000 and so on. * Every fraction too of which the denominator i is followed by cyphers may just as readily be written as a decimal, thus A =3 10 ^- =-07 100 9 ='009 1000 ^463=24-63, &c. 100 We have only to write down the numerator and to point off from the right as many decimal places as there are cyphers in the denominator, supplying this necessary number of places by cyphers immediately after the decimal point, should the number of figures in the nume- rator be too few. Fractions, whatever be their denominators, may also be converted into decimals, as will be seen presently. Addition of Decimals From what has been already said it will be seen that the important thing in the addition of decimals is to take care that the decimal dots all come under one another, just as in the addition of whole USE OF DECIMALS numbers the units have to come under the units, the tens under the tens, and so on. If this point is attended to the matter is perfectly simple, and is conducted exactly like simple addition. A few examples are given below : — 1. Add together 2*345, -64, 237, -02. 2. 7*432, i6'207, -021, '4628. 3. -005, 61-4, -368, 7*2. (0 (2) (3) 2345 7*432 -005 •64 16*207 61 4 237 -021 -368 •02 -4628 7-2 26*705 24*1228 68*973 Subtraction of Decimals In subtracting decimals, as in adding them, the important thing is to see that the decimal dots come under one another, and if this is done the subtraction of decimals is carried out in exactly the same way as simple subtraction. A few examples of subtraction are also given : — 1. Subtract 3*725 from 5*103. 2. 27*846 from 31-3. 3. '026 from 12*4. • . (0 (2) (3) 5*103 31*3 12*4 3*725 27*846 •026 1*378 3*454 12*374 * In the third example of addition two cyphers appear immediately to the right of the decimal dot. These o's serve to indicate the position, and therefore the value, of the figure to the right of them • thus ^005 indicates that there are no tenths nor hundredths, and that the five stands for five thousandths ; and similarly in the third example of subtraction -026 indicates that there are no tenths, but that the 2 stands for two hundredths and the 6 for six thousandths. Multiplication of Decimals deciLt" l^^^ t"^"^^ ^''" '""" '^^' ^" "^"^^^P^y ^ "™ber involving decimals by 10 by simply removing the decimal point one place to (3) a 3 I, jn -j.i-,j^^ ^e^gww 1157-281 INTRODUCTION the right ; we multiply by 100 by removing the point two places to the right, and so on. Thus : •6 X 10=6 ; -6 X 100=60 ; -006 x ioo=*6. •42 x io=4*2 ; 42 X 100=42 ; 4*2 x 100=420. In order to multiply a number containing decimals by any whole number-that is, by any number without decimals-we proceed exactly as we should do if there were no decimals at all ; only when the product is obtained we must point off, as decimals, as many places as there are places pointed off in the number 24*623 multiplied. Thus, if we have to multiply 24-623 by 47, we proceed as in the margin, and so in all similar cases. As the number multiplied has three decimal places, we mark off three places of decimals in the pro- duct. . 1 u u • If we have to multiply together two numbers which both contam decimals we proceed as in simple multiplication, and place the decimal dot in the answer in such a position that the number of decimals is the same in the answer as in the two numbers when their decimal places are added together. Thus : i-2Xi-i = i*32 ; -12 x*i2=-oi44; •222x3-1 =-6882; -o33X-22=-oo726. Division of Decimals In dividing a number containing decimals by a whole number we place the decimal dot in the quotient as soon as we bring down a decimal of the dividend. Thus to divide 2 7 344 by 4 we proceed as follows : — 4 )2 7 '344 6-836* After dividing 27 by 4 we come to the decimal -3, and so the deci^mal dot had to be placed between the 6 and 8 of the quotient. If we have to divide by a number that will not go into the decimal part of the dividend we must be careful to record the fact by putting a cypher in the quotient. Thus -372-f-4 gives 4)172 •093 and 0372 ^4 gives 4)^0372 •0093 (4) USE OF DECIMALS The values of the 9 and the 3 depend on ihQu position, and they must be put in their right place by prefixing cyphers to the left of them if necessary. Placing cyphers to the right of a decimal dot alters the value of the number. Placing cyphers to the right of a decimal number with no other number after the cyphers makes no difference in its value. With whole numbers it is just the opposite of this. Thus: .73=_73_. .073-- 73_. .0073 = ^-11- 100 1000 I 0000 ; -730= ^^^ or ^ \ 1000 100 These facts have to be borne in mmd in the division of decimals. We may add as many cyphers as we please to the right of a decimal number, and so carry our division as far as we choose. Thus 43 h- 7 may just as well be called 4*30000 -J- 7- It makes no difference in the value, but there is no need to actually write the cyphers in working out the sum. We may put 7)4^3000000 ^^ 7)4^3 •6142857 -6142857* and the result is the same. The benefit of proceeding in this way is that we may get an answer that is more nearly correct than if we left off at the last figure of the dividend. Thus the result of 43 -f- 7 is approximately — , more nearly ^' , still more nearly -^-^, and so 10 100 on. 1000 If both the divisor and the dividend contain decimals there must be as many decimal places in the divisor and quotient together as there are in the dividend. This is obvious from what has been said in regard to multiplication. It was there shown that •222 X3-i=-6882, and so if we have to divide 6882 by 222 we have •222)-6882(3-I 666 222 222 There are three decimal places in the divisor -2 2 2, and four in the dividend 6882, so there must be one in the quotient 3-1 to add to the three in the divisor to make up the four in the dividend. In applying this rule it must be borne in mind that the number of decimal places in the dividend means the number actually used in division, and the number of cyphers added to it ranks as decimal may'see. ^'^^^'^'^^'^r^ ^' 37*38 or 37*387 or 37*3875, as we (5) X ^ INTRODUCTION •24)8-97300o(37*3S75 177 168 93 72 210 192 180 168 120 120 There are one, or two, or three, or four places of decimals in the answer, depending upon the extent to which we carry the division. Obviously the answer cannot sometimes be 373 I i.e. 37 A j, some- times 373 (i.e. 3^^ , and so on : it must always be 37 and a little more. Hence the number of decimal places used in the dividend have to be noted, and the number in the quotient added to those in the divisor must make up the number used in the dividend. Some examples of division are appended. (i) 44-406-M2 (2) 44-406-T--I2 12) 44-406 •12) 44-4060 37005 370*05 (3) •44406-^1-2 i*2)-444o6o •37005 !il (4) 89-648^347-3 347"3)^9*^4^ooooo(-258i284 6946 20188 17365 28230 27784 4460 3473 9870 6946 29240 27784 14560 13892 668 (6) "" USE OF DECIMALS For most of the purposes for which the tables in this book are likely to be used four or five places of decimals is amply sufficient, and it is unnecessary to carry the calculations any further. Fractions and Decimals We have already shown how readily decimals may be converted into fractions, and we must now show how fractions may be converted into decimals. We saw that a decimal may be thought of as a fraction with the decimal as numerator, and for denominator i followed by as many cyphers as there are decimal places in the I 2 '2 decimal. Thus -i = — ; -23 = ^^, and so on. Now it is obvious 10 100 we do not alter the value of any fraction if we multiply both the numerator and denominator by the same quantity. Thus -=- = „=—; = — , and so on. All these fractions are of the same 2 4 8 16 32 value. If, therefore, we multiply the denominator by a quantity that makes it equal to 10 or 100, or any other multiple of 10, and then multiply the numerator by the same quantity as we multiplied the denominator by, we at once get a fraction that can be converted into a decimal at sight. Thus I _- 5 ID = h =5 I _ 25 _ . 4 100 2 _ j^ 5"~io "" "^ It is often, however, a clumsy way of working to divide 10 or some power of lo by the denominator, and then multiply the numerator by the result. To do so may involve a long multiplica- tion sum. We therefore multiply the numerator by i followed by any number of cyphers we want and divide by the denominator. In other words, we divide the numerator by the denominator. Thus in converting - into a decimal it makes no difference in the result whether we have ^^'°±5^2 xj^£^ ^^ whether we have 5Xio-r5 5x2 10 2-0 — =-4. 5 But it makes a great deal of difference in the working whether in converting, say, ^—-^ into a decimal we first divide i by 3736 and (7) 1 INTRODUCTION multiply the result by 1868, or whether we divide 1868 by 3736 and get '5 as our answer at once. A few examples of converting fractions into decimals are appended. 2-5^ 4 •25; ^ = 75; ^ = *>25i I 403 •i • =-6 These are useful fractions of which to know the corresponding decimals. A recurring decimal is marked with a dot above it, and means that it is repeated continuously. Where a group of several figures recurs it is marked with a dot over the first and last of the group. Thus ' — "33333 and as many more threes as we care to 3 write. It is shortly expressed as '3. If we wish to convert into a decimal, we have 7)1 •142857, which means that at this stage there is i over, and the numbers 142857 would be repeated indefinitely if the division were con- tinued for an indefinitely long time. Other examples are : — 4^ = 4375; 7,^^ = 7-5625; ^^=809523; :;^ = *o375335 + 9 _ 16 i7_ 21 INTEREST TABLES On pp. xx-xl and 50-124 Interest Tables of various kinds are given. Their construction and use is here explained, in order to facilitate their employment, and to make it possible for those unfamiliar with the subject to perform calculations at other rates and for other periods than those given in the table. Unless otherwise stated the tables throughout the book are calculated at compound interest, not at simple interest. Compound interest, of course, means that the interest as it becomes due is added to the original debt, and the interest for subsequent periods is calculated on the original debt increased by all the previous accumulations of interest. The Amount of ;£i On pp. 50-85 are tables which show for various rates of interest — (i) The sum which ^i will amount to in any number of years from I to 100. (8) THE AMOUNT OF £t (2) The present value of ^i due at the end of any number of years from i to 100. (3) The sum to which j£i per annum will amount in any number of years from i to 100. (4) The present value of ;£^i per annum to be received for any number of years. We will consider these in the order stated, taking our illus- trations principally from the 4 % table on pp. 70 and 71. It will be convenient to give the explanations by quite simple algebra first, and then to give the arithmetical explanations or numerical examples. If by / we represent the rate of interest, it is clear that one pound, or one dollar, or any other unit, will amount in one year to i -H / ; and if we represent the amount by s, we have s =• i +/'. If the rate of interest is 4%, or 4 on one hundred, it is '04 on a unit and !-(-/= 1*04. At the beginning of the second year, if the interest has not been paid, the loan or investment, s, is i -f- /, = i '04, and the interest on this is / (i +/), = 1*04 X '04 = -0416. To find the amount at the end of the second year we must add the second year's interest to the amount at the beginning of the second year. Thus we have ( i + /) 4- i(i 4- /) = (i 4- X (1 4- /) = (i 4- i)\ or 1*04 4- ('04 x 1-04) = I '04 4- '0416 = I -0816 = 1*04 X 1-04 = 1*04^ We begin the third year with s = (i 4-/)(i4-0» ^^^ the interest for the third year is this amount multiplied by / = /(i +/)(i +/), and, adding this to the amount at the beginning of the third year, we have(i + /)(i -H /)(i 4- /) = (i 4- /)^ = 10816 -f- (04 x 10816) = i'o8i6 4- '043264= 1*124864 = 1*04^ Thus the amount of one in any number of years, «, is the amount of one in one year raised to the «'* power. This is expressed as (i4-/)% and, if / = *o4, then {i ■\- i)" = i'o^\ If « = 5 this is I '04 '\ This may be seen below. • Year I 2 3 4 5 Amount at Beginning of Year Process Amount at End of Year I X I "04 = I -04 = I -04 104 X 104=: 1042= I 0816 I 0816 X 1-04= I •04'' =1-1 24864 II24864 X 104= 1-04^ = 1-16985856 1-16985856 X 1-04= 104'*= 1-2166529024 This tells us the amount of i, and, if we want to know what any other sum comes to, we must multiply the sum by the amount of i. What is the amount of j^iy in five years at 4 % ? (9) r ; I INTRODUCTION The amount of ^ I is 1-21665 The amount of 17 is therefore ;^2o*68305 We might get this result more exact by using more places of decimals. Thus, 1-2166529024 x 17 = 20-6830993408, which is •0000493408 more than we previously had. The difference is less than — ^ — - of /?i, which is — ^ of a shilling, or almost - of a I 00000 1000 20 farthing. This shows that five places of decimals, as given in the tables, give results quite near enough for most purposes. It is explained later on (pp. 206-228) how easily a table of this kind can be constructed by means of logarithms the practical use of which is extremely simple, and if other rates of interest than those tabulated are needed they should be obtained by logarithms. It should be noted that the table gives the amount of one pound at the end of the year, i.e. just after the year's interest has been added. The amount at the beginning of any year is the same as the amount at the end of the preceding year. Before explaining some of the uses of these tables it will be best to explain the contents of the other columns on these pages. We at present assume that the interest is reckoned annually, but later on we shall consider the case of interest convertible half-yearly and at other intervals. The Present Value of ;£i If, as we have seen, £^\ amounts to ^1*04 in one year the present value of this ^i'04 is obviously £^\. In other words, £^\ invested now at 4% will amount to ^^104 in one year. But if the present value of ^^1-04=1 the present value of I = -^— , and using v to represent the present value of i one year 1-04 hence we have v=. ., and 2/"=— - .. , where, as before, n represents the term. If /= -04 and « = 5 we have I I z;-^ = (1+/)* 1*21665 Whatever the term may be = -82193. «' = i + / = 1+/ I V (10) THE AMOUNT OF £,\ PER ANNUM Thus to take 10 years at 4 % 1+/ = 67556 I 1*48024 1-48024= •67556 1*48024 X "67556 = =-v _ I V •99999 By calculating the values of / and v to more places of decimals we may obtain as close an approximation as we please to i by multiplying v\yj (i + i). To find the present value of any other sum than i we multiply the sum by the present value of i for the number of years required. Thus, the present value of ^^83 due at the end of 10 years at 4 % is •67556 X 83 =;i^56-o7 148. It will be noticed that the table of present values, like the table of amounts, refers to the end of the year. See also pp. xviii, 218 The Amount of ;£i per Annum « The third table on each page gives the amount of /^i per annum immediately after each annual payment is made. Thus the first line is in all cases i -00000. This table may be found from the amount o^ £_A by a series of additions. Thus at 4 %, if to the initial payment of ;^i we add 1*04000, the amount of ;£i in one year, we obtain 2*04000, which is the amount of ;^i per annum immediately after the second annual payment has been made. If to this amount we add 1*08160, the amount of ;^i at the end of the second year, we obtain ^^3-12160, the amount of ;£"! per annum immediately after the third annual payment has been made. We can, however, obtain the result in another way. The amount of ;£i in five years at 4 % is 1-2 1665, of which amount i was the original payment and 2 1665 the accumulated interest. Now ^i yields •04 every year at interest at 4 %, therefore the amount of 04 per annum for 5 years is -21665. ^^t if -04 per annum amounts to *2i665 i" 5 years 'oi per annum will amount to one fourth of this sum, which is -054163, and i amounts to 100 times this sum, which is 5*41632, which we see to be the amount of £^\ per annum in 5 years. Hence it follows that we can obtain the amount of £^\ per annum by subtracting unity from the amount of ;^i and dividing the result by the rate of interest. Hence we get the following expression : Sn. -. , where s-\ is the amount of £,\ per annum in n years, / is the rate of interest, and (i + /)" is the amount of ^^i in n years. (II) f INTRODUCTION To find the amount of any other sum for any number of years we take from the table the amount of;£"i per annum at the rate of interest and for the number of years required, and multiply this amount by the sum with which we have to deal. Thus the amount of ;6'75 per annum for 30 years at 4 % = ^56-08494 (p. 70) x 75 = ;£^42o6*57o5. For further details see p. 224. The Present Value of £1 per Annum By similar reasoning we see that the present value of £1 per annum may be obtained from the present value of £1 — that is to say, by a series of additions the present value of ;^i per annum can be obtained from the present value of ;^i. It may also be obtained by a second method similar to the second method of finding the amount of ;£i per annum from the amount of ;^i. Thus the present value of j^i at the end of 10 years is '67556, and the difference between this amount and unity is '32444, which is the present value of '04 per annum for 10 years. The value of 'oi per annum is one fourth of this amoujit, which is '08111. The present value of i per annum is 100 times this amount, viz. 8-iii, which is seen (p. 70) to be the present value of ;£"! per annum for 10 years at 4 %. It will be noticed that the present value of £1 per annum for 10 years is stated to be 8'i 1090, not 8'i 1 1. This slight discrepancy is due to the fact that the present value of £1 is only given to five places of decimals. If we calculate the present value of ;£"! due at the end of 10 years at 4 % to six places of decimals instead of five we find that it comes to '675564. Subtracting this amount from unity we obtain '324436, which divided by 4 and multiplied by 100 .gives us 8*1 1090 as the present value of £1 per annum for 10 years, which is in accordance with the table. This relation between the present value of ^^i and £1 per annum may be expressed by the formula i—v" ^H\ = ■ n\ where a„ is the present value of ;^i per annum for n years, v" is the present value of i due at the end of n years, and / is the rate of interest. A knowledge of the methods by which the tables are constructed greatly facilitates their use. Hence in all cases we first describe the construction of the tables arid then give some account of the purposes to which they may be applied. See also pp. xviii, 222. The table giving the present value of ;£"! per annum is applicable to many different purposes. Thus if we want to know the present value of an annuity, or pension for a definite number of years — the (12) PRESENT VALUE OF A PERPETUITY value, that is to say, of what is called an * annuity certain,' or the value of a lease, or of any other property yielding a fixed and certain yearly income, we can readily obtain it from this table. Thus a lease, or annuity, yielding £1 per annum, with 25 years to run, if purchased for ;^i 5*62208, would yield the purchaser 4% on his money and replace the capital by the end of 25 years. If the annuity were ^10 a year its value would be ten times as much ; if ^^20 a year, twenty times as much, and so on. We sometimes want to know what rate of interest will be yielded by purchasing an annuity for a given amount at a certain price, which may not be exactly any rate of interest that is here tabulated. In order to ascertain this we must see what an annuity of £1 per annum would cost at the same price, and then turning to tables at various rates we shall be able to see approximately what rate the investment would yield. Thus, if we buy an annuity of £^0 a year, for 20 years, for ;;^45o we see that an annuity of ;^i per annum at the same price would cost £1$- A reference to the tables on pp. 64 and 66 shows that this is less than we should pay to yield 2 J % on the investment, and more than we should pay to yield interest at 3%; but the return would be more nearly 3 % than 2f % being, in fact, a trifle over 2|%. It is sometimes convenient to be able to see the results at different rates of interest in this way ; consequently on pp. 86-93 abbreviated tables showing the amount and present value of ;£i and of ;^i per annum are printed. These are only extracts from the tables on pp. 50-85 arranged in a different form with a few other rates of interest added. The Present Value of a Perpetuity On p. 94 is given the present value of a perpetuity of ;^i per annum for every ^% up to 10%. These results are obtained by dividing 100 by the rate of interest. From this table the value of freehold property, advowsons, &c., can be obtained, it of course being necessary to ascertain the net annual value of the property on which to base the price to be paid for it. Thus a freehold yielding ;^8o per annum, after deduction of all expenses connected with it, would yield 4 %, if purchased for;^2,ooo, for 25 x 80 = 2,000. If the same property were purchased for ;^ 1,800, which is at the rate of ;^22 los. (for 1,800 H-80 = 22-5) for each £1 per annum, the yield upon the capital invested would be between 4| and 4^ %. Present Value of Reversions On pp. xxxii-xxxix and 95-98 is given the present value of a Rever- sion to a Perpetuity of ;^i. On p. 94 we have the present value of a (13) 1 INTRODUCTION perpetuity to be entered upon immediately, and on pp. xx-xxxi and 50-85 we have the present value of an annuity for any number of years from I to 100. By subtracting the present value of an annuity for a certain number of years from the present value of a perpetuity we obtain the present value of a perpetuity deferred for that certain number of years. Thus we see that the present value of a perpetuity of ;^i per annum at 4% is £2$ (p. 94). The present value of an annuity of £1 per annum for 20 years at 4% is ;^i 3*59033 (p. 70). Deducting this amount from ;£^25, we have ;^i 1*40967 as the present value of the Reversion after 20 years of a Perpetuity of ;£"!, which is the amount given on p. 98. The present value of a per- petuity of any other amount than ;^i is obtained by multiplying the value of a perpetuity of £1 by the amount of the perpetuity the value of which it is desired to obtain. Commutation of Fines for Renewing Estates Estates held in perpetuity are sometimes subject to a renewal fine to be paid by the holder at regular specified intervals. These periodical fines may be compounded for by a single payment down. The first table on p. 99 shows what this payment ought to be, so that the holder of the estate may redeem all these continually recurring fines and at the same time be allowed such interest upon the money thus paid in advance as may be agreed upon. Thus if the renewal fine is payable every 7 years for ever then the redemp- tion money to bear 5 % interest is found by the table to be 2*4564. This means that ;^2*4564 must be paid to redeem a fine of ;^i pay- able every 7 years. To redeem a fine that is equivalent to one year's rent a sum equal to 2*4564 times the annual rent must be paid. It is obvious that the redemption money must be that sum the interest upon which, if allowed to accumulate at compound interest at the rate agreed upon for the period between the fines, will just suffice to pay the fine. A reference to p. 74 shows that the amount of ;^i for seven years is ;^i*407io. Deducting from this amount the original £1 invested, we see that the interest on ;£"! invested for 7 years is ;;^*407io. If now we multiply *407io by 2*4564, the amount required to redeem a fine of £1 payable every 7 years, reckoning interest at 5 %, we have '40710 x 2*4564=1. Thus it will be seen that in every 7 years the interest on the redemption money amounts to exactly enough to pay the fine. Renewal of any Number of Years Expired in a Lease The second table on p. 99 and the tables on pp. 100-103 show the number of years' purchase for the renewal of any number of years (14) f RENEWAL OF LEASES expired in leases of various length. A reference to p. 70 shows that the present value of;^i per annum for 10 years is;^8*iio9o, and on p. 99 we see that the amount to be paid for the renewal of a 10 years' lease is this same sum of ;;^8*iio9o, which may be read as either ;£'8*iio9o for every £1 of income annually derived from the lease, or as 8*11090 years' purchase of the annual income from the lease. But if we own a lease that has, say, 5 years to run and we want to convert it into a lease that has 10 years to run, it is obvious that we must pay something for the extension of the lease. Reckoning interest at 4 % we have just seen that the value of a lease for 10 years is 8*11090 times its annual value, and another reference to p* 70 shows that the value of the 5 years' lease we at present possess is £4'4S^^2 for every £1 of annual income ; in other words, the value of the 5 years' lease we hold is 4*45182 times the annual value of the lease. Deducting this value of the 5 years' lease we own from the total value of the 10 years' lease we wish to obtain, we have 3*65908 as the number of years' purchase to be paid for extending our 5 -year lease into a lo-year lease. We could obtain the same result from the table on p. 70 showing the present value of £1 instead of the present value of £1 per annum. We are obviously entitled to the benefit of the lease for the next 5 years, and the additional benefit we have to pay for by having the lease extended to 10 years is equivalent to the present value of £1 due at the end of 6 years = * 7 9031 £1 £1 £1 £1 >> >i fy >j » I) »> >J Total 7 »> = 75992 8 » = 73069 9 j> = •70259 10 » = •67556 • 1 3*65907 This gives us ;^3*659o7 as the present value of £1 per annum for the 6th to the loth years, or 3*65907 years' purchase of the annual value of the lease, and is the same result as we obtained before, except that the last figure is a 7 instead of an 8, which is due to the number of decimal places to which the calculations were carried not being suflftcient to produce absolutely identical results. The tables referring to the Renewals of any number of years in leases for 20, 21, and 40 years are calculated in the same way, and the renewal of leases for different times, or at other rates of interest than those given on pp. 99-103, may be readily calculated from the present value of ^i per annum given on pp. 50-85 by subtracting the present value of £1 per annum for the number of years the lease we own has to run from the present value of £1 per annum for (15) K ! INTRODUCTION the number of years for which the fresh lease will be granted. It will be noticed that the last column in the table dealing with the lo years' lease is headed 17 95 % ; in the 20 years' lease 12 304 % ; in the 21 years' lease 11-564 % ; and in the 40 years' lease S.%. These rates of interest are respectively equivalent to a fine of I year's rent every 4, 7, 7, and 14 years. The extraordinary rates of interest here referred to result from customs that must presumably have originated from ignorance of the real rates of interest involved. Yield per cent, and Years' Purchase The percentage per annum which each number of years' purchase of a perpetuity yields to a purchaser is obtained by dividing 100 by the number of years' purchase. The results are given on p. 104. Interest, Amount, and Discount On p. 105 are shown the interest, amount, and discount of ;;fi in a year, and in 9, 6, and 3 months. The interest is calculated annually, and consequently in 9 months it is | of the interest earned in a year; in 6 months i, and in 3 months J of the annual interest. The * amount ' of £1 is simply the addition of the interest to the original £1, Were the interest to be calculated at other intervals than that of i year the figures here given would be different, as we shall see (p. 18) when we come to refer to the question in detail. Discount is the value at the beginning of a period of the interest to be received at the end— in other words, discount is the interest paid in advance. Thus the present value of £1 due at the end of a year, reckoning interest at 4 %, is ;£-96i54 (P- 7o)- l^^e value of £1 now due is, of course, £iy and the discount is the difference between these two amounts, which is ;^o3846 ; that is to say, if we owe an amount of £1 which is due to be paid one year hence, and, to suit the convenience of a creditor, we pay it twelve months in advance, we ought to be allowed a discount of ;£-o3846 ; that is to say, we should pay £961 S"^ ^^^w instead of paying £1 a year hence. This is obviously fair, since if we invested the;£-96i54 at 4 % for a year it would at the end of that time amount to the £1 we should have to pay. Sinking Fund On pp. 1 06-1 1 5 is given the annual amount to be set aside and invested in order to replace the capital at the end of the selected period. This table is obtained by dividing unity by the amount of one pound per annum, as given on pp. 50-85. Thus, comparing the amount of £1 per annum at 4 %, as given on p. 70, divided into unity with the Sinking Fund in the 4 % column on p. 112, we have for (16) SIl^Kl NG FUND Year I, I -f- „ 10, I „ 20, I » 3o» I I 00000 I2'Oo6lI 29*77808 56-08494 I "oooooo , •083291 ; •033582 ; •017830. This may be stated the other way about, and we may say that ^•083291 per annum accumulated for ten years at 4 % amounts to £it or 083291 X 1200611 = I. In this table no provision is made for paying interest on the capital. If this has to be done the amounts given in the sinking fund table must be increased each year by the interest on £1, Thus to repay^^-i in ten years, and to pay interest annually at 4 %, needs an annual payment of 083291 + 04 = -123291. Of this amount 04 pays the interest each year, and ^083291 accumulated at 4 % replaces the original £1 invested. If we take •123291 and accumulate it at 4 %, we find that in ten years It amounts to •123291 x 1200611 = 148024, which, from p. 70, we find IS the amount to which £1 amounts in ten years at 4 % if the mterest on it is allowed to accumulate instead of beinc drawn annually. ® In using this table care must be taken to notice whether the purpose for which it is required calls for interest on the original mvestment to be paid annually or not. See pp. 225 and 219 If the purchaser of a leasehold property wishes to set aside out of the net rent received sufficient to replace the purchase price by the time the lease expires, the table must be used as it stands, the difference between the net rent and the sinking fund constituting the mterest on the purchase price of the lease. If, on the other hand, a loan has to be repaid, say, in 10 years, with interest at 4%, either the interest on the loan must be paid annually, in addition to the sinking fund as given in the table, or •04 must be added to the sinking fund for every £1 borrowed, and allowed to accumulate with it. ^ , ^ If the interest is at i % there must be an addition of •©! to the 01 02 , if at 5 %, of -05 ; if at 10 %, of -I ; and so on. (17) I ) INTRODUCTION Value of Annuity to Yield Interest on Capital at One Rate, and Replace Capital at a Lower Rate On pp. 1 16- 1 2 if are given the annual payments required to pay interest at comparatively high rates, and to replace the capital by a sinking fund accumulating at a lower rate. From p. no we learn that ;£-o8723i per annum at 3% for 10 years will amount to £1. But if we have to pay 5 % per annum upon the £\ we must add ;^o5 to the sinking fund payment of ;^o8723i. These two amounts come to ^-137231, and would suffice, if paid annually for 10 years, to pay 5 % per annum on the original loan of £\, and to replace the ^i by accumulation at 3 %. The present value of- this annuity of ;£i3723i on these terms as to interest is therefore obviously pfi. But if the value of an annuity of £'i31^Z^ is £^* the value of an annuity of ^i is — ^- — =7287, which, on reference to p. 120, we ^ -137231 . , see to be the value of an annuity of £1 yieldmg mterest on capital at 5 %, and replacing capital when invested at 3 %. These terms are very onerous to the borrower, since he has to pay interest at a high rate on the whole capitil for the whole term, although by the accumulation of the sinking fund the capital may be rightly considered as partly repaid. These tables may be readily extended to other periods and rates of interest by taking the reciprocal of the amount obtained by adding to the sinking fund payment the annual interest on the loan. The reciprocal of a number is obtained by dividing unity by the number. The value of an annuity of any other amount than £1 per annum is obtained by multiplying the figures in the table by the amount oi the annuity. See also p. 226. Nominal and Effective Rates of Interest On p. 122 is given a table comparing nominal and effective rates of interest. This subject is a somewhat intricate one, but the main principles underlying it may be grasped without much diffi- culty. Hitherto we have been. considering that the rate of interest was calculated annually. We now have to deal with the case of interest calculated half-yearly, quarterly, and monthly. Suppose the nominal rate to be 4 % per annum ; it will obviously be 2 % for 6 months, and at the end of the first half-year an original investment of ^i will amount to ;^io2. For the second half-year interest at the rate of 2% for every 6 months is now earned upon ;^ 10 2 instead of upon only ^1. This brings the amount of the original investment at the end of the second half-year to ;£io404 instead of (18) NOMINAL AND EFFECTIVE RATES OF INTEREST to only ;£"i 04, which is the amount it would have been if the inte- rest had been calculated annually instead of half-yearly. A reference to p. 58 will show that this is the amount that £1 amounts to in 2 years at 2 %. Hence we see that if we want to calculate interest at more frequent intervals than i year we can divide the nominal rate of interest by the number of periods (at which interest is to be calcu- lated) that are contained in a year, and take the interest for this number of years at the resulting rate of interest. In other words, we see that instead of talking about years we can talk about periods, and if we want to talk about interest that is nominally 4 % per annum, but really 2 % for 6 months, or if convertible quarterly i % for 3 months, we may turn to a 2 % table and look at the result after 2 periods and a i % table to find the result after 4 periods. Thus on p. 50 we see that £1 accumulated for 4 periods at i % amounts to ^1-0406, the interest being ;£"-o4o6, which is the effective annual rate when interest is convertible quarterly, shown on p. 122 as corresponding to a nominal annual rate of 4%. The same thing holds if interest is convertible monthly. The amount of £1 accumulated for 12 periods, whatever their length, at ^ % per period, would amount ^o ;£^i '061678, and -061678 is shown on p. 122 to be the effective annual rate when interest is convertible monthly, if the nominal rate is 6 % per annum. The lower part of the table is the converse of the upper. If the real or effective rate is 4 % per annum the nominal annual rate, when interest is convertible half-yearly, is ^£^039608, or •019804 per half-year. Thus £1 for 6 months at 019804 % per 6 months amounts to ;£i -019804. During a second period of 6 months this amount at the same rate of interest earns ^^020 196, which added to the ;^i -019804 makes up ;£'io4, which is equi- valent to the amount of ^i at an effective annual rate of 4 %. The higher the rate of interest and the more frequently the interest is convertible the greater is the difference between the effective and the nominal rates. See Preface to 26th Edition. Annuities Payable Half-yearly, Quarterly, and Monthly If we are entitled to receive an annuity of ^i per annum, payable yearly, but, instead of receiving it annually, receive it every 6 months, we obviously receive the amount of the half-yearly payment sooner than we are entitled to; and if that half-yearly payment were invested for 6 months, the 2 half-yearly payments, together with this 6 months' interest on one of them, would amount to more than the annual payment to which we are entitled supposing the half- yearly payments were exactly half the yearly payment. That is to say, if the annuity to which we are entitled annually ie divided into 2, or (19) b a INTRODUCTION DECIMALS OF ONE YEAR 4, or 12 equal parts, and paid half-yearly, quarterly, or monthly, its capital value is greater than if the annuity were paid annually. As a concrete instance of this we have, on p. 123, the value of an annuity of £1 per annum for 25 years at 4%. If the annuity is payable annually and the interest convertible annually, the present value 01 the annuity is ;^i5-622o8, which is the figure given for its value on p. 70, as also on p. 123. To find the value of an annuity of 10s. every 6 months for 25 years at 4% we multiply ;£i5-622o8 by 10099, the factor given in the upper table on p. 123. This gives us 1577677 as the value of an annuity of 10^. every 6 months for twenty-five years, reckoning interest at 4 % per annum. Similarly an annuity of £1 per annum payable quarterly— that is, $s. every three months— is worth 1 5 62208 x 1 -01488, or^^ 1 5'85449- The value of an annuity payable monthly is calculated on similar principles, the constant factor by which to multiply the value of the annuity payable yearly being 1-0182. If the interest is convertible half-yearly, and the annuity payable half-yearly, we can obtain the value of the annuity from the tables on pp. 50-85, by considering that we have an annuity of one-half per period for 50 periods at 2 % instead of an annuity of i for 25 periods at 4%. A reference to p. 58 shows us that the present value of £1 per annum for 50 periods is ;;^3i*4236i, the half of which is ;^i57ii8o, which is the value given in the middle table on p. 123 for an annuity payable half-yearly when the interest is con- vertible half-yearly. Similarly an annuity of 5J. every three months at 4 % per annum convertible quarterly, which is i % every three months, is \ of ;^63-o2888, which on p. 51 is seen to be the amount of £1 per annum for 100 periods at i %. Now ;^63-o2888-f-4= ^15-75722, which on p. 123 is seen to be the value of an annuity for 25 years at 4 % payable quarterly, with interest convertible quarterly. This subject is dealt with and the appropriate formulae given . in the * Theory of Compound Interest and Annuities ' by F^dor Thoman.* Present Value and Discount The bottom table on p. 123 gives to 9 places of decimals the present value of £1 due one year hence, which has already been given to fewer places of decimals on pp. 50-85, and explained on p. 10. The discount has been given for most rates of interest, but fewer places of decimals, on p. 105, and explained on p. 16. No farther explanation is therefore necessary here, but for some pur- * London : Crosby Lockwood and Son. poses it is convenient to have these items calculated with greater approach to accuracy, as is here done. Time in which an Amount Doubles at Interest On p. 124 is stated the number of years in which an amount is doubled at simple and compound interest. At simple interest all we have to do is to divide 100 by the rate of interest ; thus, ^100 at 4% yields £/^ per annum, and dividing 100 by 4 we obtain 25 years as the time it will take for the interest to amount to the same as the principal, or, in other words, double the principal. At compound interest we obtain the number of years in which the interest will amount to the capital approximately by dividing -69 by the rate of interest, and still more nearly by dividing -693 by the rate of interest and adding '35 to the result. Thus — ^^ -f -35 = 13-86-^35=14-2 J. Decimals of One Year On p. 124 are given the decimals of i year, representing various numbers of weeks, months, and days. From what has been said on p. 7 it will readily be apparent how these figures are arrived at. There being 52 weeks in a year, 13 weeks, for example, is obviously ^ of a year. To convert the fraction ^ into a decimal we divide 52 52 13 by 52 and find that it goes -25 times. We assume the year to contain exactly 52 weeks, exactly 12 months, and exactly 365 days, the con- sequence being that though the figures given are right for practical purposes they are not entirely accurate. There are more than 52 weeks and more than 365 days in a year, while no calendar month is exactly -- of a year. 12 If we meet with the decimal of a year different from any given in the table, and desire to know how many weeks, or months, or days it corresponds to, we must multiply by 12 to get the answer in months, multiply by 52 to get the answer m weeks, and multiply by 365 to get the answer in days. Decimals of £1 On pp. 125-128 is given the decimal corresponding to every farthing in the £1. The first and last columns on each page give (21) !:;; INTRODUCTION the pence and farthings up to ii|^., while at the top of each of the other columns the shillings are stated to which the figures in the columns refer. Thus if we wish to know the decimal corresponding to 4^. 3^. we look in the column marked 4^. on the line marked 3^., and find that the required decimal is £ -21250. Again, if we want the decimal corresponding to 13J. l\d. we look on p. 127, column 13J., line 7}^., and find the required decimal to be ;£-68o2i. To obtain these results we must first convert the farthings into the decimal of a penny, then the pence and decimals of a penny into the decimal of a shilling, finally the shillings and decimals of a 'shilling into the decimal of a pound. Thus in the example we have just taken of 135. ']\d. One farthing = 4 = -25 of a penny, 7-25 pence = ^— ^ = '6042 of a shilling, 136042 shillings = ^^^^^^=-6802 1 of a pound, which is the result given in the table. To find the number of shillings, pence, and farthings corre- sponding to a given decimal we have only to look for the decimal nearest to the one we are dealing with, which is easily found in the table, as the decimals come in regular order throughout. To calculate the shillings, pence, and farthings corresponding to a given decimal we have only to carry out the converse of the process just described, multiplying first by 20 to get the shillings and decimals of a shilling, then multiplying the decimal part of a shilling by 1 2 to get the pence, and muhiplying the decimal part of the penny by 4 to get the farthings. Thus : •68021 of a ;^ X20 •6042 of a shilling X 12 •25 of a penny x 4 13*6042 shiUings 7*25 pence I farthing It will be convenient to remember that \s, is -05 of a £, 2s. is •I of a^, and every even number of shillings is expressed by half the number with a decimal dot to the left of it. Thus 45. = ;£-2, 1 2s, = £'(i, and so on. In the same way an odd number of shillings is always represented by a decimal ending in 5, and is half its own amount. Thus 5^. = £'2^ of a ;£ ; 95. = ;£-45» and so on. The figures in the column headed o shillings on p. 125 may be conveniently studied, for it will be seen that the last four of them are repeated exactly in all the columns headed with an even number of shillings, while in the columns headed with an odd number of MORTALITY TABLES shillings the last three 'of them are repeated exactly, and the figure in the second decimal place is in every instance increased by 5. Familiarity with the figures in this first column, especially those relating to an exact number of pence, when combined with the rule just referred to relating to shillings, will enable any one with a little practice to know the number of shillings and pence represented by a given decimal as readily as if the shillings and pence were actually written down, and conversely the decimal corresponding to any number of shillings and pence will be at once known without any calculation being consciously made. MORTALITY TABLES On pp. 130-136 certain statistics are given concerning the duration of human life. On pp. 1 30-1 31 the expectation or average duration of life is stated according to various mortality tables. The first table mentioned is the Northampton, prepared by Dr. Price in 1 780. This table for many years after its publication was much used, and many calculations based upon it are retained in the present volume. It contains, however, a great many serious defects, and its use for transactions on a large scale as a guide to the duration of Life has long since been abandoned. The Carlisle Table, published in 18 15, was greatly superior to the Northampton, and may still be used with advantage in many transactions in which the duration of life is concerned. The Experiences of the Equitable Society and of Seventeen Offices, published in 1834 and 1843 respectively, deal with assured lives, but are of less importance in connection with the valuation of life interests of all kinds than either the Carlisle or the Actuaries' Healthy Males Table. The English Experience (No. 3) is a very valuable table, dealing with the mortality recorded by the Registrar- General, and is the most reliable for questions of mortality among the general population. The Actuaries' Healthy Males Table, published in 1869, is the most reliable record of assured lives, and is the result of the experience accumulated by a large number of life offices. It is the best record of mortality among this class of people — that is to say, among people who have been subjected to a medical examination before going under observation, but who have since lived the ordinary lives of middle-class English people. Another table of considerable importance in connection with annuity transactions is the Government Annuitants, in regard to which some information will be given later on. The fundamental facts to be learnt from a life table are the (23) II A' "- •>^pJfai INTRODUCTION number living at the beginning of each year tnd the number dying during the year. When this information is available it is easy to calculate the probable number out of every loo alive at the beginning of the year who will survive the year and who will die during the year ; the percentage surviving and dying in each year together adds up to ICG, as may be seen in columns 4 and 5 on pp. 134 and 135. The expectation of life given on pp. 130 and 131 shows the average duration of life among a large number of people, and is determined by dividing the total number of years that a given number of people will live by the given number of people under observation. Thus, if ,we examine the table on p. 135, from age 90 we see that of 1,460 living at age 90 1,052 reach the age of 91 723 jj >* 92 469 >) i> 93 274 )s )) 94 135 )J >» 95 49 » M 96 9 n )} 97 2,711 Adding together the number who survive to the different ages, we find that the 1,460 people with which we commenced live between them 2,711 complete years ; and, dividing this number by 1,460, we get an average of i'857 complete years as the duration of life of each of the 1,460 people whom we commenced to observe at the age 90. This, however, considers only the en/ire years that are survived ; lives that live to 91 years and 11 months are treated as if they only lived to 91. It is, however, much more likely that the deaths will be fairly evenly distributed throughout the year, and they may, therefore, be reckoned as happening in the middle of each year. In these figures, therefore, we are reckoning that each one of the lives under observation would live six months less than would actually be the case, and if we add this half-year to the 1*857 years, we arrive at 2*357, which is the average expectation of life given in the Hm column on p. 131. We sometimes hear of the Curtate (or cut short) expectation of life, which means the number of complete years of life which people of the given age may, on the average, expect to live ; the Curtate expectation of life at age 90 is the 1*857 years, which we obtained above, and it is always half a year less than the complete expecta-^ tion of life given on p. 131. The expectation of life cannot properly be used in calculations (24) VALUES OF ANNUITIES with which interest is concerned, for the reasons to be given here- after (p. 26) ; nor can we learn from the expectation anything about the probable duration of life of any individual. It is, however, a re- markable fact that, while the time at which any individual will die is uncertain in the extreme, the average duration of life among large numbers of people is very uniform. The expectation of life should also be distinguished from the Vie Probable, or probable lifetime. This means the number of years that have to elapse before exactly half the number of people alive at a given age have died. Thus from the table on p. 135 we find that 51,373 people are alive at age 64. By age 75 we find that only half this number survives, the other half having died in the meantime. The Vie Probable at age 64 is therefore the difference between 64 and 75, viz. 11 years. Mortality of Single Lives and Interest The tables on pp. 138-154 are concerned with single lives and interest. They give the values of annuities and the single and annual payments to secure J[^\ at death, together with the values of reversions. Values of Annuities The tables that are in many ways the most important are those which give the values of annuities to be received annually through- out the lifetime of the person of the age stated. In every case, unless specially mentioned as being otherwise, an annuity means an annual payment of ;^i, or of course ^i, or any other unit, the value being given in pounds if the annuity is;^i, in dollars if the annuity is ;Jii, and so on. Annuity values derive their importance not merely from the immediate use that may be made of the table, but also from the facility with which other benefits dependent upon the duration of life may be derived from them. It is therefore worth while to explain in some detail how the annuity values may be determined. If we know that i year hence we have to pay J[^\, reckoning interest at 3 %, we can tell from p. 66 that we must have ;£"*97o874 in hand now in order to possess ^i in a year's time, while, according to the Carlisle Table on p. 136, we see thav out of 30 people alive at age 95 seven will die during the year, and that consequently there will be 23 people alive i year hence to receive £^\ each, assuming we have contracted with the 30 people to pay each of them ;^i per annum as long as they are alive. In order to make this first payment to our annuitants we must therefore have 23 times ;^*97o874, viz. ;;^2 2*33oio2, and so on in succeeding years, as set out in the following table : — (25) i w I 'S \ «!■ I INTRODUCTION C J Table Showing the Yalne of an Annuity of £1 per Annnm payable at the End of the Tear to each Survivor of 30 Perioni, Age 95 Year Number living at End of Year Present Value of / 1 due at End of Year Present Value of £i to each Survivor I 2 3 4 I 9 23 18 14 II 9 7 5 3 I £ •970874 •942596 •915142 •888487 •862608 •837484 •8 1 3091 •789491 •766417 £ 22^3301 1 6 9667 12-8120 97734 77635 5-8624 4-0655 23685 •7664 Total • •• ■ • • 82 7085 Total cost of 30 annuities, ;^82-7o85. Cost of I annuity, ;^82 -7085 -{- 30 = ;^2 -7 5695. From this we see that, assuming mortality to occur according to the Carlisle Table, we need to have ;£82-7o85 in hand now, and to be able to earn interest upon it at 3 % in order to pay an annuity to each of 30 people at present age 95. If this is the value of 30 annuities, the value of i annuity is ^2-75695, or, stated to the nearest third decimal, jQ^'TSl ^^ given in the 3 % column on p. 141. The advanced age of 95 was chosen as an illustration, in order to avoid the lengthy table required to illustrate the value for younger ages. It will be noticed that it is necessary to proceed year by year up to the end of the mortality table. It is not correct, as is some- times supposed, to take the average duration of life and then see the present value of ;£" i per annum for that number of years. Thus, acco^-ding to the Carlisle Table, the average duration of life at age 35 is 31 years. If we take the present value of ;£'i per annum for 31 years from the tables given on pp. 66-80, and compare them with the annuity values on p. 140, we have the following results :— Rate of Interest Value of Annuity according to Error in Excess Expectation Table, p. 140 Per Cent. 3 4 1 1 £ 20 000 17-588 15593 13-929 12-532 11*350 £ 18-433 16-041 14-127 12-573 1 1 -295 10235 £ 1-567 1-547 1-466 1-356 1-237 1-115 (26) PAYMENTS TO SECURE jCi AX DEATH If interest had not to be considered, the value of an annuity could correctly be obtained from the average duration of life, since if, say, 100 people at age 35 live 3,100 years between them we must obviously have ;£"3,ioo to pay them j£i per annum during life. But when the accumulation of interest comes in we can no longer base our calculations upon the expectation of life, even with the use of an interest table, without getting, as shown above, erroneous results. In these tables no provision is made for any expenses con- nected with the granting of annuities, such as has to be provided in the case of life assurance companies who grant them. Although the word annuity is used throughout the tables, the tables of course apply to income derived from any source, whether ordinarily called an annuity or not. Thus, suppose we wish to ascertain the value of a life interest derived from trust funds, or from a lease dependent upon the duration of life, these tables of annuity values of course apply. Private individuals who use these tables for the purpose of dealing with annuities must remember that dealing with only a few lives is a very speculative transaction. A purchaser may buy a life interest to-day, and the life on whose duration the income depends may die to-morrow, and the bargain prove a bad one, or may live an abnor- mally long while, and the bargain prove a good one ; so that no tables can give any idea of the value of an annuity on only one life. They give correctly the average value of annuities on many lives, and where many lives are concerned are a reliable guide. This is a point that should always be borne in mind by people dealing in life interests of any kind on a small scale. On pp. 142 and 143 the values of annuities are given according to the Healthy Males Table published by the Institute of Actuaries. These are not the most suitable tables to use for determining the value of an income for life considered by itself, but they are the best tables for many other purposes, and the annuity values are very con- venient for calculating the values of other benefits. On pp. 144 and 145 annuity values are given according to the experience of Government annuitants. These tables are at present the most reliable guide to the average value of annuities. It is well known that annuitants live "long, and consequently tables that correctly record the mortality experience of annuitants are not usually appropriate for determining the value of assurance, and vice versa. Several very heavy losses have been made in times past by this now most obvious fact having been overlooked. Single and Annual Payments to secure £1 at Death On pp. 146- 15 1 the single and annual payments to secure £1 at death are tabulated. There is a very clo.se connection between these (27) fl ss ! INTRODUCTION items and the values of annuities. Advantage is taken of this connec- tion to derive the values of assurances from those of annuities by means of Premium Conversion Tables, such as are given on pp. 185 and 186, in describing which this connection is explained (p. 35). For the moment it will be sufficient to notice that the single payments to secure ;£^ i at death can be readily obtained from the annuity values, pp. 138-145, by means of conversion tables, and the annual payments to secure ^i at death can also be obtained from the same pages. For details see pp. 35-39. Value of Reversions If we wish to know the average value of the reversion to a sum of money on the death of a person of a given age we can at once obtain it by multiplying the single payment to secure ;£^i at death by the sum in question. If, however, we wish to know the value of a rever- sion to a perpetuity — that is to say, to a perpetual income such as may be derived from freehold property — it is convenient to proceed some- what differently. On p. 94 we have the present value of a perpetuity to' be entered upon at once, but if it is not to be entered upon until the death of a person of a given age it is obviously worth less than if we were to obtain possession at once. The difference between the present value of immediate and of deferred possession is the pre- sent value of the benefit the existing holder will receive from it ; in other words, the difference between the value of immediate and of deferred possession is the value of an annuity on the life of the present holder. Thus at 4 % the value of a perpetuity with immediate possession is ;;^25. The value of an annuity at age 50 according to the Carlisle Table is ;^ 12 '869, so that the value of a perpetuity to be entered upon at the death of a person of age 50, according to the Carlisle Table at 4 %, is 25*000 — 12*869= 1 2*1 31, which is the amount given on p. 154. Hence it appears that to obtain the present value of the reversion to a perpetuity at the death of a person of a given age we must deduct the value of an annuity during the life of that person from the value of a perpetuity to be entered upon im- mediately, as given on p. 94. The present value of reversions of this kind are given at con- siderable detail on pp. 152 and 153, according to the Government Experience Table, because this is on the whole the most reliable table for the purpose. The values according to other tables and for other ages may readily be obtained by the simple rule just stated. MORTALITY OF TWO LIVES AND INTEREST Two Lives and Interest The tables on pp. 156-181 deal with various benefits that are dependent upon the duration of one or both of two lives. In such cases it is necessary to distinguish carefully in what way the lives enter into the question. We sometimes have to deal with joint lives, in which case an annuity is payable so long as do/A lives continue and ceases at the end of either of them, or in the case of joint life assurance the sum is paid on the occurrence of the/rj/ death. Then we have benefits such as annuities or assurances dependent on the duration of the longer of the two lives ; that is to say, an annuity payable to the last survivor continues so long as either of the two people concerned is alive, or in the case of assurance the suni assured is paid at the death of the second of the two. Yet again we have Contingent Survivorship benefits, such as the assur- ance of a sum of money to be paid at the death of X, if Y is living when X dies, nothing being paid in the event of Y dying before X. Joint Life Benefits We will deal first with the values of annuities payable during the joint life of two persons— payable, that is to say, so long as both persons are alive, and ceasing when either of them dies. We have already explained on p. 26 how the value of an annuity can be calculated if we know the probable number out of every 100 alive at the beginning of a year who will survive to the end of the year, and we must now explain how to ascertain this probability in regard to pairs of lives as distinguished from individual lives, with which we were formerly dealing. We may use in illustration the Healthy Males Mortality Table given on pp. 134 and 135, taking one life at age 30 and the other at age 60. The probability that a life aged 30 will survive one year is seen to be 99-2277 out of every 100, and that of a life aged 60 is 97*0322 out of 100. If we multiply these two probabilities together, we obtain the probability of both persons surviving the year, which works out at 96*283 out of 100. We can deal with successive years in the same way, and so make a fresh Mortality Table for pairs of lives instead of for individuals. Such a table for ten year^ is given below for two lives aged respectively 30 and 60 at the time they came under observation ;— (28) (aol r "^^ INTRODUCTION Table Showing probable Duration of Pairs of Lives. Hm Table Younger Life Elder Life Age Probable Number out of every loo who survive the Year Age (l) (2) 30 99-2277 31 992083 32 99 1 895 33 991715 34 991496 35 99-1226 36 99*0891 37 990536 38 99 0220 39 98-9918 40 61 62 63 64 65 66 68 69 70 Probable Number out of every 100 who survive the Year (4) 97 -0322 96-7962 96-5364 96-2510 959590 95-6569 953431 95 -01 1 1 94-6766 94-2660 Pairs of Lives Probable Number out of every 100 who survive the Year (5) 96-283 96 030 95754 95 454 95 143 94 -'8 1 8 94 '475 94-112 93751 93316 Number of Pairs living at Beginning of each Year (6) 10,000 9,628 9,246 8,853 8,451 8,040 7.624 7.203 6,778 6,355 5»93o The probable number of individuals who will survive out of every hundred at each age is given in column 4 on pp. 134 and 135, and by multiplying together the fractions obtained by putting these numbers as numerators and 100 as denominators we obtain the probability that a pair of lives of these ages will survive one year. The first column gives the age of the younger life and the third column the age of the elder life, and the details given in columns 5 and 6 refer to pairs of lives of the ages given in columns i and 3. Columns 2 and 4 are copied from the mortality table on pp. 134 and 135. In column 5 we have the probable number out of every 100 pairs of lives who survive the year. This is obtained for ages 30 and 60 by multiplying 99-2277 ^97:0322^ ^^^^^ equals 91^^-3 ^s 100 100 ^ lOOOO the probability for each pair, or 96283 pairs per 100. The details for other years are obtained in the same way. The last column gives the number living at the beginning of each year out of every 10,000 pairs alive at the commencement. This corresponds to column 2 of the mortality table on pp. 134 and 135. By multiply- ing the number living at one pair of ages by the probability of sur- viving one year we obtain the numbef living at the commencement of the next age. Thus : — * 10000x9^3=9628. 100 9628 X 95:^3^9246. and so on throughout. 100 (30) Uv ■V JOINT LIFE AND SURVIVORSHIP BENEFITS . If the above table were continued till one or other member of all the pairs of lives had ceased to exist, we could determine the value of joint life annuities in the same way as we calculated the values of annuities on single lives on p. 26. Joint life annuity values are given on pp. 156-165 according to the Northampton, Carlisle, Government Experience (1883), and Institute of Actuaries, Healthy Males Tables. For the most part they are given at every five years of age for both lives. To give them for every year of age would take up a great deal of room. They may, however, be found for every year of age, according to the Government Experience, in 7oint Life Annuity Tables,' published by the Institute of Actuaries; according to the Healthy Males Table in the * Institute of Actuaries Life Tables;' and according to the Carlisle Table in 'Jones on Annuities.' The single payment to secure £1 at the cessation of the joint life— that is to say, at the death of either of two lives— is given according to the Northampton, Carlisle, and Healthy Males Tables on pp. 166-169. The figures in these tables may readily be found by means of conversion tables from the tables of joint life annuities, as already mentioned and as hereafter explained. By the use of these tables the annual payments during the joint continuance of two lives to secure £1 at the first death can also be obtained by inspection by the use of conversion tables. They are given according to the Institute of Actuaries Table on p. 170. Survivorship Benefits On pp. 1 71-173 are given the values of annuities during the continuance of either of two lives. These differ from the joint life tables just considered, inasmuch as joint life annuities are payable only so long as l^o^/i persons exist, and the last survivor annuities are payable so long as eif/ier of the two persons lives. If we have tables of joint life annuities and of single life annuities we can readily find the values of annuities payable during the continuance of either of two lives. If we undertake to pay £1 per annum to each of two lives we can tell the value of that undertaking from the single annuity values given on pp. 138-145. Suppose the lives to be 30 and 60, then the value of the annuity on the life aged 30 by the Carlisle Table at 3 % is ^19-556, and on the life aged 60 pf 10-491, the value of the two together being ;£"3oo47. To pay these annuities would mvolve paying £2 per annum so long as both persons were alive, and £1 per annum to the survivor of the two. But the annuities we are now considering, those given on p. 172, only require ^^^i per annum to be paid during the joint continuance of the two lives, and (31) f i INTRODUCTION j^\ per annum to the survivor of the two. The difference between these two arrangements is, therefore, £^\ per annum during their joint lives, and from the joint life annuity tables on p. 157 we know the value of this to be ^9*529. Hence we get the rule that to find the value of an annuity on the survivor of two lives we must take the value of an annuity on each of the single lives, and deduct from the sum of these two the value of an annuity on the two joint lives. Thus according to the Carlisle Table at 3 % the value of an annuity On a life age 50 is (p. 140) . . . . On a life age 70 is (p. 141) . . . . On the two single lives is . . . . On the joint lives is (p. 157) . During the continuance of either of the two 1 lives is (p. 172) / 14*303 7123 21*426 6-338 15-088 In this way survivorship annuities for other ages and by other tables than those given on pp. 171-173 may readily be arrived at. The single payment to secure £^\ at the death of the last of two lives is given on pp. 174-176. These amounts, like so many others, may be at once obtained by means of premium conversion tables. The same remark applies to the annual payments to secure the same benefit, which are given on p. 177, it being noted that the annual payments have to be continued during the continuance of either of the two lives. Reversions to Perpetuities On p. 178 the values of the Reversion to a Perpetuity on the death of the first and on the death of the last of two lives are given. It has already been explained (p. 28) how the value of a reversion to a perpetuity on the death of a single life may be obtained. Where two lives are concerned the process is exactly the same. Thus at 4 % the value of a perpetuity to be entered upon imme- diately is (p. 94) £^2^ ; the value of an annuity during the joint continuance of two lives, each aged 60, according to the Healthy Males Table at 4 %, is j£6Tjg. Deducting this amount from the previous one we have (25ooo-6-779=r) ;^i8-22i, which is the amount given in the upper table on p. 178. Similarly the value of an annuity during the continuance of either of two lives, each age 60, is, according to the Healthy Males Table at 4% (p. 173), ;^i2i39. Deducting this from the value of a perpetuity to be entered upon immediately, we have (25000 — 12*139=) 1 2 -86 1, which is the amount given in the lower table on p. 178. (32) REVERSIONARY ANNUITIES Reversionary Annuities be age 45 and his son to be age M lis^ll\T""t ''"" '° value of the annuity to be ent:f:d up ' by V In o" t ^7^"' death and to continue during the time that thl 1 . "'^'' ' amount given on n r^n oc ^u \ ; *S;^7 487, which is the or^ agel^afte" L'll^ ot Tged 4° ^" ^""""^ '"'-' ""^ "^^ is n2TitrJ!:r,et"£et^h?^^^^^ ""="'^"°" ^^^^ ^^ -^^ - the results ^ ^^ '^'"^' '^°'^ "^" « ^^^ samples of never come into the annu^ at Si 1„ ,t "'^"'' "°"''' - have the certainty that^^willt a. vVauhTrthT^'ThT' suppose we wish to ascertain the v:,ln. J ^^"^' living, we may ta.ethe age"? tt^t^ ^"SsSltt T. nominated at the death^fata"U:rAci:'H'^^ "'k '^ '° "^ Table at 3 o/„ the presenHa u^ of y. o hf ^'°*!.^"'"'^ death of a man aeed ^c U /,. t^ /-"^ ^ received at the annuity on a Hfe ajj^^i ^^^.^f > £g«5, and the value of an value of an annuit^ the' first paymfrf wWch L 'to br"", " "' year after purchase h„f if ic u . ^ ^^ "^ ^^^^ one of an annuity during the life of v a-r^rf ^^"6 Carlisle Table at 3% the death of^r aeed .c v .f ^t ^' "^^ " '° be nominated at annuity imme^diafe J at Ahl Z^'o^"S7'°''' '° ^^^ °" '"^ tion to illustrate the point hifnt tSiedthTfextT' ^'T"'^" "ves^a^drel^nXlnroTXetit^r^^^^^^^^ ''^ "" W how to calculate the values o'f aSil's rsucceLiru:::' " (33) ''1 I INTRODUCTION Contingent Assurances On pp. 180 and 181 we have the single payments to secure;^! at the death of x provided he dies before >'. This is a somewhat more comphcated matter to calculate than any that we have dealt with pre- viously. To obtain it we must take the single premium for joint life assurance on the two Hves,and add to it the value of an annuity on two joint lives, one a year younger than x, the other of the age oiy, divided by the probability of a life one year younger than x living one year. Then take the value of an annuity on two joint lives, one the age of x, the other one year younger than j, divided by the chance of a life one year younger than y living one year, subtract this result from the former result, and divide by 2. This process may be more clearly apprehended by the following formula and example : — Ai,= '/A„+^?^'-''' =:(A. Px-x P% v;hcre A;^ = the single premium for an assurance on the life f x provided y be then alive. A^ = the single premium for an assurance payable at the first death of ^ or ^. a^.y = the value of a joint hfe annuity on x and j'. p^ = the probability of a life age x dying within a year. As an example let ^=^30 and \>'=5o, and let us employ the Healthy Males Table with interest at 3 %. Then : A^ = A30 50 = (see p. 1 68) -6077 = ^3950 and r7^.^,, are not given in this book. ANNUITIES ON THREE LIVES Annuities on Three Lives On pp. 182 and 183 the values of annuities for the joint con- tmuance of three lives are given. Full tables for annuities on three ives would be very extensive, and it is therefore generally necessary to obtam them from the values of annuities on two joint lives bv some such method as the following :— Take the present value of the annuity on the joint lives of the two oldest and find at what age the present value of an annuity on a single life will be equal thereto; the value of an annuity on the joint lives of the youngest of the three lives and the life of the age just found will be approximately the value of the annuity on the three lives In general we shall be nearer the truth if we subtract ^05 from the value just found. The two-life tables given in this book are not sufficiently full to enable the calculation of three-life annuities to be made in very many cases. On p. 184 is given the value of an annuity during the longest of three lives. The values are obtained by adding together the values of the annuities on each single life, and subtracting from the sum the value of the annuity on each pair of joint lives, then adding the value of the annuity on the three joint lives. In this table, as in the previous one, complete tables of annuities on two joint lives are necessary to enable these values to be calculated. Premium Conversion Tables Pages 185 and 186 contain short Premium Conversion Tables by means of which the single and annual premiums to secure /"i at death may be found by inspection. On p. ,42 we see that according to the Institute of Actuaries Table at 3 % the value of an annuity on a life aged 40 is ^17 176, and on p. 148 we find the single payment to secure ^i at cleath is ^-4706. This latter value may readily be found from the Single Premium Conversion Table on p. ,8.; Re- fernng to the 3 % column, we find that the single premium' corre- sponding to an annuity value of ^17 iS;^-47573. The difference in the single premium corresponding to the decimal part of the annuity value IS found from the lower table on p. 185, and must be subtracted trom the premium corresponding to the annuity value oi £11 The difference corresponding to •I •07 •006 •0002 ' (34) •00291 •6204 •017 •I •00513 !i 1-' (35) c 2 INTRODUCTION f We thus have the single premium corresponding to an annuity of ;£" 1 7 .... ='47573 Subtract difference . . . .' ='00513 Single premium for annuity of £^i 7*1 762 = -47060 which is the amount given on p. 148. The differences, as can be seen from the above example, vary with the position of the figures in them in relation to the decimal point. Thus at 3 % :— The difference for 'i is -00291 for "oi it is -000291 for 'ooi it is -0000291 and so on. The explanation of this connection is very simple. The annuity value designated a gives the present value of ;^i per annum on the supposition that the first payment of the annuity has to be made one year hence, and that the last payment is to be made on the anniversary of the first which immediately precedes the death of the annuitant. If, however, one further annual payment is to be made after the death of the annuitant, and we know the value of an annuity on these conditions, the difference between the value of an annuity with the last payment before the death of the annuitant and that of an annuity * providing for one payment after death will give the value oi £^\ to be received at^ death. The value of an annuity providing for this one extra payment is obtained by taking the present value of i +« due one year hence, which may be ex- pressed by the formula z; (i -f fl), where z/is the value of ^i due one year hence. Clearly, after the first payment has been made on such an annuity as this, there still remains the same number of payments to make as under an ordinary annuity. Therefore, if we know the present value of the first payment of ^i which has to be made one year hence, and the present value of an ordinary annuity one year hence, we have the value of an annuity providing for one pay- ment after the death of the annuitant. Using the same example as before, we have :— » a = 17-1762 (see p. 142) \-\- a = 18-1762 V = '97087 (see p. 123) z> (i +«) = 18-1762 X -97087 = 17-6468 Deducts 17-1762 V (i +a) — a = _*47^ N (36) PREMIUM CONVERSION TABLES This amount ;^-47o6 is the single premium to secure /"i at death given on p. 148. This table may be used to find the single premium for assurance on smgle lives, joint lives, the last survivor or survivors of any number of lives, and on successive lives ; but not for contingent assurances The s.ingle premium for the assurance of £1 at death may very easily be found from the annuity value by a quite simple calculation even when no Conversion Table is available. We have just seen that v{i-j-a)-a = A,or the single premium. Now v, which is the present value of ^i due i year hence, is equal to i -^, where d is t^e discount on i for i year. Hence we find that v (i-^a)-a -(I -d) (!+«)- «, which is the same as i - ^ (i + a). The value ot a is given on p. 123 for various rates of interest. Therefore the single premium is at once found by adding i to the value of the annuity, multiplying it by the rate of discount ^, and subtracting the result from unity. Thus, to refer again to the example given above 1+^=18-1762, ^ = -02913 (p. 123). Therefore i-d(i^a) -I -•02913x18-1762 = I --5294= .4706, which is the value of the single premium previously found. Page 186 gives a table for finding the annual premium payable - throughout life for the assurance of ^i at death. The present value of all these annual payments is, of course, the same as the single premium to secure the same benefit, assuming the same Mortality Table and the same rate of interest to be employed in the calcula- tions. Inasmuch as the annual premiums to be paid for assurance commence when the assurance is effected, so that the first premium has to be paid immediately, the number of annual premiums that have to be paid is one more than the number of annuity payments on the same life, since the first ordinary annuity payment is made one year after the annuity is taken, and the last is made prior to the death of the annuitant. Hence the single premium is the present value of an annuity the amount of which is the annual premium to secure /^i at death plus the extra premium that has to be paid when the assur- ance is effected. Thus the annuity value plus i multiplied by the annual premium equals the single premium. That is to say, P(i + ^7) - A, where P is the annual premium, A the single premium, and a the annuity value. We may put this another way and say that the single premium divided by the annuity value plus i equals the annual premium or P = ^ . I +« We have just seen, however, that the single premium A can be expressed in terms of an annuity-value forA= i^d(i -{-a)- hence I + a I ^ a ' (37) 'HI I t 'I I INTRODUCTION If, therefore, we wish to know the annual premium for the assur- ance of ;£"i at death on a life aged 40 according to the Actuaries Table at 3 % we have I + a= 181 76 (p. 142), -J — —^-^—~ = -05502, I +a 18176 ^^ — d= '05502 — '02913 = '02589, which is the annual pay- I 4- « ment during life to secure ;^i at death given on p. 150. If we make use of the Annual Premium Conversion Table on p. 186, we can only approximate to this result. The Conversion Table is only a short one and deals with the annuity value to the first decimal place. Looking on Hne * 17 — i7'9,' column 'i, we find that the annual premium corresponding to an annuity value of i7'i is '026 1, which is a larger amount than the true value. If we look on the same line in column '2 we find the annual premium corre- sponding to an annuity value of 17*2 is '0258, which is less than the true value. The annuity value being 17-176 is approximately ^ of the way between these two amounts, so that if we take f of their difference, which is '0003 x | equals -0002, and subtract it from •0261, we have -0259, which corresponds very nearly with the annual premium given on p. 150. In the Annual Premium Conversion Table we have no differences to deal with of the same kind as we have in the Single Premium Conversion Table. What we are concerned with in the Annual Premium Conversion Table is the variation in the rate of discount. If we want to know the annual premium to assure j£i at death on a life aged 40, according to the Hm Table, with interest at 4 % instead of at 3 %, as previously, we must take the 4 % annuity value from p. 142, where it is given as 15 135, find from p. 186 the annual premium corresponding to this annuity value, which is -0329, and subtract from it -0093 (difference p. 186), so obtaining -0236 as the annual premium at 4 %, which corresponds fairly well with the amount given on p. 150. If a closer approximation to the truth is required it can be obtained, as mentioned above, by adding i to the annuity value, dividing unity by this amount, and subtracting the rate of discount given on p. 123. Thus, to repeat the last example, we have the annuity value 15-1347, which with i added amounts to 161347. Dividing unity by this amount, we have -06198, and subtracting the rate of discount '03846 we obtain -02352, which is the exact amount given on p. 150. Repeating the calculation in connection with the symbols we have P= i+« -d=: 16-1347 I — -03846= 06 1 98— 03846 =-0235 2. (38) POST OFFICE ANNUITIES AND ASSURANCES Annual premiums, like single premiums, may be obtained from annuity values in this way in connection with single lives, joint lives, the last survivor or survivors of any number of lives, and successive lives. The premiums for contmgent assurances cannot be obtained in this way. Post Office Annuities and Assurances Hitherto we have been considering the values of annuities and other benefits on what may be called a theoretical basis. That is to say, we have been supposing deaths to occur in exact accordance with certain mortality tables, and interest to be earned at various specified rates. We have now to consider the terms on which annuities and other benefits can be obtained from various Government Depart- ments. Page 189 gives the cost of immediate life annuities of £1 per annum when purchased through the Post Office. A distinction is made between the cost of annuities on male and female lives, and the annuities are payable by half-yeariy instalments on January 5 and July 5, or April 5 and October 10, according to the date of purchase, the first half-yeariy instalment becoming due on the second quarteriy day of payment next following the day of purchase. The table gives the cost of an annuity of ;^i, and an annuity of a larger amount costs a larger sum in exact proportion. For instance, an annuity of ^10 a year would cost ten times the amount given in the table. The cost of deferred life annuities under which the purchase money will be returned on application or on the death of the nominee if an instalment of the annuity shall not have become due, is given on p. 190. The annuities are payable half-yeariy, the first payment of the annuity being made six months after the number of years they are deferred has expired. Thus the first payment under an annuity deferred 10 years will become due and payable on the second quarteriy day of payment next following the expiration of ten years. The Table of Annual Payments shows the amount of each annual payment that has to be made for a number of years exceeding by one the number of years the annuity is deferred, Thus if the annuity is deferred ten years, 1 1 payments have to be made ; if it is deferred twenty years, 2 1 payments have to be made, and so on. On p. 191 a corresponding table is given, showing the cost of deferred life annuities under which the purchase price is not return- able in the event of the life on which the annuity is granted ceasing before the first payment of the annuity becomes due. (39) I ■>\\ « i^: i INTRODUCTION Pages 192- 194 give the premiums for life assurance effected through the Post Office. It will be noticed that the sum assured is sometimes payable at death and sometimes payable in various numbers of years after being effected or at death if previous. The annual premiums for life assurances given on p. 194 differ, in regard to assurances pay- able at a certain age, from the ordinary practice of life assurance companies. The great majority of life assurance offices, when they assure an amount payable at a specified age or at death if previous, only require as a maximum number of payments the difference between the age at entry and the age at maturity. Thus an endow- ment assurance effected by a man aged thirty, payable at age sixty or at death if previous, only calls for (60 — 30 =)3o annual payments in the eventof the assured surviving till the age of sixty, while Post Office assurance in such a case as this would require 31 annual premiums to be paid. Government annuities are also granted by the National Debt Office, and are made chargeable upon the Consolidated Fund of the United Kingdom. Further particulars in connection with these annuities are given at the bottom of the table on p. 195. i Annuities and Assurances Granted by Life Offices It is probable that any person wanting to purchase an annuity or to assure to the best advantage would go to a well-established life assurance company rather than to a Government department. He would obtain much better value for money by so doing, and the security offered by the best life offices is so ample and altogether beyond question that no advantage attaches to Government guarantee as compared with the guarantee of first-class life assurance companies. The rates given on p. 196 for annuities and assurances granted by British life offices are only the average rates. Many companies of the highest standing guarantee these benefits on terms much more favourable than the average. Details for each company may be obtained from various publica- tions, such as Whitaker's Almanack. They are also given, much more fully, in Bourne's ' Insurance Directory ' and Bourne's ' Assur- ance Manual.' r¥ INCOME TAX The Income Tax Tables on pp. 198-204 require little explana- tion. The amounts are arrived at by multiplying the income by the pence in the tax per pound, and dividing the result by 12 and 20 to obtain the answer in pounds. Thus the income tax on ;^i30 (40) ^v= LOGARITHMIC TABLES J", d £ s. a, at $d, = -^5 3 = 54 2 = 2 14 2 ; 12 -r > at6?op^ 53° This is between 2 % and 2J %, but nearer 2 J- %. or 3, ooo=log 3*477121 . 53o=log 2*724276 I in 80 years = log 0*752845 I „ I year =log o*752845-j-8o=log 0*00941 1 = 1*0219 The rate of interest therefore is 2-19 %. Present Value of a Sum to be Received in the Future (5) // is required to know the present value of jC^^S *<> ^» 350= '29799 X 350- ^1043 approximately <7) At the end of 20 years an institution will enter into possession of a property which, it is agreed, will then be worth (43) Sup, 86 238 246 216 70 262 291 235 240 292 230 70 72 ^ EXAMPLES ;£"5,ooo. Meantime it receives no income^ but must spend ^ ;^ioo upon the property at the end of 5 years ^ jQioo in 10 y ears ^ and £^\oo in 1$ years. Find the present value of the property^ reckonifig interest at ^ %. Present value of 5,000 in 20 years=*55368 x 5000=2768*4 100 „ 5 „ =86*261 it » >9 100 100 »» ») 10 15 »> 11 If = 74*409 = 64*186 expenditure =224*856 = 224*9 property according tp conditions =;^2q43-5 (8) Find the present value of jQiyOoo due at the end of 120 years at 2\ %, P.V. of 1,000 due in 100 years =84*65 » 84-65 „ 20 „ =8465 X -61027=^ 51^59 or iooo=log 3*0 P.V. of I in I2oyrs.=log o* — log 1*286864 (year 12 log r" x 10) =log 2*713136 Present value of 1,000 in 120 years =log i*7i3i36=;^5i-66 Amount of j£i per Annum (9) Find the amount of jC^2tP^^ annum in 2^ years at 3^ %. Amount of ^^ i per annum in 27 years = jQ 4375906 » ^93 = 4375906 X 93 = ^4069*59258 or 93 = log 1-968483 Amount of i in 27 years = log 0-4033894 „ I p. a. „ = log 1*237^785 „ 93 p. a. in 27 years = log 3 "6095 51 = ^4069-59 (10) Find the amount of^-jT^Sper annum in ^4 years at 2| %. £7S5 P- a. in 34 years at 2J ?^=log 4*6i7542i = ^4'45i-68 or £1 per annum at 3 % = 57*73018 £1 per annum at 2f% = 55*10023 Difference = 2*62995 (44) Seep. 66 66 66 66 63 62 279 247 68 262 287 224 287 243 225 66 64 EXAMPLES £1 p.a. at 2|+^ ciifr.=55-ioo23 + r3i497=S6*4iS2o ^735 at 2j % =56*4152 X 735 = ^^41465 roughly. The error here is considerable. Taking half the difference between 2 J and 3 % to obtain 2 J % is only a means of roughly approximating to the correct amount. Present Value of Annuity (11) Find the present value of £4 7*25 per annum for 30 years <^t 5 .%• P.V. of ;^i per annum = 15*37245 »> ;£47'25 per annum= 15*37245 X47*25=^72£34i or ^— ^ Log 11867434-log 1*674402 -log 2*861145=^ 726*35 (12) Find the value of a lease yielding jQi^tl P^^ annum for 27 years to make 3 % and to get back the principal by the end of the term. £1 p.a. for 27 years=^i8*32703 or 18*32703 yrs. purchase v^i37 », 11 = 18*32703x137= ^2510*8 or i37=log 2*136721 £1 p.a, for 27 years=log 1*263092 ^137 i> ,» =^ log 3*399813=^2510:8 (13) Find the present value of £1 per annum for i^ years at 37 %. Present value=log 1*40235 5 5 =^25^25^ (14) Jf leasehold property yielding a net annual income of £\oo a year for ^o years is bought for £2^000^ find the yield per cent. If ^100 per annum costs ^2,000,^1 per annum costs ^20. This is seen to be between 2 j and 3 % or £\ p.a. costs ;^2o=log 1*30103 log o — log 1*30 1 03= log 2 69897 2J %=log o— log 2*7oo69 = log li*2993i = 19*92 This is very close to 20, and therefore the required rate is a trifle less than 2\ %. ^ (45) Seep. 74 223 66 230 283 236 224 92 234 222 282 i ■I i! i I I? ^ ■ ' EXAMPLES Present Value of a Perpetuity (15) Jund the value of a perpetuity of JP^do a year ^ reckoning interest at 3I %. 29*62963 X 60= 17777778 (16) Find the value of a property yielding ^25 per annum for the next 15 years and £^\\o in perpetuity thereafter^ reckoning interest at ^%. Take the value of a perpetuity of j£iio per annum and deduct the value of (no — 25 ^)^85 per annum for 15 years. Perpetuity =33 x 1 10= 3666*666 P.V. of ;^85 p. a. for 15 years=ir93794 x85= 1014725 Value required = ;£^2 65 1 '94 1 or P.V. of;^25 p. a. for 15 years=ii'93794X 25= 298*448 P.V. of perpetuity ^no deferred 15 years = 21-39539x110= 2353*493 Value required =/^265r94i (17) Find the value of the reversion to a perpetuity of jQ^()6 per annum after 22 years at 2^%. Value of perpetuity of ^i at 2| %= 3^*09524 P.V. of ;;^i p. a. for 22 years at 2j%=i6'7654i » ,» » 2I %= 16-34350 Difference = '42191 P.V. at 2 J % (=16-34350-1- -2 1095)= 16*55445 Approximate P.V. of perpetuity of ;^i p. a. at 2| % deferred 22 years= 21-54079 Approximate P.V. of perpetuity of ;£^496 p. a. at 2| % deferred 22 years = 2 1 54079 x 496 =^10684 >' or Value of perpetuity at 2i %=38-0952 P.V. of j£i p. a. for 22 years at 2^ % =log 1-2188635 = 16-5525 P.V. of perp. deferred 22 years=2i*5427 = log 1*333300 496=log 2*695482 P.V. of perp. of ^496 deferred 22 years at 2| % =log 4-028782= ^x0685 (46) Seep. 94 94 66 66 97 94 62 64 94 280 234 244 231 EXAMPLES Sinking Fund I (18) Find the sum to be set aside annually to amount to jCts^ in 30 years reckoning interest at 4 %. The sum to amount to ;^i= ^^'01783 »» .» ;^75o='oi783 X 75o= ;^i3-3725 P- a. or 750 = log 2*875061 Annuity 1 will buy = log 2-762154 »>. 750 „ = log 1-637215= 43*373 Deduct 4 % on 750 = -04 x 750 = 30000 Annual sum to amount to ;;^75o in 30 years = ^13*373 Annuity a Given Sum will Purchase (19) Find the annuity for 35 years that may be bought for ;^i»573) reckoning interest at 3^ %. 1573 =log 3*196729 Annuity i will buy = log 2*698956 ». 1573 or = log I -895685 = ^^78*6475 20*00066 will buy an annuity of ;jg"i p. a. 1573 will buy an annuity of l^JA = /■78*6474 20*00066 -^— ™— 1™ Annuities and Assurances on Lives (20) Find the value of an annuity of £2^0 on the life of a male aged 45, according to the Government Experience Table at 3%. Value of ^ I p. a. = £iy^S2 »» ;^250 „ = 15*152 X 250 = ^3788 (21) Find the value of £1,^00 to be received at the death of a male aged 50, according to the Healthy Males Table at 3i%. •52023 X i5oo = ; »g78o*345 (22) Find the annual payment to secure ^^1,500 at the death of a male aged 50, according to the Healthy Males Table at 3i%. •03667 X 1500 = ^55-005 ^ (23) Find the value of the reversion to a perpetuity of £\oq per annum at the death of a male aged 60, according to the Government Experience Table at 3 %, and accordinz^o the Healthy Males Table at ^%. (47) Seep, 112 256 291 243 232 287 256 68 144 T48 150 EXAMPLES ( ' i i By Government Experience 22732X 100 = ;^2273'2 By Healthy Males — Value of a perpetuity of 100 = • 3333*3 100 p. a. for life = 102 36 » n deferred perpetuity = ;^23097 (24) Find value of annuity of ;^i35 so long as two female lives ^ aged 25 and 45, both continue to live. Government Table 3 %. 14-650 X I35=; ^i97775 (25) Find value of annuity of £^2^0 so long as either of two male livesy aged 30 and 50, continue to live. Healthy Males Table 3i %. 197251 X 250 = ^4931-275 (26) Find the single payment to secure ;^i,25o {a) at the death of the first and {8) at the death of the last of two male lives^ aged 45 and 60. Healthy Males Table 4 %. {a) At death of first '64328 x 1250 = ;^8o4i {b) „ „ last 3814 X 1250 =^4767^ Single and Annual Premiums by Conversion Tables (27) Find the single payment to secure ;^i,ooo at death of a person aged 43. Northampton Table 3 %. Annuity on life aged 43 = 14" 162 Single payment for annuity of 14 =, '5631 1 » »» >» »l »> » ») )) >} •I =00291 •06 =001748 •002 = 000058 •00472 » )> „ I4I62 = -55839 Single payment to secure 1,000 = ;655^ 39 or 1000 [i — 029126 (14-162 + i)] = ;^558-39i6 (28) Find the annual payment to secure £1^000 at the death of a person aged 43. Carlisle Table 4 %. Annuity on life aged 43 = 14*505 Annual premium for annuity of 14*5 = 0354 — 0093 = -0261 )} » ;^i,ooo at death = ;^26-i. ^^ (j^.-— ^ --03846^ = 64-50 -38-46 = ^26-04 (48) 1000 Seep. 94 143 28 158 173 169 176 138 18s '8s i8s 185 36 37 140 186 37 • 1 i INTEREST TABLES AMOUNT AND PRESENT VALUE OP ONE POUND AND OP ONE POUND PER ANNUM VALUES OF PERPETUITIES AND REVERSIONS NOMINAL AND EFFECTIVE RATES OF INTEREST AND OTHER TABLES For explanation see pp. 8-23 4» B , 1°/. INTEREST TABLES ONE FOUND ONE POUND ] PEB ANNUM Years Y^u'fl Amount Present Value Amount Present Value X 6VUV I I'OIOOO •99010 i-ooooo 0-99010 I 2 I '02010 •98030 2'OIOOO 1-97040 I 2 3 I -03030 •97059 3-03010 2-94099 1 3 4 1*04060 •96098 4-06040 3-90197 4 5 1-05101 •95147 5-10101 4-85343 5 6 1-06152 •94205 6^1 5202 579548 6 7 I -07214 •93272 j 7-21354 6-72819 I 8 I -08286 •92348 1 8^28567 7-65168 9 1-09369 -91434 9-36853 8-56602 1 9 10 1-10462 1 •90529 10-46221 9^47 1 30 10 II I -1 1567 •89632 1 1 -56683 10-36763 II 12 I -12683 •88745 . 12-68250 11-25508 12 13 I -13809 •87866 ' 13-80933 "2-13374 13 14 I -14947 •86996 14-94742 13-00370 14 15 I -16097 •86135 16-09690 13-86505 15 i6 1-17258 •85282 17-25786 14-71787 16 17 1-18430 •84438 18-43044 15-56225 n i8 1-19615 •83602 19-61475 16-39827 18 19 I -2081 1 -82774 20-81089 17-22601 19 ao I -22019 •81954 22-01900 18-04555 20 31 I -23239 •81 143 2323919 18-85698 21 22 I •2447a •80340 24-47159 19-66038 22 23 I -25716 '79544 25-71630 20-45582 23 24 1-26973 •78757 26-97346 21-24339 24 25 I -28243 •77977 28-24320 22-02316 25 26 I 29526 •77205 2952563 22-79520 26 ^ I -30821 •76440 30-82089 2355961 27 28 I -32129 •75684 32-12910 24-31644 28 29 1-33450 74934 33-45039 25-06579 29 30 I 34785 •74192 34-78489 25-80771 30 31 1-36133 73458 36^13274 26-54229 31 32 I -37494 •72730 37-49407 27-26959 32 33 I -38869 ■72010 38-86901 2798969 33 34 I 40258 •71297 40-25770 28^70267 34 35 1-41660 •70591 . 41-66028 29^40858 35 36 1-43077 •69892 43-07688 30^10750 36 I -44508 69200 44-50765 307995J 37 38 1-45953 •68515 45-95272 31-48466 38 39 I -47412 •67837 47-41225 32-16303 39 40 I -48886 •67165 48-88637 32-83469 40 41 I -50375 •66500 50-37524 3349969 i 41 42 I -51879 •65842 51-87899 34-15811 42 43 153398 •65190 53-39778 34-81001 43 44 1-54932 •64545 54-93176 35-45545 44 45 1-56481 •63906 56-48107 3609451 45 46 I 58046 •63273 5804588 36-72724 46 47 I 59626 -62646 59-62634 3735370 i^ 48 I -61223 -62026 61-22261 37-97396 49 I -62835 •61412 62^83483 38 58808 49 50 I -64463 •60804 64-46318 39-19612 50 For explanation see pp. 8- 13 (50) ■MriM INTEREST TABLES 17« Tears ONE FOUND 51 52 53 54 55 56 57 58 59 60 61 62 65 66 69 70 71 72 73 74 75 76 79 80 81 82 P 84 85 86 8: u 89 90 91 92 93 94 95 96 97 98 99 100 Amount Present Value I -66108 I ^67769 I ^69447 I-71141 1-72852 1-74581 I -76327 1-78090 I -7987 1 I -81670 I -83486 I -85321 I -87 1 74 I •89046 1-90937 I -92846 I -94774 I '96722 I ^98689 2^00676 2^02683 2^04710 206757 2^08825 2^i09i3 2-13022 2-15152 2-17304 2-19477 221672 2-23888 2^26127 2 28388 2^30672 232979 2-35309 2 37662 2 40038 2-42439 2-44863 247312 2-49785 2-52283 2 54806 2-57354 2-59927 2-62527 2-65152 2 67803 2-70481 •60202 •59606 •59016 •58431 •57853 •57280 •56713 -56151 •55595 -55045 •54500 •53960 •53426 •52897 -52373 •51855 •51341 •50833 -50330 •49831 •49338 •48850 •48366 •47887 •47413 •46944 •46479 -46019 •45563 •451 12 •44665 . -44223 •43785 •43352 •42922 •42497 -42077 -41660 •41248 •40839 •40435 -40034 •39638 •39246 •38857 •38472 •38091 •37714 •37341 •36971 ONE POUND PER ANNUM Amount 66^1078 1 67^76889 69-44658 7i^i4io5 72 •85246. 74^58098 76-32679 78-09006 79-87096 81-66967 83-48637 85-32123 87-17444 89-04619 90-93665 92-84601 94-77447 96-72222 98-68944 100-67634 102-68310 104-70993 106-75703 108-82460 1 10-91285 113-02197 115-15219 117-30372 119-47675 121 -67152 123-88824 126-12712 12838839 1 30 '67227 1 32 '97900 135^30879 137-66187 140-03849 142-43888 144-86327 147-31190 149 "78502 152^28287 154-80570 157-35375 159-92729 162-52656 165-15183 167-80335 170-48138 See also Tables on pp. xx-xxxi Present Value 39-79814 40-39419 40-98435 41-56866 42-14719 42-71999 43^28712 43-84863 44-40459 44-95504 45 50004 46-03964 46-57390 47-10287 47-62661 48-14516 48-65857 49-16690 49-67020 50-16851 50-66190 51-15039 51-63405 52-11292 52-58705 53-05649 53-52127 53-98146 54-43709 54-88821 55-33486 5577709 56-21494 56-64845 57-07768 57-50265 57-92342 58-34002 58-75249 59*16088 5956523 59-96557 60-36195 60-75441 61-14298 61-52770 61-90862 62 28576 62^65917 63^02888 Years 51 52 53 54 55 56 57 58 60 61 I 62 65 66 67 68 69 70 71 72 73 74 75 76 79 80 81 83 5* 85 86 u 89 90 91 92 93 94 95 96 97 98 99 100 1 ■ I I ! (SI) B 3 lk% INTEREST TABLES ! ONE POUND ONE POUNB FEB ANNUM Years I Years Amount Present Value Amount Present Value I 01250 •98765 I'OOOOO 0-98765 I 2 I 02516 •97546 201250 I -963 1 2 2 3 I -03797 •96342 3-03766 2-92653 3 4 I "05095 -95152 4-07563 3-87806 4 5 I -06408 • -93978 5-12657 4-81783 5 6 I -07738 •92817 6-19065 5-74601 6 7 I 09085 •91672 7 -26804 6-66273 I 8 1*10449 -90540 8-35889 7-56812 9 I -1 1829 •89422 9-46337 8-46234 9 10 I-13227 •88318 10-58167 9-34553 10 II 1-14642 •87228 1 1 -71394 10-21780 II 12 1-16075 •861 5 1 12-86036 1 1 -0793 1 12 13 1-17526 •85087 14-02112 1 1 -93018 »3 M 1 1-18995 •84037 15-19638 12-77055 M 15 1 I -20483 •82999 16-38633 1360055 15 i6 j 1-21989 •81975 17-59116 14-42029 16 H 1-23514 •80963 i8^8iio5 15*22992 \l i8 I -25058 •79963 20^04619 1602955 19 1-26621 •78976 21^29677 16-81931 19 20 I -28204 •78001 22-56298 17-59932 20 21 1-29806 \ -77038 23-84502 18-36969 21 22 1-31429 •76087 25 •14308 19-13056 22 23 I -33072 •75147 26^45737 19-88204 23 34 1-34735 •74220 27^78808 20-62423 24 25 I -36419 •73303 29-13544 21-35727 25 26 I -38125 •72398 30-49963 22-08125 26 27 I -39851 -71505 31^88087 22 79630 27 28 1-41599 •70622 33-27938 23^50252 28 29 1-43369 •69750 34-69538 24*20002 29 30 1-45161 •68889 36-12907 24-88891 30 31 I -46976 •68038 37-58068 2556929 31 32 I -48813 -67198 39-05044 26-24127 32 33 1-50673 •66369 40-53857 26-90496 33 34 1-52557 -65549 42-04530 27-56046 34 35 I -54464 -64740 J 43-57087 28-20786 35 36 I -56394 -63941 45-11551 2884727 36 37 1-58349 -63152 ' 4667945 29-47878 38 1-60329 •62372 48-26294 30-10250 39 I -62333 •61602 4988623 30-71852 39 40 I -64362 •60841 1 51-48956 31 32693 40 41 I -66416 •60090 53-13318 31 92784 41 42 i I -68497 -59348 54-79734 32-52132 42 43 ; 1-70603 •58616 i 56-48231 33-10748 43 44 1-72735 •57892 1 58-18834 3368640 44 45 1-74895 •57177 59-91569 34-25817 45 46 1-77081 •56471 61 -66464 34-82288 46 47 I -79294 •55774 63-43545 35-38062 % 48 1-81535 •55086 1 65 22839 3593148 49 1-83805 •54406 1 6704374 36-47554 49 50 1-86102 •53734 ' 68-88179 37 01 288 50 For explanation see pp. 8- 13 (52) INTEREST TABLES ir/< Years ONE POUND 51 52 55 54 55 56 57 58 61 62 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 ^ 85 86 87 88 j 89 I 90 91 92 93 94 95 96 97 98 99 xoo Amount I I 88429 I -90784 1-93169 I 95583 I 98028 2-00503 2-03010 205547 208117 2-10718 2-13352 2-16019 2-18719 2-21453 2-24221 2 27024 2 29862 2-32735 2-35644 2-38590 241572 2-44592 2 47649 2-50745 2-53879 2-57053 2-60266 2-63519 266813 2-70149 273525 2-76944 2-80406 2-83911 2-87460 2-91053 2-94692 2-98375 3-02105 3-05881 3-09705 3-13576 .3-17496 3-21464 3-25483 3-29551 3-33671 3-37842 3-42065 3-46340 Present Value •53071 •52415 •51768 -51 129 -50498 -49874 -49259 -48651 '48050 -47457 •46871 •46292 •45721 •45156 -44599 -44048 -43504 -42967 -42437 -41913 •41395 •40884 •40380 -39881 •39389 •38903 •38422 •37948 •37479 -37017 -36560 •36108 •35663 •35222 •34787 •34358 •33934 -33515 •33101 •32692 •32289 -31890 -31496 •3 1 108 •30724 -30344 •29970 -29600 •29234 •28873 ONE POUND PEK ANNUM Present Value Amount See also Tables on pp. xx-xxxi 70^74281 72-62710 74-53494 76-46662 78-42246 80-40274 8240777 84-43787 86-49334 88-57451 90-68169 92-81521 94-97540 97-16259 99-37713 loi -61934 103-88958 106-18820 108-51555 110-87200 113-25790 1 15 67362 118-11954 120-59604 123-10349 125-64228 128-21281 130-81547 133-45066 136-11880 138-82028 141-55554 144-32498 147-12904 149-96815 152-84276 155-75329 158-70021 161 -68396 164-70501 167-76382 170-86087 173-99663 177-17159 180-38623 183-64106 186-93658 190-27328 193-65170 197-07234 Years 51 52 53 54 55 56 57 58 59 60 61 62 65 66 3754358 3S06773 38-58542 3909671 39-60169 40-10043 4059302 41 07952 41^56002 42-03459 42-50330 42 96622 43-42343 43-87499 44-32098 44-76146 45-19651 45-62618 46-05055 69 46-46968 70 46-88363 71 4729247 72 4769627 73 48 09508 74 48-48897 75 48-87800 76 49-26222 77 49-64170 78 50-01649 yn 50-38666 io 50-75225 81 51-11334 82 51-46996 83 51-82219 84 52-17006 8s 52-51364 86 52-85298 87 53-18813 88 53-51914 89 53-84606 90 54-16895 91 54-48785 92 54-80282 93 55-11389 94 55-42113 95 55-72457 96 56-02427 97 5632026 I 98 56-61261 99 56-90134 ; 100 (53) 11°/ ONE P( INTEREST TABLES )UND ONE POUND PER ANNUM Years Tears Amount Present Value Amount Present Value I 1-01500 -98522 I 00000 098522 I 2 I -03023 •97066 2^01500 I -95588 2 3 I -04568 • -95632 3-04523 2 •91220 3 4 I 06136 -94218 4 09090 3^85438 4 5 I -07728 •92826 5-15227 4-78265 5 6 I -09344 •91454 622955 5-69719 6 7 I -10984 •90103 7.32299 6-59821 I 8 1-12649 •88771 8^43284 7-48593 9 I 14339 •87459 9-55933 8-36052 9 10 I -16054 •86167 10-70272 9-22219 10 II I -17795 •84893 1 1 -86326 IOO7II2 II 12 I -19562 •83639 1304121 10-90751 12 13 I 21355 •82403 14-23683 II-73153 13 14 I -23176 •81 185 15-45038 12-54338 14 IS I -25023 •79985 16-68214 13-34323 15 i6 I -26899 -78803 17-93237 I4-I3126 16 \l I -28802 •77639 19-20136 14-90765 17 1-30734 -76491 20-48938 15-67256 18 19 I 32695 •75361 21-79672 16-42617 19 20 I 34686 -74247 23-12367 17-16864 ao 1 21 I -36706 •73150 2447052 17-90014 21 ! 22 1-38756 -72069 25-83758 18-62083 22 23 1-40838 -71004 27-22515 19-33086 23 24 I -42950 -69954 2863352 20-03041 24 25 1-45095 •68921 30 06302 20-71961 25 26 1-47271 -67902 31-51397 21-39863 26 27 I -49480 -66899 3298668 22-06762 U 28 1-51722 •65910 34-48148 22*72672 29 1-53998 -64936 35-99870 23-37608 29 30 1-56308 -63976 37-53868 24-01584 30 31 I 58653 -63031 39-10176 24-64615 31 32 1-61032 -62099 40-68829 25-26714 32 33 1-63448 -61 182 42-29862 25-87896 33 34 1-65900 •60277 43-93309 26-48173 34 35 1-68388 •59387 4559209 27-07560 35 36 1-70914 •58509 47-27597 27 66068 36 1-73478 •57644 48-98511 28-23713 38 1-76080 •56792 50-71989 28-80505 38 39 I -78721 •55953 52-48068 29-36458 39 40 I -81402 •55126 54-26789 29-91585 40 41 1-84123 •54312 5608191 30-45896 41 42 I -86885 •53509 57-92314 3099405 42 43 I -89688 •52718 59-79199 31-52123 43 44 1-92533 •51939 61-68887 32-04062 44 45 I -95421 •51171 63-61420 32^55234 45 46 1-98353 •50415 65-56841 33^05649 46 :? 2-01328 •49670 67-55194 33^55319 47 2-04348 •48936 69-56522 34-04255 48 49 2-07413 •48213 71-60870 34-52468 49 s> 2-10524 •47500 73-68283 34-99969 SO For explanation see pp. 8-13 (54) INTEREST TABLES Ymn 51 52 53 54 55 56 57 58 60 61 62 63 65 66 57 68 69 70 71 72 73 74 75 76 81 82 P 85 86 87 88 89 90 91 92 93 94 95 96 U 99 100 ir/o ONE POUND ONE POUND PEE ANRUK Amounfc 2 •13682 2^16887 2-20141 2-23443 2-26794 2 30196 2-33649 2-37154 2 -407 1 1 2-44322 247987 2-51707 2-55482 2-59314 2 -63204 2-67152 2-7II60 2-75227 2-79355 2^83546 2-87799 2-92116 2-96498 3-00945 3^05459 3'ioo4i 3 •14692 3-19412 3-24203 3-29066 3-34002 3-39012 3-44097 3-49259 3-54498 3-59815 3-65213 3-70691 3-76251 3-81895 387623 393438 3-99339 4*05329 4-1 1409 4-17580 4-23844 4-30202 4^36655 4*43205 Present Value •46798 •46107 •45426 •44754 •44093 -43441 •42799 •42167 •41544 -40930 -40325 •39729 •39142 •38563 •37993 •37432 •36879 •36334 •35797 •35268 •34746 •34233 '33727 •33229 '3273^ -32254 -31777 •31308 •3084s •30389 -29940 •29497 •29062 •28632 •28209 •27792 •27381 •26977 •26578 •26185 •25798 -25417 •25041 •24671 •24307 •23947 •23594 •23245 •22901 •22563 See also Tables on pp. xx-xxxi Amount Present Value 75'7SSo7 77^92489 80-09376 82-29517 84-52962 86-79754 89-09951 91 -43600 93-80754 96-21465 98-65787 loi -13774 103-65481 106-20963 108-80277 III -43481 114-10634 i 116-81793 1 19^57020 122-36375 125-19921 128-07720 130-99836 133-96333 136-97278 140-02737 143-12778 146-27470 149-46882 152-71085 156-00152 159-34154 162-73166 166-17264 169-66523 173-21020 176-80836 180-46048 184-16739 187-92990 191-74885 195-62508 199-55946 203-55285 207-60614 211-72023 215-89604 220*13448 224-43650 228 -80304 35-46767 35-92874 36-38300 36-83054 37-27147 37-70588 38-13387 38-55554 38-97097 39-38027 39-78352 40-18080 40-57222 40-95785 41-33779 41-71211 42-08089 42-44423 42*80220 43-15487 43*50234 4384467 44-18194 44*51422 44-84160 45*16414 45-48191 45-79499 46-10343 46-40732 46-70672 47*00170 47 '2923 1 47^57863 47^86072 48-13864 48-41246 48-68222 48-94800 49-20985 49-46784 49-72201 49-97242 50-21913 5046220 50-70168 50-93761 51-17006 51*39907 5i^6247o Years 51 52 53 54 55 56 57 58 61 62 63 i 65 i 66 67 68 69 70 71 72 73 74 75 76 77 78 P 80 81 82 84 85 86 87 88 89 90 91 92 93 94 95 96 u 99 100 V] (55) ir/< INTEREST TABLES INTEREST TABLES Years I 2 3 4 5 6 I 9 10 II 12 13 14 IS i6 \l 19 20 21 ONE POUND 23 24 25 26 29 30 31 32 33 34 35 36 39 40 41 42 43 44 45 46 47 48 49 5P Amount 1 01750 I 03531 I 05342 1-07186 1-09062 I -10970 I'I29I2 1-14888 I -16899 1-18944 I -21026 I -23144 I -25299 I -27492 I 29723 1-31993 I 34303 I 36653 I 39045 1-41478 1-43954 I -46473 I 49036 1-51644 I 54298 I 56998 1-59746 I -62541 1 65386 I 68280 I -71225 I -74221 1-77270 I -80372 1-83529 I -86741 1-90009 1 -93334 1-96717 200160 2 03663 2 07227 2-10853 2-14543 2-18298 2-22118 2-26005 2 29960 233984 2-38079 Present Value •98280 •96590 •94929 •93296 •9169I -901 14 -88564 -87041 •85544 •84073 -82627 -81206 -79809 •78436 '770S7 •75762 -74459 -73178 -71919 -70682 -69467 -68272 i •67098 i •65944 •64810 I -63695 •62599 •61523 -60465 -59425 j -58403 •57398 •5641 1 -55441 -54487 -53550 -52629 •51724 •50834 •49960 -49IOI -48256 -47426 -4661 1 •45809 •45021 •44247 -43486 -42738 •42003 ONE FOUND FEB ANNUM Amount I-OOOOO 2-01750 3-05281 4-10623 5-17809 6-26871 7-37841 850753 9-65641 10-82540 12-01484 13*22510 14-45654 15-70953 16-98445 18-28168 I9-60161 20-94463 22-31117 23-70161 25 11639 26-55593 28-02065 29-51102 31-02746 32-57044 34-14042 35-73788 37-36329 3901715 40-69995 42-41220 44-15441 45-92712 47 73084 49-56613 51-43354 5333362 55-26696 57-23413 59-23573 61 -27236 63-34462 65-45315 6759858 6978156 72 00274 74-26278 76-56238 78-90222 Present Value 0-98280 1 -94870 2-89798 383094 474786 5-64900 653464 7-40505 8-26049 9-10122 992749 iO'7395S 1 1 53764 12^32201 13 09288 13 85050 14 59508 15 32686 16^04606 16-75288 17^44755 1813027 1880125 19-46069 20 10878 20-74573 21-37173 21 98695 22-59160 2318585 23-76988 2434386 24-90797 25-46238 26-00725 26-54275 27-06904 27-58628 28 09463 28-59423 2908524 29-56780 3004207 3050817 3096626 31-41647 31-85894 32-29380 32-72118 3314121 I 2 3 4 5 6 I 9 10 II 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 29 30 31 32 33 34 35 36 ^7 38 39 40 41 42 43 44 45 46 47 48 49 50 U% Years ONE FOUND 51 52 53 54 55 56 57 58 & 61 62 65 66 67 68 69 70 71 72 73 74 75 76 U 81 82 , 83 ^ 85 86 Si u 89 90 91 92 93 94 95 96 U 99 100 ONE FOUND FEB ANNUM Amount 2-42245 2-46485 250798 2-55187 259653 2-64197 2-68820 2-73524 2-78311 2-83182 2-88137 293180 2-98310 303531 3-08843 3 14247 3 19747 325342 331036 336829 342723 348721 3^54824 361033 3-67351 3-73780 380321 386977 3 93749 400639 4-07650 4-14784 4*22043 4 29429 4-36944 4-44590 4-52371 4 60287 4-68342 4-76538 4-84877 4^93363 501997 5^10782 5 '19720 5-28815 538070 5^47486 5^57067 5-66816 Present Value -41280 •40570 '39S73 •39187 •38513 •37851 •37200 •36560 •35931 •35313 •34706 •34109 •33522 •32946 •32379 • •31822 •31275 -30737 •30208 •29689 •29178 -28676 •28183 -27698 -27222 -26754 •26294 •25841 •25397 •24960 •24531 •24109 •23694 •23287 •22886 •22493 -22106 -21726 •21352 •20985 -20624 -20269 -19920 •19578 •1924 1 -18910 •18585 •18265 •17951 •17642 Amount For explanation see pp. 8-13 81 •28301 83^70547 86-17031 88-67829 91-23016 93^82669 96-46866 9915686 101*89210 104*67522 107*50703 110-38841 113-32020 116*30331 119-33861 122*42704 12556951 128-76698 132*02040 13533076 138-69905 142 1 2628 14561349 149-16173 15277206 156-44557 160-18336 163-98657 167-85634 171-79382 175^80022 179^87672 184-02456 1 88 ^24499 192-53928 196-90872 201 35462 205-87833 210*48120 215-16462 219-93000 224*77877 229*71240 234-73237 23984018 245^03739 250-32554 25570624 261-18110 266-75177 Present Value (56) See also Tables on pp. xx-xxxi 33-55401 33-95972 34-35845 34-75032 35^13545 35^51395 35-88595 36-25155 36-61086 3696399 37*31104 37-65213 37-98735 38-31681 38-64060 3895882 39-27157 39-57893 39 '88102 40*17790 4046968 40-75645 41 03828 41-31526 41-58748 41-85502 42-11795 42-37636 42-63033 42-87994 4312524 4336633 4360328 4383614 4406501 4428993 44 5 1099 44^72824 44-94176 45-15161 45^35785 45-56054 45 75974 45^95552 46 14793 46-33704 4652288 46-70554 46-88505 47-06147 Tears 51 I 52 53 54 55 56 59 60 61 62 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 2^ 85 86 8^ u 89 90 91 92 93 94 95 96 97 98 99 100 1 j (57) •2°/, !■ 1 Years INTEREST TABLES ONE FOUND Amount I I -02000 2 I '04040 3 I 06121 4 I 08243 5 1*10408 6 1-12616 2 1-14869 1-17166 9 I -19509 zo I -21899 xz 124337 Z3 I 26824 13 I -29361 14 1-31948 »S I 34587 z6 1 37279 17 I -40024 z8 1 '42825 19 I -45681 20 i 1-48595 2X ^ 1-51567 22 1-54598 23 1-57690 24 1-60844 25 I -64061 26 1-67342 27 1 70689 28 I -74102 29 1-77584 30 1 -811 36 31 1-84759 32 1 -88454 33 I 92223 34 I 96068 35 1-99989 36 2-03989 37 2-08068 38 2-12230 39 2-16474 40 2 -20803 41 2-25220 42 2-29724 43 2-34319 44 2-39005 45 i 2-43785 46 2-48661 ^l 2-53634 48 2-58707 49 2-63881 SO 2-69159 Present Value •98039 -96117 -94232 •92385 •90573 •88797 -87056 •85349 •83676 •82035 •80426 •78849 •77303 -75788 -74301 •72845 -71416 •70016 -68643 •67297 •65978 •64684 -63416 -62172 -60953 •59758 -58586 •57437 -5631 1 -55207 -54125 •53063 •52023 -51003 -50003 49022 -48061 •471 19 •46195 •45289 -44401 •43530 -42677 -41840 /4IO20 -40215 •39427 •38654 •37896 •37153 ONE FOUND FEE ANNUH Amount i-ooooo 2 -02000 3*06040 412161 5-20404 6-30812 7-43428 8 58297 975463 10 94972 1216872 1341209 14-68033 15-97394 1 7 29342 1863928 20 01 207 21-41231 22-84056 24-29737 25 78332 27 -29898 28*84496 30 42 186 32*03030 33*67090 3534432 3705121 3879223 40*56808 42-37944 44-22703 46-171-7 48-033SO 49*99447 51-99436 5403425 56-11494 58-23723 60*40198 62^61002 64-86222 67-15947 69-50265 71-89271 74-33056 76-81717 79-35352 81-94059 84-57940 L I Present Value •98039 I -94156 2-88388 3-^773 4-71346 5-60143 6-47199 7-32548 8-16224 898258 9-78685 10-57534 11-34837 12-10625 12-84926 13-57771 14-29187 14-99203 15 67846 16*35143 17*01121 17-65805 18*29220 18*91393 19-52346 20*12104 20 70690 21-28127 21 84438 22*39646 22*93770 23-46833 2398856 24-49859 24-99862 25-48884 25-96945 26 -44064 26-90259 2735548 27 79949 28-23479 2866156 29-07996 29-49016 29-89231 3028658 30-67312 31-05208 3142361 Tears Z 3 3 4 5 6 7 8 9 10 IX Z2 13 14 15 z6 \l 19 20 2Z 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 SO Years For explanation see pp. 8- 13 51 52 53 54 55 56 57 IS 61 62 65 66 $7 68 69 70 71 72 73 74 75 76 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 INTEREST TABLES 2% ONE FOUND Amount 2-74542 2-80033 2-85633 2-91346 2-97173 3-03I17 309179 3-15362 3-21670 3-28103 3^34665 3^41358 3-48186 3-55149 3-62252 3-69497 3-76887 3-84425 3-92114 3-99956 4-07955 4-16114 4-24436 Present Value •36424 •35710 -35010 •34323 •33650 •32991 •32344 -31710 •31088 -30478 •29881 •29295 -28720 •28157 •27605 •27064 -26533 •26013 -25503 •25003 -24513 -24032 23561 4-32925 •23099 4-41584 •22646 4-50415 •22202 4-59424 •21766 4-68612 •21340 4-77984 •20921 4-87544 •20511 4-97295 •20109 5-07241 •19715 5-17385 -19328 5-27733 •18949 5-38288 •18577 5-49054 •18213 5-60035 •17856 5^71235 •17506 5-82660 •17163 5-94313 •16826 6-06200 •16496 6-18324 •16173 6 30690 •15856 6-43304 •15545 6 56 I 70 •15240 6-69293 •14941 6-82679 •14648 696333 •14361 7-10259 •14079 7-24465 •13803 ONE FOUND FEE ANNUM Amount Present Value 87^27098 90-01640 92-81673 95^67307 98-58653 101 -55826 104-58943 107-68121 no 83484 11405154 117-33257 120-67922 124-09280 127-57466 13I-I26I5 134-74868 138-44365 142-21252 146-05677 149-97791 153-97747 158-05702 162 21816 166-46252 170-79177 175-20761 I79-7II76 184 30599 188-99211 193-77195 198-64739 203-62034 208 69275 213-86660 219-14394 224-52681 23001735 23561770 241-33005 247-15665 253-09979 259«i6i78 265-34502 271-65192 278-08496 28464666 291-33959 298-16638 305-12971 312-23230 31 78785 32-14495 3249505 32^83828 33-17479 33-50469 33-82813 34-14523 34-45610 34-76089 3505969 35-35264 35-63984 35-92141 3619746 36-46810 36-73343 36-99356 37-24859 37-49862 37-74374 37-98406 38-21967 38-45066 38-67711 38-89913 39-11679 39-33019 39-53940 39^74451 39-94560 40-14275 40-33603 40-52551 40-71129 40-89342 41^07198 41-24704 41 41867 41-58693 41-75189 41-91362 42-07217 42^22762 42 38002 4252943 42-67591 42^81952 42^96032 43-09835 Years 51 52 53 54 55 S6 P 6z 62 64 65 66 67 68 69 70 71 72 73 74 75 76 79 80 8z 82 2^ 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 (58) See also Tables on pp. xx-xxxi m I (59) t ^1 i fo INTEREST TABLES • ONE POUND ONE POUND PEB ANNUM Years 1 Years Amoiint Present Value Amount Present Value I I -02250 -97800 i-ooooo 0-97800 I 2 I 04551 •95647 2-02250 I 93447 3 3 1*06903 •93543 3-06801 2-86990 3 4 4 f 09308 -91484 4-13704 378474 5 I 11768 •89471 5-23012 4-67945 5 6 I 14283 •87502 6-34780 5-55448 6 7 1-16854 •85577 7-49062 6-41025 7 8 I 19483 -83694 8-65916 7-24718 8 9 1-22171 •81852 985399 806571 9 lO I -24920 -80051 11-07571 886622 10 II ! 1-27731 -78290 12-32491 9 649 11 II 12 ' I -30605 -76567 13-60222 10-41478 12 13 1*33544 •74882 14-90827 11-16360 13 M 1-36548 •73234 1624371 11-89594 14 15 1-39621 •71623 17-60919 12-61217 15 i6 I 42762 •70047 19-00540 1331263 16 '2 I -45974 •68505 20-43302 13-99768 17 i8 I -49259 •66998 21-89276 14-66766 18 19 1-52617 •65523 23-38535 15-32290 19 20 I -5605 1 -64082 24-91152 15-96371 20 21 1-59562 -62672 2647203 1659043 21 22 1-63152 •61292 28-06765 17-20335 22 23 I 66823 •59944 29-69917 1 7 80279 ^ 24 1-70577 •58625 31 36740 18^38904 24 25 I -74415 •57335 3307317 18 96238 25 26 1 78339 •56073 34^81732 19-52311 26 27 I -82352 •54839 36-60071 20-07150 27 28 I -86454 •53632 38-42422 20-60783 28 29 1-90650 •52452 40-28877 21 13235 29 30 I -94939 •51298 42-19526 21-64533 30 31 I 99325 •50169 44-14466 22-14702 3< 32 2-03810 •49065 46-13791 22-63767 32 33 208396 •47986 48-17602 23-11753 33 34 2-13085 •46930 50-25998 23-58683 34 35 2-17879 •45897 52-39083 24-04580 35 36 2-22782 •44887 54-56962 24-49467 36 37 2-27794 •43899 56-79744 24-93366 38 2-32920 •42933 59-07539 25-36299 08 39 2-38160 -41989 61-40457 25-78288 39 40 2-43519 •41065 63-78618 26-19352 40 41 2-48998 -40161 66-22137 26-59513 41 42 2-54601 •39277 68-71135 26 98790 42 43 2-60329 •38413 71 25735 27-37203 43 44 2-66i86 •37568 7386064 27-74771 44 45 2-72176 •36741 76-52251 28-11512 45 46 2-78300 •35932 7924426 28-47444 ; 46 ^2 2-84561 •35142 82 02726 28-82586 47 15 2-90964 •34369 84-87287 29-16955 48 i^ 1 2-9751 1 •33612 87-78251 29-50567 49 50 304205 •32873 9075762 2983440 50 for explanation see pp. 8-13 ^60) INTEREST TABLES 21°/. Yean 51 52 53 54 55 56 61 62 65 66 57 68 69 70 71 72 73 74 75 76 81 82 83 86 Si 89 90 91 92 93 94 95 96 97 98 99 100 ONE POUND Amount Present Value 3-1 1049 3^i8o48 3-25204 3-32521 3-40003 3^47653 3^55475 363473 3-71651 3-80013 3-88564 397306 4-06246 4-15386 424733 4-34289 4-44061 4 54052 4*64268 4-74714 4^85395 4-96317 5-07484 5-18902 5-30577 542515 5-54722 5-67203 579965 593015 6-06357 6'20000 6-33950 6-48214 6-62799 6-77712 6 92961 7 08552 7 -24495 7-40796 7-57464 774507 791933 8-09752 8 27971 8-46600 8 65649 8-85126 9-05041 9-25405 ONE POUND PEB ANNUM •32149 •31442 •30750 -30073 ■29412 •28764 •28131 •27512 •26907 •26315 -25736 -25169 -24616 •24074 •23544 •23026 •22519 •22024 •21539 •21065 •20602 •20148 •19705 •19271 •18847 •18433 •18027 •17630 •17242 •16863 •16492 •16129 •15774 •15427 •15088 -14756 •14431 •14113 •13803 •13499 •13202 •12911 •12627 •12349 •12078 •11812 •11552 •I 1298 -1 1049 -10806 Amount 9379966 96-91016 100-09064 103-34267 106-66788 no '06791 "3 54444 117-09919 120-73392 124-45043 128 25057 132-13621 136-10927 14017173 144-32559 148-57292 152-91581 157-35642 161 -89694 166-53962 171-28676 1 76 1407 1 181-10388 186-17871 191-36774 196-67351 202-09866 207-64588 213-31792 21911757 225-04771 231-11129 237 3 1 1 29 243-65080 250-13294 256*76093 263-53805 270-46766 277-55318 284-79813 292 -20608 299-78072 307-52579 315-44512 32354263 331-82234 340-28834 348-94483 357-79609 366-84650 Present Value 30-15589 30-47031 30-77781 31-07854 31 37265 31*66030 31-94161 32-21673 32-48580 32-74895 33-00631 33-25800 3350416 33 74490 3398034 34-21060 34-43580 3465604 34-87143 35-08208 35-28810 35^48959 3568664 35-87935 3606783 36-25215 3643242 36-60873 36-78115 36-94978 37-11470 37-27599 37 43373 37-58800 3773888 37-88643 3803074 38-17187 38-30990 38-44489 38-57691 38-70602 3883230 38-95579 39-07657 3919469 39-31021 39-42319 3953368 39-64174 Years 51 52 53 54 55 56 IS 61 62 63 65 66 u 69 70 71 72 73 74 75 76 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 99 100 (I '■♦I I J See also Tables on pp. xx-xxxi (61) 11 2I7« INTEREST TABLES INTEREST TABLES 2I°A I 2 3 4 5 6 7 8 9 10 II 12 13 15 i6 17 i8 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 ONE POUND Amount Present Value I 'oascx) •97561 I 05062 •95181 I -07689 -92860 1-10381 •90595 1-13141 •88385 I -15969 •86230 I -18869 -84127 1-21840 -82075 I -24886 -80073 I -28008 •78120 I -31209 •76214 I 34489 •74356 1-37851 •72542 1-41297 •70773 I -44830 -69047 1-48451 -67363 1-52162 •65720 1-55966 -641 17 I 59865 62553 I 63862 -61027 I -67958 •59539 I -72157 -58086 I -76461 •56670 1-80873 •55288 I 85394 •53939 1-90029 -52623 I 94780 -51340 I -99650 -50088 2 -04640 •48866 209757 -47674 2-15000 •465 1 1 2 20376 •45377 2-25885 2-31532 2-37321 2-43254 2-49335 2-55568 2-61957 2 68506 2-75219 2-82100 2-89152 2-96381 3-03790 3^"385 3-19169 3-27149 3-35328 3*43711 -44270 •43191 •42137 -41 109 -40107 -39128 •38174 •37243 •36335 •35448 •34584 •33740 •32917 •32115 •31331 •30567 -29822 •29094 ONE FOUND FEB ANNUM Amount I -00000 2-02500 3-07562 4^15252 5^25633 6-38774 7^54743 8-73612 995452 1 1 -20338 12-48347 13-79555 15-14044 16-51895 17-93193 19-38022 20-86473 22-38635 23-94601 25-54466 27-18327 28-86286 30-58443 32-34904 34-15776 36-01171 37-91200 3985980 41 85630 43-90270 46 -00027 48-15028 5035403 52-61289 54^92821 57-30141 59-73395 62-22730 64-78298 67 40256 70-08762 72-83981 75-66081 78-55232 81-51613 84-55403 87-66788 90-85958 94-13107 97-48435 Present Value •97561 I -92742 2-85602 3-76197 4-64583 5-50812 6-34939 7-17014 7-97087 8-75206 9-51421 10-25776 10-98318 1 1 -69091 12-38138 13-05500 13-71220 14-35336 ■ 14-97889 15-58916 16-18455 16-76541 17-33211 17-88499 18-42438 18-95061 1 9^4640 1 19^96489 2045355 20-93029 21-39540 21-84918 22-29188 22 72379 23-14516 23-55625 23-95732 24-34860 24-73034 25-10277 25-46612 25-82061 26-16645 26-50385 26-83302 27-15417 27-46748 27-77315 28-07137 28-36231 Years I 2 3 4 5 6 2 9 ID II 12 13 14 15 16 17 18 19 20 21 23 24 25 26 29 30 31 32 33 34 35 36 39 40 41 42 43 44 45 46 47 48 49 50 Yeara ONE FOUND 51 52 53 M 55 56 61 62 65 66 67 68 69 70 71 72 73 74 75 76 81 82 83 86 !7 88 89 90 91 92 93 94 95 96 99 100 Amount 3*52304 3-61111 3*70139 379392 . 3-88877 398599 4-08564 4-18778 4-29248 4-39979 4-50978 4-62253 4-73809 485654 4-97796 5*10241 5-22997 5-36072 5-49473 5-63210 5-77291 5-91723 6 065 16 6-21679 6-37221 ^•53151 6^69480 6-86217 7-03372 7-20957 7-38981 7-57455 7-76392 7-95801 8-15696 8-36089 8-56991 878416 9-00376 9-22886 9-45958 9-69607 9*93847 10-18693 10-44160 10-70264 10-97021 1 1 -24447 11-52558 II -81372 Present Value ONE FOUND FEB ANNUM •28385 •27692 •27017 *26358 •25715 •25088 -24476 •23879 -23296 -22728 •22174 -21633 -21106 •20591 •20089 •19599 •19121 •18654 -18199 *i7755 -17322 •16900 -16488 -16085 •15693 •15310 •14937 *H573 -14217 -13870 -13532 -13202 •12880 -12566 -12259 •11960 •11669 •11384 •11106 -10836 -10571 -10313 •10062 •09817 -09577 -09343 -091 16 -08893 -08676 -08465 Amount 100-92 146 104-44449 108-05561 III-75700 "5*55092 119-43969 123-42569 127-51133 131-69911 135-99159 140-39138 144*901 16 149-52369 154-26179 159-I1833 164-09629 1 69^1 9869 174^42866 179-78938 1 85 -284 1 1 190-91622 196-68912 202 -60635 208-67151 214-88829 221-26050 227-79201 234-48681 241-34898 248-38271 255-59228 262 '98209 270-55664 278-32056 286-27857 294-43553 302-79642 311-36633 320-15049 329-15425 338-38311 347-84269 357*53875 367*47722 377*66415 388-10576 398-80840 409-77861 421-02308 432*54865 Present Value 28 •6461 6 28-92308 29-19325 29*45683 29-71398 29-96486 30-20962 30-44841 30-68137 30-90866 31-13040 31*34673 31-55778 31*76369 31-96458 32-16056 32-35177 32-53831 32 72030 3289786 33-07108 33-24008 33-40495 33-56581 33*72274 33-87584 34-02521 3417094 34-31311 34*45182 34-58714 34-71916 34-84796 34*97362 35-09621 35-21582 35*33251 35*44635 35*55741 35*66577 35-77148 35-87462 35-97523 36-07340 36-16917 36-26261 3635376 36-44269 36-52946 36-61410 Years 51 52 53 54 55 56 59 60 61 62 63 65 66 57 68 69 70 71 72 73 74 75 76 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 For explanation see pp. 8-13 (62) bee also Tables on pp. xx-xxxi I (63) 21°/ INTEREST TABLES Yean ONE POUND Amount I "02750 105576 I '08479 I 1 1462 I 14527 I 17677 1*20913 1 24238 1-27655 1-31165 I -34772 I -38478 I -42287 I -46199 I -50220 1-54351 1-58596 I '62957 I 67438 I 72043 1-76774 I -81635 I 86630 1-91763 I 97036 2-02455 2*08022 2-13743 2-19621 2-25660 2-31866 2-38242 2-44794 2-51526 2-58443 2-65550 2 72852 2-80356 2-88066 2-95987 3-04127 3-I249I 3*21084 3*29914 338986 3-48309 357887 367729 3-77842 388232 For explanation see pp; 8-13 Present Value •97324 -94719 -92184 •89717 •87315 •84978 *82704 *8o49i •78336 -76240 •74199 •72213 •70281 •68400 •66569 •64787 -63053 *6i366 •59723 •58125 •56569 •55055 -53582 •52148 -50752 •49394 •48072 •46785 •45533 •44314 •43128 •41974 •40851 •39757 •38693 •37658 •36650 •35669 -34714 •33785 •32881 •32001 •31 144 •3031 1 •29500 •28710 •27942 -27194 -26466 •25758 ONE POUND PEB ANNUM Amount I -00000 2-02750 3*08326 4^i68o5 5-28267 6-42794 7-60471 8-81384 10-05622 11-33276 12-64442 13-99214 15-37692 16-79979 18-26178 19-76398 21-30749 22-89344 24-52301 26-19740 27-91783 29-68557 31-50192 33-36822 35^28585 37-25621 39-28075 41-36098 43-49840 45-69461 47-95121 50-26987 52-65229 55-10023 57-61548 60-19991 62-85541 65-58393 68-38749 71-26815 74-22802 77-26929 80-39419 83-60504 86-90417 90-29404 93-77712 9735600 1 01 -03329 104-81170 (64) Present Value 0-97324 I -92042 2-84226 3*73943 4-61258 546237 6-28941 7-09431 7-87768 8 '64008 9-38207 10-10420 10-80701 11-49101 12-15670 12-80457 13-43511 14-04877 14-64600 15-22725 15-79295 16-34350 16-87932 17-40080 17-90832 18-40226 1888297 19-35083 19-80616 20-24930 20-68059 21-10033 2i^5o883 21^90641 22 29334 22-66992 23-03642 23 393 I I 23-74025 24-07810 24-40691 24-72692 25-03837 2534147 25-63647 2592357 26 -20299 26-47493 26 -73959 26-99717 Years I 2 3 4 5 6 7 8 9 10 zx za 13 14 15 16 \l 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 39 40 41 42 43 44 45 46 49 SO INTEREST TABLES 2r/o Years ONE POUND Amount 51 52 53 54 55 71 72 73 74 75 76 79 80 8z 82 83 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 3-98909 4-09879 4-21150 4-32732 4 '44632 56 4-56859 57 4-69423 58 4-82332 S 4-95596 5-09225 61 5-23229 62 5-37618 63 5-52402 64 5-67593 65 5-83202 66 5-99240 67 6-15719 68 6-32651 69 6 -50049 70 6 67926 6*86294 7-05167 7-24559 7-44484 7 '64957 7-85994 8 07609 8-29818 8-52638 8-76085 9-00178 9-24933 9-50368 976503 10-03357 10-30950 10-59301 10-88431 1 1 -18363 11-49118 1 1 -80719 12-13189 12-46552 12-80832 13-16055 13-52246 13-89433 14-27642 14-66902 15-07242 Present Value ONE POUND PER ANNUM Amount •25068 -24397 •23744 •23109 -22491 •21889 -21303 -20733 •20178 -19638 -19112 •18601 -18103 •17618 •17147 •16688 •16241 •15806 -15383 •14972 •I4571 •14181 •13802 -13432 -13073 •12723 •12382 •12051 •II728 •II414 -III09 •I0812 •10522 •1024 1 -09967 -09700 •09440 •09188 -08942 •08702 •08469 -08243 -08022 -07807 -07598 -07395 -07197 •07005 -06817 •06635 108-69402 1 12-6831 1 I16-78189 120-99340 125-32071 129-76703 134-33563 139-02986 143-85318 148-80914 153-90139 1 59^1 3368 164-50986 170-03388 i75^7098i 181 -54183 187-53423 193-69142 200-01793 206-51843 213-19768 220-06062 227-11229 234-35788 241-80272 249-45229 257-31223 265-38832 273 68649 282-21287 290-97373 299-97551 309-22483 318-72851 328-49355 338-52712 34883662 359-42962 370-31394 381-49757 392-98876 404-79595 416-92783 42939335 442 '20167 455-36221 468 88467 482 77900 497-05542 511-72445 See also Tables on pp. xx-xxxi (6$) Present Value Years 27-24785 27-49183 27-72927 27-96036 28-18527 28-40415 28-61718 28-82451 29-02628 29-22266 29-41378 29^59979 29-78082 29^95700 30^12846 3029534 30-45775 3061582 30-76965 30-91937 31 06508 31-20689 31 •34491 31-47923 31-60995 31-73718 31-86100 31-98151 32-09880 32-21294 32-32403 32-43214 32-53737 32-63977 32-73944 32-83644 32-93084 33-02271 33-11213 33-19915 33-28385 33-36628 3344650 33-52457 33-60056 33-67451 33-74648 33-81652 3388469 ! 33-95104 i 51 52 S3 54 55 56 57 58 60 61 62 63 65 66 57 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 s* 95 86 8^ u «9 90 91 92 93 94 95 96 97 98 99 100 II 3°/' INTEREST TABLES For explanation see pp. 8- 1 3 (66) ONE POUND ONE FOUND PES ANNUM Years Tears Amount Present Value Amount Present Value I 1-03000 •97087 I -00000 •97087 I 2 1*06090 -94260 2*03000 1*91347 2 3 I -09273 •91514 3-09090 2*82861 3 4 1-12551 •88849 4-18363 3^7i7io 4 5 1-15927 •86261 5 •30914 4-57971 5 6 I -19405 •83748 6 -4684 1 5-4I7I9 6 7 I -22987 -81309 7-66246 6-23028 i 8 1 -26677 -78941 8*89234 7-01969 9 1-30477 •76642 10*15911 7-78611 9 10 I '34392 -74409 1 1 -46388 8*53020 10 II 1-38423 •72242 12-80780 9 25262 II 12 I -42576 -70138 14-19203 9*95400 12 13 I -46853 •68095 15-61779 10-63496 13 14 I -51259 -661 12 17 08632 1 1 29607 M 15 1-55797 •64186 18-59891 11-93794 IS 16 I -60471 -62317 20-15688 12-56110 16 ^l I -65285 •60502 21-76159 13-16612 % 18 I -70243 -58739 23*41444 13-75351 19 I -75351 -57029 25-11687 14-32380 19 20 I -8061 1 -55368 2687037 14-87748 20 21 I 86029 •53755 28*67649 1 5 •41502' 21 22 1-91610 -52189 30^53678 15-93692 22 23 1-97359 •50669 32^45288 16-44361 23 24 2-03279 -49193 34-42647 16-93554 24 25 2-09378 -47761 36*45926 17-41315 25 26 2-15659 -46369 38-55304 17-87684 26 ^ 2*22129 •45019 40-70963 18-32703 27 28 2-28793 -43708 42 93092 18-7641 1 28 29 2-35657 •42435 45-21885 19-18846 29 30 2*42726 •41 199 47-57542 19-60044 30 31 2 50008 . -39999 50-00268 20-00043 31 32 257508 •38834 52-50276 20-38877 32 33 265234 •37703 55^07784 2076579 33 34 2-73191 •36604 57 •73018 21-13184 34 35 281386 •35538 60-46208 21-48722 35 36 2-89828 •34503 63^27594 21 83225 36 37 298523 •33498 66-17422 22-16724 38 3-07478 •32523 69-15945 22*49246 38 39 3-16703 •31575 72-23423 22 -80822 39 40 3*26204 •30656 75*40126 23*11477 40 41 ! 3-35990 •29763 78*66330 23*41240 41 42 i 3-46070 •28896 82*02320 23*70136 j 42 43 3-56452 •28054 i 85-48389 23*98190 43 44 3-67145 -27237 89*04841 24*25427 44 45 3-78160 •26444 92-71986 24-51871 45 46 3-89504 •25674 96-50146 24^77545 46 47 4-01 190 •24926 100*39650 25 -0247 1 47 48 4-13225 •24200 104*40840 25-26671 48 49 4-25622 •23495 108 54065 25-50166 49 50 4-38391 , -2281 1 112*79687 25-72976 j 50 INTEREST TABLES 3°/< Tears 51 52 53 54 55 56 57 58 I 61 62 65 66 $7 68 69 70 71 72 73 74 75 76 77 78 81 82 83 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 ONE POUND Amount 4^51542 4-65089 4^79041 4^93412 5-08215 5 •23461 5^39165 5 55340 5 72000 5^89160 6*06835 6 *25040 6*43791 6*63105 682998 7*03488 7-24593 7^46331 7-68721 7-91782 8-15536 8-40002 8*65202 8*91158 9-17893 945429 9-73792 10*03006 10*33096 10*64089 10*96012 1 1 ^28892 1 1 *62759 1 1 *97642 12*33571 12-70578 13-08695 13-47956 13-88395 14-30047 14-72948 15-17137 15*62651 16*09530 16*57816 17-07551 ^75^777 18*11540 18*65887 19-21863 Present Value -22146 -2 1 501 -20875 -20267 •19677 •19104 •18547 •18007 •17483 •16973 •16479 •15999 •15533 -15081 14641 -I4215 -13801 •13399 •13009 •12630 •12262 •I 1905 •II558 •II22I •10895 •10577 •10269 •09970 •09680 •09398 •09124 •08858 •08600 •08350 •08107 •07870 •07641 •07419 •07203 -06993 •06789 •06591 •06399 •06213 •06032 •05856 •05686 •05520 -05359 •05203 ONE POUND PEE ANNUM Amount ii7^i8o77 121-69620 126-34708 131 •13749 136-07162 141 -15377 146-38838 151 78003 157^33343 16305344 168*94504 1 75 •01339 181*26379 187*70171 194^33276 201*16274 208*19762 215^44355 222*90686 230*59406 238 •SI 1 89 246 -66724 255-06726 263-71928 272*63086 281*80978 291 *26407 301*00200 311*03206 321*36302 332*00391 342 96403 354-25295 365*88054 37785695 390*19266 402 *89844 415^98539 42946495 443-34890 457^64937 ^72'Z7^^S 487*55022 503*17672 519*27203 535-85019 552^92569 570*51346 588*62887 607-28773 Present Value 25-95123 26-16624 26*37499 26*57766 . 26*77443 26 96546 27-15094 27*33101 27-50583 2767556 27*84035 28*00034 28*15567 28^30648 28^45289 2859504 28-73305 28*86704 28*99712 29*12342 29*24604 29-36509 29*48067 29-59288 29-70183 29-80760 29-91029 30 00999 30-10679 30-20076 30-29200 30-38059 30-46659 30*55009 3063115 30-70986 30 78627 30*86045 30*93248 31*00241 31^07030 31-13621 31*20021 31 26234 31-32266 31-38122 3 1 43808 31-49328 31-54687 31-59891 Years 51 52 53 54 55 56 57 58 60 61 62 65 66 % 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 1 See also Tables on pp. xx-xxxi (67) c 2 02 10 INTEREST TABLES ONE FOUND ONE POUND FEB ANNUM Years Years Amoiint Present Value Amount Present Vidue I I -03500 -96618 I -00000 •96618 I 2 1-07122 •93351 2-03500 1-89969 2 3 I -10872 -90194 3^io623 2-80164 3 4 1-14752 -87144 4-21494 3 67308 4 5 1-18769 -84197 5^36247 4^51505 5 6 I -22926 •81350 6-55015 5^32855 6 7 I -27228 -78599 7-77941 6-11454 7 8 1-31681 •75941 9 "05 1 69 6-87396 8 9 I -36290 -73373 10-36850 7 60769 9 10 I -41060 •70892 "•73I39 8-31661 10 II I -45997 -68495 13-14199 9-00155 II 12 I -5 1 107 •66178 14-60196 9-66333 12 13 1-56396 -63940 16-11303 10-30274 13 14 I -61869 •61778 1767699 10-92052 14 15 1-67535 -59689 19-29568 11-51741 15 i6 173399 -57671 20-97103 12-09412 16 'Z I -79467 •55720 22-70501 12-65132 17 i8 I 85749 •53836 24-49969 13-18968 18 19 I -92250 -52016 26-35718 13-70984 19 20 1-98979 •50257 28-27968 14-21240 20 21 2-05943 -48557 30^26947 14-69797 21 22 2-13151 -46915 32-3*2890 15-16713 22 23 2'206ll •45329 34-46041 15-62041 23 24 2-28333 •43796 3666653 1605837 24 25 2-36324 •42315 ^ 38 94986 16-48152 25 26 2-44596 -40884 41-31310 16-89035 26 27 253157 -39501 43^75906 17-28537 27 28 2-62017 •38165 46 29063 17-66702 28 29 2-71188 •36875 48-91080 18-03577 29 30 2 80679 •35628 51-62267 18-39205 30 31 2-90503 •34423 54-42947 18-73628 31 32 3-00671 -33259 57-33450 1906887 32 33 3-11194 -32134 60-34121 19-39021 33 34 3 22086 •31048 63-45315 19-70068 34 35 3 33359 -29998 66-67401 20 00066 35 36 3-45027 ■28983 70-00760 20-29049 36 37 3-57103 •28003 73^45787 20-57053 37 38 3-69601 •27056 77-02889 20-84109 38 39 3-82537 -2614I 80-72490 21-10250 39 40 395926 •25257 j 84-55028 2i^35507 40 41 4-09783 •24403 i 88-50953 21 59910 41 42 4-24126 •23578 92-60737 21-83488 42 43 4-38970 •22781 9684863 22 06269 43 44 4*54334 -22010 loi 23833 22 28279 44 45 4-70236 -21266 105-78167 22-49545 45 46 4-86694 •20547 110-48403 1 22 -70092 46 % 5-03728 -19852 "535097 2289944 47 5-21359 -19181 120-38826 23-09125 48 49 539606 •18532 125-60184 23-27657 49 50 5-58493 -17905 130-99791 2345562 50 For explanation see pp. 8- 13 (68) INTEREST TABLES 02 /o Years ONE POUND Amount 5^78040 598271 6-19211 640883 6-63314 6-86530 7^10559 7-35428 7 -61 168 7-87809 8-15382 8-43921 8-73458 ^ 904029 9-35670 9-68418 10023 13 10-37394 1073703 1 1 -1 1282 1 1 -501 77 11-90434 12-32099 12 75222 13-19855 13-66050 14-13862 14-63347 15-14564 1567574 16-22439 16-79224 ^7 '37997 17-98827 18-61786 19-26948 19-94391 20 64 I 95 21-36442 22-11217 22-88610 23-68711 24-51616 25-37423 26 -26233 27-18151 28-13286 29-11751 30-13662 31-19141 Present Value •17300 •16714 •16150 •15603 •15076 •14566 . '14073 •13598 •13138 •12693 -12264 -1 1849 -1 1449 -1 1062 -10688 -10326 -09977 -09640 -09314 •08999 08694 -08400 -081 16 -07842 -07S77 -07320 •07073 •06834 -06603 •06379 -06164 -05955 •05754 •05559 •05371 -05190 -05014 -04845 -04681 •04522 •04369 -04222 •04079 •03941 -03808 •03679 •03555 •03434 -03318 -03206 ONE POUND PER ANNUM See also Tables on pp. xx-xxxi Amount 136-58283 142-36324 148-34595 154-53805 1 60 94689 167 58003 ^74-44533 181-55092 188-90520 196-51688 204-39497 212-54879 22098800 229-72258 23876287 248-11957 257-80376 267-82689 278-20083 288'g^7S6 300^05069 311-55244 323-45680 33577778 34853001 361^72856 375-38906 389-52768 404 -161 15 419-30678 434-98252 451-20691 467-99915 485-37912 503-36739 521-98525 541-25474 561-19865 581-84060 603-20503 625-31720 648 -20330 671-89042 696-40658 721-78082 748^04314 775-22465 803-35752 832-47503 862-61166 Present Value 23 62862 23-79577 23-95726 24-11330 24 -26405 24-40971 24-55045 24 -68642 24 -8 1 780 24-94474 25-06738 25 •18587 25-30036 25-41097 25-51785 25 -621 1 1 25 72088 25 8 I 728 25-91041 26 ^00040 26 08734 26-17134 26-25251 26 33092 26-40669 26-47989 26 55062 26-61896 26-68498 26-74878 26^8i04i 26-86996 26-92750 26-98309 27-03680 27-08870 27-13884 27-18729 27-23409 27-27932 27-32301 27-36523 27-40602 27-44543 27-48351 27-52029 27-55584 27-59018 27-62337 2765543 Years 51 52 53 54 55 56 57 58 61 62 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 8: 89 90 91 92 93 94 95 96 99 100 (69) 4°/. INTEREST TABLES ONE POUNB Years Amonnt Present Value I I'04CKX) •96154 2 I -08160 -92456 3 1-12486 -88900 4 1-16986 •85480 5 1-21665 -82193 6 I -26532 -79031 7 1-31593 75992 8 I -36857 -73069 9 I -42331 -70259 10 I -48024 -67556 II 1-53945 •64958 12 I -60103 -62460 13 I -66507 •60057 14 1-73168 -57748 15 1-80094 •55526 i6 I -87298 •53391 'Z I -94:90 -51337 i8 2-02582 -49363 19 2-10685 •47464 20 2-19112 -45639 21 2-27877 •43883 22 2-36992 •42196 23 2 -46472 •40573 24 2 56330 -39012 25 266584 -37512 26 277247 -36069 27 2-88337 -34682 28 2 99870 -33348 29 3-11865 -32065 30 3-24340 -30832 31 3-37313 -29646 32 3-50806 -28506 33 3-64838 -27409 34 379432 •26355 35 3-94609 •25342 36 4-10393 -24367 37 4-26809 •23430 3« 4-43881 -22529 39 4-61637 •21662 40 4-80102 -20829 41 4-99306 •20028 42 5-19278 •19257 43 5-40050 •18517 44 5-61652 •17805 45 5 -841 18 •17120 46 6-07482 •16461 % 6-31782 •15828 6-57053 •15219 49 6-83335 •14634 SO 7-10668 •1407 1 ONE POUND PER ANNUM Amount I 00000 2-04000 3-12160 4-24646 5-41632 6-63298 7 -89829 9-21423 10-58280 120061 1 13-48635 15-02581 16-62684 i8^29i9i 20^02359 21^82453 23-69751 25-64541 27-67123 29-77808 31-96920 34-24797 36-61789 39-08260 41-64591 44-31174 47-08421 49-96758 52-96629 56-08494 59-32834 62^70147 66^20953 69-85791 7365222 77-59831 81 -70225 85-97034 90-40915 95-02552 9982654 i04^8i96o iio^oi238 ii5^4i288 1 2 1 ^02939 126-87057 132-94539 139-26321 145-83373 1 52 66708 For explanation bee pp. 8-13 Present Value -96154 I 88609 277509 3 62990 445182 5^24214 6 ^00205 6^73275 7-43533 8-11090 8-76048 9-38507 9-98565 0-56312 I -1 1839 I 65230 2^16567 265930 3-13394 3-59033 4^02916 445112 4-85684 5-24696 5 -62208 5-98277 6-32959 6^66306 6 ^98372 7-29203 7-58849 7-87355 8-14765 8-41 120 8-66461 8-90828 9-14258 9-36787 9-58449 9-79277 999305 20-18563 20-37080 20-54884 20 72004 20^88465 21^04294 21-19513 21-34147 21-48219 Yeara I 2 3 4 5 6 7 8 9 10 II 12 13 14 15 16 % 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 % 49 50 INTEREST TABLES 4^/. Years ONE POUND 51 52 53 54 55 56 [ 61 62 65 66 % 69 70 71 72 73 74 75 76 81 82 83 84 85 86 I? 89 90 91 92 93 94 95 96 97 98 99 100 Amount Present Value 7-39095 7-68659 7-99405 8-31381 8-64637 8 99222 9-35191 9-72599 10-11503 1051963 1 0^9404 1 11-37803 II -83315 12-30648 12-79874 13-31068 13-8431 1 14-39684 14-97271 15-57162 16-19448 16-84226 17^51595 18-21659 18-94525 1970307 20-49119 21-31084 22-16327 23-04980 23-97179 24-93066 25-92789 26 -96500 28 04360 29-16535 30-33196 31-54524 32-80705 3411933 35-48411 36-90347 38-37961 39-91479 41-51139 43-17184 44-89872 46-69467 48-56245 50-50495 •13530 •13010 •12509 •12028 •11566 -11121 -10693 -10282 -09886 -09506 -09140 -08789 -08451 -08126 -07813 -07513 -07224 -06946 -06679 •06422 -06175 -05937 •05709 -05490 -05278 •05075 -04880 -04692 -04512 -04338 •04172 -0401 1 •03857 •03709 -03566 •03429 -03297 -03170 •03048 •02931 •02818 -02710 •02606 •02505 •02409 •02316 -02227 •02142 •02059 -01980 ONE POUND PER ANNUM Amount 159-77377 167-16472 174-85131 182-84536 191-15917 199-80554 208-79776 218-14967 227-87566 237-99069 248-51031 259-45073 270-82875 282^66190 294-96838 307-76712 321-07780 334-92091 349-31775 364 -29046 379-86208 396-05656 412-89892 430-41478 448-63137 467 -57662 487-27969 507-77087 529-08171 551-24498 574-29478 598-26657 623-19723 649-12512 676*09012 704-13373 733-29908 763-63104 795-17628 827-98333 862-10267 897-58677 934-49024 972-86985 IOI2 -78465 1054-29603 1097-46788 1142-36659 1 189-06125 1237-62370 (70) See also Tables on pp. xx-xxxi Present Value 21-61749 21-74758 21-87268 21-99296 22-10861 22-21982 22-32675 22-42957 22-52843 22 -62349 22-71490 22 -80278 22-88729 22 -96855 23-04668 23-I2181 23-19405 23-26351 23-33030 23-39452 23-45627 23-51564 23-57273 23-62763 23 6804 I 23-73116 23-77996 23-82689 23-87201 23-91539 23-95711 23-99722 24-03579 24 -07287 24-10853 24 •14282 24-17579 24-20749 24-23797 24 26728 24-29546 24 32256 24 3486 I 24-37367 24-39776 24^42092 24-44319 24-46461 24-48520 24-50500 Years 51 52 53 54 55 56 % 59 60 61 62 63 ^ 65 66 % 69 70 71 72 73 74 75 76 79 80 81 82 83 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 I I (71) 4r/o INTEREST TABLES Years I 2 3 4 5 6 7 8 9 10 II 12 13 14 15 i6 17 i8 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 i 40 41 42 43 44 45 46 47 48 49 50 ONE FOUND Amount I "04500 I -09203 1-14117 1-19252 I -246 1 8 I -30226 1-36086 1-42210 1-48610 1*55297 I 62285 1-69588' 1*77220 I -85194 1 -93528 2 02237 2-II338 2-20848 2 30786 2-41171 2 -52024 263365 2-75217 2-87601 3-00543 3-14068 3-28201 3-42970 3-58404 3-74532 3-91386 4-08998 4-27403 4-46636 4-66735 4-87738 5 09686 5 -32622 5-56590 5-81636 6 078 10 6-35161 6-63744 6-93612 7-24825 7-57442 7-91527 8-27145 8-64367 9-03264 Present Value •95694 •91573 •87630 -83856 -80245 -76790 •73483 -70319 -67290 •64393 -61620 •58966 •56427 •53997 •51672 •49447 •47318 -45280 -43330 -41464 -39679 •37970 •36335 •34770 ■33273 •31840 •30469 •29157 -27901 -26700 •25550 -24450 -23397 •22390 •21425 •20503 •19620 -18775 •17967 -17193 -16453 •15744 •15066 •I4417 •13796 •13202 •12634 •12090 •I 1569 •IIO71 ONE FOUND FEB ANNUM Amount I'OOOOO 2 -04500 3-13702 427819 5-47071 6-71689 8-01915 9-38001 10-80211 12-28821 13-84118 15-46403 17-15991 18-93210 20-78405 22-71933 24-74170 26-85508 2906356 31-37142 33-78314 36-30338 3^-93703 41-68919 44-56521 47-57064 50-71132 53-99333 57-42303 61-00707 64-75238 68-66624 72-75622 77-03026 81-49662 86-16396 91-04134 ' 96-13820 loi -46442 107-03032 112-84668 118-92479 125-27640 131 -91384 138-84996 1 46 0982 1 153-67263 161-58790 169-85935 178-50303 For explanation see pp. 8-13 (72) Present Value •95694 I -87267 2-74896 3-58753 4-38998 5-15787 5^8927o 6-59589 7-26879 7-91272 8-52892 9-11858 9-68285 10-22283 10-73955 1 1 -23401 II -70719 12-15999 12-59329 13-00794 13-40472 13-78442 14-14777 14-49548 14-82821 15^14661 15-45130 15-74287 1602189 1628889 16-54439 16-78889 17-02286 17-24676 17-46101 17-66604 17-86224 18-04999 18-22966 18-40158 18-56611 18-72355 18-87421 19-01838 19-15635 19-28837 19-41471 19-53561 19-65130 19-76201 Years I 2 3 4 5 6 I 9 10 II 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 48 49 SO INTEREST TABLES 4I°A Years 51 52 53 54 55 56 57 58 ^ 61 62 64 65 66 67 68 69 70 71 72 73 74 75 76 81 82 83 84 «5 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 I- ONE FOUND Amount 9-43910 9-86386 10-30774 10-77159 1 1 -2563 1 1 1 -76284 12-29217 12-84532 13-42336 14-02741 14-65864 15-31828 16^00760 16-72794 17-48070 18-26733 19-08936 19-94838 20 84606 21 78413 22^76442 23^78882 24-85931 25-97798 27 14699 28^36861 29^64520 30-97923 32-37329 33-83009 35-35245 36-94331 38-60576 40-34302 42-15845 44-05558 46-03808 48-10980 50-27474 52-53710 5490127 57-37183 5995356 62-65147 65-47079 68-41697 71-49574 74-71305 78-07514 81-58852 Present Value •10594 •10138 -09701 -09284 -08884 -08501 •08135 •07785 •07450 -07129 -06822 •06528 •06247 •05978 •05721 -05474 -05239 -05013 -04797 •04590 •04393 -04204 -04023 -03849 -03684 •03525 •03373 -03228 -03089 •02956 •02829 •02707 •02590 -02479 -02372 -02270 •02172 -02079 •01989 -01903 -0182I -01743 •01668 -01596 -01527 •01462 •01399 •01338 -01 28 1 •01226 ONE FOUND FER ANNUM Amount 187-53566 196-97477 20683863 217-14637 227^91796 239-17427 250-93711 263^22928 276-07459 289-49795 303-52536 318-18400 333-50228 349-50988 366-23783 383-71853 401 -98586 421-07523 441^02362 461^86968 483-65381 506-41823 530-20706 555-06637 581-04436 608-19136 . 636-55997 666-20517 697-18440 729-55770 763-38779 798-74024 835-68355 874-28931 914-63233 956-79079 1000-84637 1046-88446 1094-99426 1 145 -26900 1 197^8061 1 1252^70738 1310^07922 1370^03278 1432-68426 1498-15505 1566-57202 163806777 1712-78082 1790-85595 See also Tables on pp. xx-xxxi Present Value 1986795 19-96933 20-06634 2015918 20-24802 20-33303 20-41438 20-49224 20-56673 20-63802 20-70624 20^77152 20-83399 2089377 20-95098 21-00572 21 -0581 1 21-10824 2I-I562I 2I-;202II 21-24604 21-28808 21-32830 21-36680 21-40363 21^43888 21^47262 21^50490 21-53579 21-56534 21-59363 21-62070 21-64660 21-67139 21-69511 2I-71781 21-73953 21-76032 21^78021 21-79924 21-81746 21-83489 21-85156 21-86753 21^88280 21^89742 2 1^91 140 21 92479 21-93760 21-94985 Years 51 52 53 54 55 56 57 58 i9 61 62 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 ^ 85 86 87 88 89 90 91 92 93 94 95 96 99 100 |:f (73) 5°/< INTEREST TABLES Years Z 2 3 4 5 6 7 8 9 10 INTEREST TABLES ONE POUND Amount I "05000 1*10250 1-15763 1-21551 I -27628 I -34010 1*40710 1-47746 I -55133 I -62889 II 1-71034 12 1-79586 13 I -88565 14 I '97993 IS 2-07893 16 2-18287 17 2 -29202 18 2-40662 19 2-52695 20 265330 21 2-78596 22 2 92526 23 3-07152 24 3-22510 25 3-38635 26 3-55567 27 3-73346 28 3-92013 29 4*11614 30 4-32194 31 4-53804 32 4-76494 .13 5-00319 34 5-25335 3.S 5-51602 36 5-79182 37 6-08141 38 6-38548 39 670475 40 7-03999 41 7-39199 42 7-76159 43 8-14967 44 8-55715 45 8-98501 46 943426 ^l 990597 48 10-40127 49 10-92133 50 1 1 -46740 Present Value •95238 -90703 -86384 *82270 •78353 *74622 •71068 •67684 •64461 -6I39I •58468 -55684 •53032 •50507 -48102 -45811 -43630 •41552 -39573 •37689 •35894 -34185 •32557 •31007 •29530 •28124 -26785 -25509 •24295 •23138 •22036 -20987 -19987 •19035 •I8I29 •17266 •16444 •I 5661 -I49I5 •14205 -13528 •12884 •12270 •I 1686 •III30 •10600 •10095 ■09614 •09156 •08720 ONE POUND PEE ANNUM Amount I -00000 2-05000 3-15250 4-31013 5-52563 6^8oi9i 814201 9-5491 1 1 1 02656 12*57789 14^20679 15-91713 I7^7i298 19-59863 21^57856 23-65749 25-84037 28 •13238 30-53900 33-06595 35-71925 38-50521 41-43048 44-50200 47*72710 51-11345 54*66913 58*40258 62-32271 66-43885 70*76079 75-29883 80-06377 85-06696 90-32031 95-83632 loi -62814 107-70955 114-09502 120-79977 127-83976 135-23175 142^99334 151-14301 159-70016 1 68 685 1 6 1 78^1 1942 1 88^02539 198^42666 209^34800 For explanation see pp. 8-13 Years Present Value •95238 I -85941 2*72325 3-54595 4-32948 5*07569 5-78637 6*46321 7*10782 7*72173 8*30641 8-86325 9*39357 9*89864 10^37966 1083777 11-27407 . 1 1 -68959 12-08532 12-46221 12-82115 13-16300 13*48857 13-79864 14-09394 14-37518 14-64303 14-89813 15-14107 15-37245 15-59281 15-80268 16-00255 16-19290 16-37419 16-54685 i6^7ii29 1686789 1 7^01704 1715909 17-29437 1 7^4232 1 17-54591 17-66277 17-77407 17-88007 17-98101 18-07716 18-16872 18-2J592 5°/o I 2 3 4 5 6 7 8 9 10 II 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 3^ 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 (74) Years SI 52 S3 54 55 S6 57 59 60 61 62 63 65 66 57 68 69 70 71 72 73 74 75 -76 77 78 81 82 83 2^ 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 ONE POUND Amount 12-04077 12-64281 13-27495 13-93870 14-63563 15-36741 16-13578 16*94257 17-78970 i8^679i9 19-61315 20-59380 2i^62349 22-70467 23-83990 25-03190 26-28349 27*59766 28*97755 30-42643 31-94775 33-54513 35-22239 36^98351 3883269 40-77432 42-81304 44-95369 47-20137 49-56144 52-03951 54^64149 57-37356 60-24224 63-25435 66^41707 69-73792 73-22482 76-88606 80-73037 84 76688 89-00523 93 45549 98-12826 103-03468 108-18641 113-59573 119-27552 125*23929 131 50126 Present Value •08305 •07910 •07533 •07174 •06833 •06507 •06197 •05902 •05621 *o5354 •05099 •04856 •04625 •04404 *0419S *03995 -03805 •03623 -03451 •03287 •03130 •02981 •02839 •02704 *o257S *o2453 •02336 *02225 •021 19 •02018 *OI922 •01830 -01743 *oi66o •01581 •01506 *oi434 •01366 •01301 •01239 •01 180 •01 124 •01070 •01019 •00971 •00924 •00880 •00838 •00798 •00760 ONE POUND PEE ANNUM Amount 220-81540 232-85617 245*49897 258-77392 272-71262 287-34825 302-71566 318-85144 335-79402 353-58372 372-26290 391-87605 412-46985 434*09334 456-79801 480-63791 505-66981 531-95330 559-55096 588-52851 618-95494 650-90268 684-44782 719-67021 756-65372 795-48640 836*26072 879-07376 924*02745 971*22882 1020*79026 1072^82978 1127-47126 1 184^84483 1245^08707 1 308^34 142 1374-75849 1444^49642 1517*72124 1594-60730 1675-33767 1760*10455 1 849 •10978 1942*56527 204069353 2 143^7282 1 2251*91462 2365-51035 2484*78586 2610*02516 Present Value 18*33898 18*41807 18-49340 18-56514 1^-63347 18-69854 18-76052 18-81954 18-87575 18-92929 18-98027 19-02883 19-07508 19-11912 19-16107 19-20102 19-23907 19-27530 19-30981 19^34268 19*37398 19-40379 I9^432i8 19-45922 19-48497 19-50949 19-53285 19*55510 19-57628 19-59646 19^6 1 568 19-63398 I9^65i4i 19-66801 19-68382 19-69887 19-71321 19-72687 19-73987 19-75226 19-76406 19-77529 19-78599 19-79618 19*80589 19-81513 19*82394 1983232 19-84030 19-84791 Yean SI 52 S3 54 SS 56 57 58 61 62 66 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 See also Tables on pp. xx-xxxi (75) II 6% INTEBEST TABLES INTEREST TABLES Years I 2 3 4 5 6 7 8 9 10 II 12 13 14 IS i6 17 x8 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 i 41 ! 42 43 44 45 46 47 48 49 so ONE FOUND ONE POUND PER ANNUM Amount I '06000 I "12360 I'I9I02 I 26248 I 33823 1*41852 1-50363 » 59385 1-68948 179085 1 -89830 2 01220 2 13293 2-26090 2-39656 2-54035 2-69277 2-85434 3-02560 3-20714 3-39956 3-60354 3-81975 4-04893 4-29187 4-54938 4-82235 5-11169 5-41839 5-74349 6 -088 10 6-45339 6 84059 7-25103 7-68609 8-14725 8*63609 9-15425 9-70351 10-28572 10-90286 11-55703 12-25045 12-98548 13-76461 14-59049 15-46592 16-39387 17-37750 18*42015 Present Value •94340 *890oo -83962 •79209 -74726 -70496 -66506 -62741 •59190 •55839 •52679 •49697 •46884 -44230 •,41727 •39365 •37136 -35034 •33051 •31180 •29416 •27751 •26180 •24698 -23300 -21981 •20737 •19563 -18456 •17411 •16425 •15496 •14619 -13791 •13011 •12274 •11579 •10924 •10306 •09722 •09172 •08653 •08163 •07701 07265 •06854 •06466 •06100 •05755 -05429 Tears Amount 1 •00000 2 06000 3-18360 4-37462 563709 6-97532 8*39384 989747 11*49132 13-18079 14-97164 16-86994 18*88214 21-01507 23-27597 25-67253 28*21288 3090565 33-75999 36-78559 39-99273 43-39229 46-99583 50^8i558 54-86451 59-15638 63-70577 68*52811 73-63980 79-05819 84^80168 90-88978 97-34316 104-18375 111-43478 1 19-12087 127-26812 135*90421 145-05846 I54^76i97 165-04768 I 75^95054 187-50758 199-75803 212-74351 226-50812 241 09861 256-56453 272-95841 290-33590 For explanation see pp. 8-13 Present Value •94340 1-83339 2*67301 3-46511 421236 4-91732 5-58238 6^20979 6*80169 7-36009 7*88687 8-38384 8*85268 9-29498 9*71225 10-10590 10-47726 10-82760 II-15812 1 1 -46992 1 1 -76408 12*04158 12-30338 12-55036 12-78336 13-00317 13-21053 13-40616 13-59072 13^76483 13-92909 14-08404 14-23023 14-36814 14-49825 14*62099 14-73678 14-84602 14-94907 15*04630 15-13802 15-22454 i5'3o6i7 I5^383i8 15-45583 15-52437 15-58903 15*65003 15-70757 15-76186 I 2 3 4 5 6 7 8 9 10 II 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 SO (76) e^A ONE POUND ONE POUND PER ANNUM Amount Present Value Amount I9^52536 20-69689 21-93870 23-25502 24-65032 26-12934 27-69710 29-35893 31-12046 32-98769 3496695 37-06497 39-28887 41-64620 44-14497 46-79367 49-60129 52-57737 55-73201 59^07593 62 -62049 66-37772 70-36038 74*58200 79-05692 83-80034 88-82836 94-15806 99-80754 105-79599 12-14375 18-87238 126-00472 f 33 -56500 [41-57890 [50-07364 [59-07806 [68-72274 [78-74010 [89-46451 200-83238 212-88232 225-65526 239-19458 253-54625 268-75903 284-88457 301 -97765 320-09631 339-30208 -05122 -04832 •04558 -04300 •04057 -03827 •03610 •03406 •63213 •03031 •02860 •02698 •02545 •02401 •02265 •02137 •02016 '01902 •01794 •01693 •01597 •01507 •0142 1 •01341 •01265 •01 193 •01 126 •01062 •01002 •00945 •00892 •00841 •00794 •00749 •00706 -00666 -00629 -00593 •00559 -00528 -00498 -00470 •00443 -00418 •00394 •00372 •00351 •00331 -00312 •00295 308-75606 328-28142 348-97831 370-91701 394^17203 418-82235 444-95169 472-64879 502-00772 533-12818 566-11587 6oi^o8282 638-14779 677-43666 719-08286 763-22783 810-02150 859-62279 912-20016 967-93217 1027 -008 10 1089-62859 1 1 56 -00630 1226-36668 1300-94868 1380-00560 1463-80594 1552-63429 1646-79235 1746-59989 1852-39588 1964-53964 2083-41202 2209-41674 2342-98174 2484-56065 2634 63428 2793-71234 2962-33508 3 141 -07519 3330-53970 3531-37208 3744-25441 3969-90967 4209-10425 4462-65050 4731-40953 5016 -2941 1 5318-27175 5638-36806 Present Value Years 15-81308 15-86139 15-90697 15-94998 15-99054 1 6 0288 1 16*06492 16-09898 16-13111 16-16143 16-19003 16-21701 16-24246 16-26647 16-28912 16-31049 16-33065 16-34967 16-36792 16-38454 16-40051 16-41 158 16-42979 16-44320 16-45585 16-46778 16-47904 16-48966 16-49968 16-50913 16-51805 16-52646 16-53440 16-54188 16-54895 16-55561 16-56190 16-56783 16-57342 16-57870 16-58368 16*58838 16-59281 16-59699 16-60093 16-60465 16-60816 16-61 147 16-61460 16*61755 See afso Tables on pp. xx-xxxl 51 52 53 54 55 56 57 58 59 60 61 62 63 ^ 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 111 (77> 7°/o INTEREST TABLES INTEREST TABLES 1 Years I 2 3 4 5 6 7 8 9 10 II 12 13 14 15 i6 \l 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 39 40 41 42 43 44 45 46 47 48 49 50 ONE POUND Amount I-07CXX) 1-14490 I 22504 1-31080 I -40255 I -50073 I -60578 1-71819 1 -83846 I -967 1 5 2-10485 2-25219 2 -40985 2-57853 2-75903 2-95216 3-15882 3*37993 3'6i653 3-86968 4-14056 4-43040 474053 5-07237 5-42743 5-80735 6-21387 6-64884 7 -1 1426 7-61226 8-14511 8-71527 9-32534 9 -978 1 1 10-67658 1 1 -42394 12-22362 13-07927 13-99482 14-97446 16-02267 17-14426 18-34435 19-62846 21-00245 22-47262 24-04571 2572891 27-52993 29-45703 Present Value •93458 -87344 •81630 -76290 -71299 -66634 -62275 -58201 •54393 •50835 •47509 -44401 -41496 •38782 •36245 33^73 -31657 -29586 -27651 -25842 -24151 •22571 •21095 •19715 •18425 -17220 -16093 •15040 •14056 •13137 -12277 -1 1474 •10723 •10022 ■09366 •08754 •08181 •07646 •07146 •06678 •06241 -05833 •05451 •05095 •04761 •04450 •04159 •03887 •03632 •03395 For explanation see pp. 8-13 ONE FOUND PER ANNUM Amount I'OOOOO 2^07000 3 •21490 4^43994 5-75074 7-15329 8-65402 10-25980 11-97799 13-81645 15-78360 17-88845 20-14064 22-55049 25-12902 27-88805 30-84022 3399903 37-37896 40-99549 44-86518 49-00574 53-43614 58-17667 63-24904 68-67647 74-48382 80-69769 87-34653 94-46079 102-07304 iio^2i8i5 118-93343 1 28^25876 138^23688 148-91346 160-33740 172-56102 185-64029 199-6351 1 214-60957 230-63224 247-77650 266-12085 285-74931 306-75176 329-22439 353-27009 378-99900 406-52893 (78) • Present Value •93458 1 -80802 2 -62432 3-38721 4-10020 4-76654 5^38929 5-97130 651523 7-02358 7-49867 7-94269 8-35765 8-74547 9-10791 9-44665 9-76322 10-05909 10-33560 10-59401 10-83553 11-06124 II^272I9 1 1 -46933 1 1 -65358 1 1^82578 ir98^7i I2^i37ii 12^27767 12^40904 12*53181 12-64656 12-75379 12-85401 12^94767 1 3 0352 1 13-11702 13-19347 13-26493 13-33171 13-39412 13-45245 13-50696 13-55791 13-60552 13-65002 13-69161 13-73047 13-76680 13^80075 Years I 2 3 '4 5 6 7 8 9 10 II 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 29 30 31 32 33 34 35 36 39 40 41 42 43 44 45 46 % 49 SO 7°/o 51 52 S3 54 5S 56 57 61 62 65 66 u 69 70 71 72 73 74 75 76 77 78 ^ 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 ONE POUND ONE POUND PEE ANNUM Amount 31*51902 3372535 36^08612 38^6i2i5 4i^3i5oo 44-20705 47-30155 50-61265 54-15554 57^94644 62-00267 66-34286 70-98686 75^95594 81-27285 86-96195 93-04929 99^56274 106-53213 113-98938 121-96864 130-50644 139-64189 149-41682 159-87600 171-06732 183-04203 195-85498 209-56483 224-23437 239-93077 256-72592 274-69674 293^92551 314-50029 336-51531 360-07139 385-27638 412-24573 441-10293 471*98014 50501875 540-37006 578-19596 618-66968 661 -97656 708-31492 757-89696 810-94975 867-71623 Present Value •03173 •02965 •02771 •02590 •02420 •02262 •02 1 14 •01976 •01847 •01726 •OI613 -01507 -01409 •01317 •01230 •01 150 •01075 •01004 •00939 •00877 •00820 •00766 •00716 •00669 •00625 •00585 •00546 •005 1 1 •00477 •00446 •00417 •00390 •00364 •00340 •00318 •00297 •00278 •00260 •00243 •00227 •00212 •00198 •00185 •00173 •00162 •001 5 1 •OOI41 -00132 •00123 -001 15 See also Tables on pp. xx-xxxf Amount 435-98595 467-50497 501 -23032 537-31644 575*92859 617-24359 661 45065 708-75219 759^36484 813-52038 87 1^4668 1 933-46949 999-81235 1070^79922 1 146-75516 1228-02802 1 3 14 -98998 1408-03928 1507^60203 1614-13417 I728'i2357 1 850^09222 1980^59867 2 1 20^24058 2269^65742 2429-53344 26oo^6oo78 2783^64283 2979-49783 3 1 89^06268 34 1 3^29707 3653 22786 3909-95381 4184-65058 4478-57612 4793^07645 5129-59180 548966323 5874-93965 6287-18543 6728-28841 7200-26859 7705 -28740 8245-65751 8823-85354 9442-52329 10104-49992 10812-81491 11570-71196 12381 -66179 (79) Present Value 13-83247 13-86212 13-88984 13-91573 13-93994 13-96256 13-98370 14-00346 14-02192 14 03918 14-05531 14-07038 14-08447 14-09764 14-10994 I4-I2144 I4-13219 14-14223 14-15162 14-16039 14-16859 14-17625 I4-18341 I4-19010 14-19636 14-20220 14-20767 14-21277 14-21755 14-22201 14-22617 14-23007 14-23371 I4-23711 14-24029 1424326 14*24604 14^24863 14-25106 14-25333 14-25545 14-25743 14-25928 14-26101 14-26262 14-26413 14-26555 14-26686 14-26810 14-26925 Years 51 52 53 54 55 56 57 58 59 60 61 62 65 66 69 I 70 71 72 74 I 75 i y6 77 78 79 80 81 82 83 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 8°/. INTEREST TABLES Interest tables For explanation see pp. 8-13 (80) ONE POITNO ONE POUND FEB ANNUM Years Years • Amount Present Value Amount Present Value I I -08000 •92593 I'OOOOO •92593 I 2 1-16640 •85734 2^08000 I -78326 2 3 I -25971 •79383 3-24640 2-57710 3 4 1-36049 •73503 4*50611 3'3i2i3 4 5 5 1-46933 •68058 5-86660 3-99271 6 I -58687 •63017 ! 7*33593 4-62288 6 I I -71382 •58349 8-92280 5-20637 7 1-85093 •54027 1 10-63663 5-74664 8 9 1-99900 •50025 i 12-48756 6-24689 9 10 10 2-15892 i •46319 14-48656 6-71008 II 2-33164 •42888 16-64549 7-13896 II 12 2-51817 •397 1 1 18-97713 7-53608 12 13 2-71962 ■36770 21^49530 790378 13 14 2-93719 •34046 24-21492 8-24424 '4 16 3-17217 •31524 27-15211 8-55948 15 16 3-42594 -29189 30^32428 3-85137 16 ^l 3-70002 •27027 3375023 9-I2I64 17 18 3-99602 •25025 37-45024 9-37189 il »9 4-31570 •23171 41^44626 9-60360 19 20 4-66096 •21455 45-76196 9-81815 20 21 5-03383 •19866 50-42292 10-01680 21 22 5-43654 •18394 55^45676 10-20074 22 23 5-87146 •17032 60-89330 10-37106 23 24 6-341 18 •15770 66-76476 10-52876 24 25 6-84848 •14602 73^10594 10-67478 25 26 7-39635 •13520 7995442 10-80998 26 27 7-98806 •I2519 87-35077 io^9.35i6 27 28 8-62711 -11591 95^33883 11-05108 28 29 9-31727 •10733 103-96593 11-15841 29 30 10-06266 -09938 1 13-28321 11-25778 30 31 10-86767 -09202 123-34587 11-34980 31 32 11-73708 •08520 1 34^2 1 354 11-43500 32 33 12-67605 •07889 145-95062 II -51389 33 34 13-69013 •07305 158-62667 1 1 58693 34 35 14-78534 •06763 172-31680 11-65457 35 36 15-96817 -06262 187-10215 11-71719 36 37 17-24563 •05799 203 -07032 1 1 -77518 %0 38 18-62528 •05369 220-31595 1 1 82887 2S 39 20-11530 -04971 238-94122 11-87858 39 40 21-72452 -Q4603 259-05652 1 1 -92461 40 41 23-46248 •04262 280-78104 11-96723 41 42 25-33948 •03946 304-24352 12-00670 42 43 27-36664 •03654 329-58301 12-04324 43 44 29-55597 •03383 35694965 12-07707 44 45 31-92045 •03133 386 50562 12-10840 45 46 34-47409 -02901 j 418-42607 12-13741 46 47 37-23201 -02686 452-90015 12-16427 47 48 40-21057 •02487 490-13216 12-18914 48 49 43-42742 •02303 530-34274 12-21216 49 50 46-90161 •02132 573-77016 12-23348 5^ 87< Years SI 52 53 54 55 56 60 61 62 64 65 66 $7 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 84 85 86 87 88 89 90 91 { 92 93 I 94 I 95 96 97 98 99 too ONE POUND Amount 5065374 54-70604 59-08252 63-80913 68-91386 74-42696 80-38112 86-81161 93-75654 101-25706 109-35763 118-10624 127-55474 137-75912 148-77985 160-68223 I73^5368i 187-41976 202-41334 218-60641 236-09492 254-98251 275-38111 297-41160 321-20453 346 90089 374-65296 404-62520 43699522 471-95483 509-71122 550-48812 594-52717 642 '08934 693-45649 748^93301 808-84765 873^55546 943^43990 1018-91509 100-42830 188-46256 283-53956 386-22273 497-12055 616-89019 746-24141 885 -94072 2036-81598 2199-76126 Present Value -01974 •01828 -01693 -01567 •OI451 -01344 -01244 -01 152 -01067 •00988 -00914 -00847 •00784 •00726 •00672 •00622 -00576 •00534 -00494 •00457 •00424 -00392 •00363 •00336 •003 1 1 •00288 •00267 •00247 00229 •00212 -00196 -00182 -00168 •00156 -00144 •00134 •00124 •00114 •00106 •00098 •00091 •00084 •00078 •00072 •00067 •00062 -00057 -00053 •00049 •00045 ONE POUND PER ANNUM Amount 620^67177 671-32551 726^03x55 785-11408 848-92320 917-83706 992 -26402 1072 645 14 1 1 59 -45676 1253-21330 1354-47036 1463^82799 1 58 1 -93423 1709-48897 1847-24808 1996-02793 2156-71016 2330^24698 2517^66673 2720-08007 293868648 3174-78140 3429-76391 3705-14502 4002-55662 4323-76115 4670-66205 5045-31501 5449-94021 5886-93543 6358-89026 6868-60148 7419-08960 8013 -61677 8655-70611 9349-16260 10098-09561 10906-94326 11780-49872 12723-93862 13742-85370 14843-28200 16031-74456 17315^28413 18701-50686 20198-62740 21815-51760 23561-75900 25447-69972 27484-51570 See also Tables on pp. xx-xxxi Present Value 12-25323 12-27151 12-28843 12-30410 I2-31861 12-33205 12-34449 12-35601 12-36668 12-37655 12-38570 12-39416 12-40200 12-40926 12-41598 12-42221 12-42797 1243330 12-43824 12-44282 12-44705 12-45098 12-45461 1245797 12-46108 12-46397 12-46664 12-46911 12-47139 12-47351 12-47548. 12-47729 12-47897 12-48053 12-48197 12-48331 12-48455 12-48569 12-48675 12-48773 12-48864 12-48948 12-49026 12-49098 1249165 12-49227 12-49284 12-49337 12-49386 12-49432 Years 51 52 53 54 55 56 57 58 60 6i 62 64 6s 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 ^ 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 11 1 I (81) 'h 9°/o INTEREST TABLES For explanation see pp. 8-13 ONE POUND ONE FOUND PER ANNUM Years Years Amount Present Value Amonnt Present Value I 1*09000 •91743 i-ooooo -91743 I 2 I -18810 -84168 2^09000 I -7591 1 2 3 I 29503 •77218 327810 2 53 I 29 3 4 1-41158 •70843 4^573i3 3-23972 4 S 1-53862 •64993 5-98471 3-88965 5 6 1-67710 •59627 7-52333 4-48592 6 7 I -82804 •54703 920043 5-03295 7 8 I -99256 -50187 1 1 ^02847 5^53482 8 9 2-17189 •46043 1 3^02104 5-99525 9 10 2-36736 -422/I I I5^i9293 6 4 I 766 10 II 2-58043 •38753 17-56029 6-80519 II 12 2-81266 •35553 20 •14072 7-16073 12 13 3-06580 •32618 22^95338 7*48690 13 14 3'34i>3 •29925 26 01919 7-78615 14 IS 3-64248 •27454 29 36092 8-06069 1 15 16 3-97031 -25187 33-00340 8 •31356 16 '2 4-32763 •23107 36-97370 8-54363 17 18 4-71712 -21 199 41-30134 8-75563 18 19 5-14166 -19449 46^01846 8-95011 19 20 5-60441 •17843 5i^i6oi2 9-12855 20 21 6-io88i •16370 56-76453 9-29224 21 22 6-65860 •I5OI8 62-87334 9-44243 22 23 T^n^i ■1377^ 69-53914 9-58021 23 24 7-91108 •12640 76 7898 I 970661 24 25 8-62308 •I 1597 84^70090 9^82258 25 26 9-39916 •10639 93-32398 9-92897 26 s 10-24508 •09761 I02^723i3 1002658 27 11-16714 •08955 1 12^96822 io^ir6i3 28 29 12-17218 •08215 124-13536 io^i9828 20 30 13-26768 •07537 136-30754 1027365 30 31 14-46177 •06915 149-57522 10^34280 31 32 15-76333 •06344 16403699 10^40624 32 33 17-18203 •05820 179-80032 10^46444 - 33 34 1 8 72841 , •05339 196-98234 10-51784 34 35 20-41397 •04899 215-71075 10^56682 35 36 22-25123 •04494 236 • 1 2472 • 1061176 36 37 24-25384 •04123 258-37595 10-65299 37 38 26-43668 •03783 282^62978 10-69082 38 39 28-81598 •03470 30906646 10-72552 39 40 31-40942 -03184 337-88245 10-75736 40 41 lA-izdz-j •02921 369^29187 io^78657 41 42 37-3^753 •02680 403-52813 10-81337 42 43 40-67611 •02458 440^84566 1083795 43 44 44-33696 •02255 481-52177 10-86051 44 45 45 48-32729 •02069 525-85873 10-88120 46 52-67674 •01898 574^18602 10-90018 46 47 ^ 57-41765 •01742 626^86276 10-91760 62-58524 •01598 684 •28041 10-93358 48 49 68-21791 -01466 74686565 10-94823 49 SO 74-35752 •01345 81508356 10-96168 50 INTEREST TABLES 9°A I t (82} Years 51 52 53 54 55 56 57 58 59 60 61 62 65 66 $7 68 69 70 71 72 73 74 75 76 79 80 81 82 P 85 86 U 89 90 91 92 93 94 95 96 u 99 100 ONE POUND Amount 81-04970 88-34417 9629514 104-96171 114*40826 1 24^70501 135^92846 1 48 •I 6202 161-49660 176-03129 191*87411 209-14278 227-96563 248-48253 270-84596 295*22210 321-79209 350-75338 382-32118 416-73009 454-23579 495*11702 539-67755 588-24853 641-19089 698-89807 761-79890 830-36080 90509327 986-55167 1075-34132 1172*12204 1277 -61302 1392-59819 1517 •-93203 1654^5459 1 1803*45504 1965*76600 2142-68494 2335^52658 2545^72397 2774^839x3 3024-57465 3296-78637 3593-49715 3916*91189 4269*43396 4653-68302 5072*51449 5529*04079 Present Value •01234 *OII32 •01038 -00953 •00874 •00802 •00736 •00675 •00619 •00568 •00521 •00478 •00439 •00402 •00369 •00339 -00311 *oo285 •00262 •00240 •00220 •00202 •00185 •00170 •00156 •00143 •00131 •00120 •001 10 •ooioi *ooo93 •00085 -00078 •00072 •00066 •00060 •00055 •00051 •00047 -00043 •00039 *ooo36 •00033 •00030 •00028 *00026 •00023 •00021 •00020 *oooi8 ONE POUND PEE ANNUM Amount 889*44108 970*49077 1 058^83494 ii55'i3oo9 1260-09180 1374*50006 1499-20506 1635-13352 1783-29553 1944-79213 2120-82342 2312-69753 2521-84031 2749-80594 2998^28847 3269^13444 3564-35654 3886^14862 4236*90200 46i9^223i8 5035-95327 5490-18906 5985-30608 6524-98362 7ii3*232i5 7754^42304 8453*32112 9215-12002 10045-48082 10950-57409 1 1937-12576 13012-46708 I4i84^589ii 1 5462^202 1 3 16854^80033 18372^73236 20027-27827 21830*73331 23796*49931 25939-18425 28274*71083 •30820*43481 33595*27394 36619*84859 39916*63497 43510-13211 47427-04400 51696*47796 56350*16098 61422*67547 Present Value 10-97402 10-98534 10-99573 1 1 -00525 1 1 -01399 1 1 -02201 1 1 -02937 11-03612 iro423i 1 1 ^04799 Years 51 52 53 54 55 56 57 58 59 60 6ee also Tables on pp. xx-zzxi 1 1 -05320 1 61 1 1 -05798 1 62 1 1 06237 63 1 1 -06640 64 1 1 -07009 65 1 1 -07347 66 1 1 -07658 67 11-07943 68 1 1 -08205 69 1 1 -08445 70 11-08665 71 1 1 ^08867 72 1 1 09052 73 1 1 -09222 74 11-09378 75 1 1 09521 76 1 1 -09653 ^ 1 1 -09773 1 1 09883 79 • 1 1 -09985 80 11-10078 81 11*10163 82 11-10241 83 11-10313 84 1 1 -10379 85 ii^i044o 86 IIT0495 87 II -10546 88 II -10593 89 11-10635 90 11-106/5 91 11-10711 92 11-10744 93 II -10774 94 II -10802 95 11-10827 96 11 -10851 U ii^io872 11-10892 99 11-10910 100 1i t^ i r t ) ' ' I I « (83) D2 107< INTEKEST TABLES ONE POUND ONE POUND PEE ANNUM 1 1 1 Tears .j Tears 1 Amount Present Value Amount Present Value I I-IOCXK) •90909 I^OOOOO •90909 I 2 I-2IOOO -82645 2^10000 1-73554 2 3 1-33100 •75131 3-31000 2^48685 3 4 1-46410 -68301 4-64100 3-16987 4 5 I -6105 1 -62092 6-10510 3^79079 5 6 I 77156 •56447 7-71561 4^35526 6 7 I -94872 -51316 9-48717 4^86842 7 8 2-14359 -46651 11-43589 5*33493 8 ' 9 2-35795 -42410 13^57948 1 5-75902 9 ' 10 2-59374 •38554 1 5^93742 1 6^14457 10 II 2-85312 -35049 18-53117 j 6^49506 II 12 3-13843 •31863 21-38428 ! 6^81369 12 1 ^3 3-45227 •28966 24-52271 1 7-10336 13 4 3-79750 •26333 27-97498 7*36669 1 14 1 ■ IS 4-17725 I -23939 31-77248 7^60608 IS i6 4*59497 -21763 35*94973 7-82371 16 17 5-05447 -19784 40^54470 8-02155 17 i8 5-55992 -17986 45-59917 8-20141 18 19 6-11591 •16351 51-15909 8^36492 19 20 6-72750 -14864 57-27500 8-51356 20 21 7-40025 -13513 64^00250 864869 21 22 8-14027 -12285 71-40275 8-77154 22 23 8-95430 -II168 79-54302 8-88322 23 24 9-84973 -IOI53 88-49733 8*98474 24 2S 10-83471 -09230 98-34706 9*07704 2S 26 11-91818 -08391 109-18177 916095 26 27 13-10999 -07628 i2i^o9994 9-23722 27 28 14-42099 -06934 134-20994 9-30657 28 29 15-86309 •06304 148-63093 9*36961 29 30 17-44940 -05731 164-49402 9-42691 30 31 19-19434 •05210 i8r94342 9-47901 31 32 21-11378 1 -04736 201-13777 9-52638 32 33 23-22515 -04306 222-25154 9-56943 33 34 25-54767 -03914 245-47670 9-60857 34 35 28-10244 •03558 27^02437 964416 35 36 30 9 I 268 -03235 299 •1268 1 9-67651 36 37 3400395 -02941 330-03949 9-70592 37 38 37-40434 •02673 364-04343 9-73265 38 39 41-14478 -02430 401-44778 9-75696 39 40 45-25926 -02209 442-59256 9-77905 40 41 49-78518 -02009 487-85181 . 9-79914 41 42 54-76370 -01826 537-63699 9^81740 42 43 60-24007 •01660 592 -40069 9^83400 43 44 66-26408 -01509 652-64076 9-84909 44 4S 72-89048 -01372 j 7i8^90484 9^86281 45 i 46 80-17953 ' -01247 791-79532 9-87528 46 ! 47 88-19749 •01 134 871-97485 9^88662 47 1 48 97-01723 •0103 1 960-17234 9-89693 48 49 106-71896 •00937 1 1057-18957 9-90630 1 49 5° 117-39085 ; •00852 1163-90853 9-91481 1 SO INTEEEST TABLES » Years 51 52 S3 54 55 56 57 59 60 61 62 63 65 66 67 68 69 70 71 72 73 74 75 76 For explanation see pp. 8-13 80 81 82 83 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 10°A ONE POUND Amount i Present Value 129-12994 142 -04293 156-24723 171 -87195 189-05914 207 -96506 228-76156 251-63772 276^80149 304-48164 334-92980 368-42278 405-26506 445-79157 490-37073 539-40780 593*34858 652-68344 717-95178 789-74696 868-72165 955-59382 105 1 -15320 1 156-26852 1271-89537 1 399 •08491 1538-99340 1692*89274 1862-18201 2048 -4002 1 2253-24024 2478-56426 2726-42069 2999-06275 3298-96903 3628-86593 3991-75253 4390*92778 4830-02056 5313-02261 5844-32487 6428-75736 7071-63310 7778-79641 8556-67605 9412-34365 10353*57802 1 1388-93582 12527-82940 13780-61234 •00774 •00704 •00640 •00582 •00529 •00481 •00437 •00397 •00361 •00328 •00299 •00271 •00247 •00224 •00204 •00185 •00169 •00153 •00139 •00127 •001 15 •00105 •00095 •00086 •00079 •00071 •00065 •00059 •00054 ■00049 •00044 -00040 •00037 •00033 •00030 -00028 -00025 -00023 •00021 •00019 •00017 •00016 •00014 •00013 •00012 -0001 1 •oooio •00009 -00008 -00007 ONE POUND PEE ANNUM Amount 1 28 1 -29938 I4IO-42932 1552-47225 1 708 -7 1948 1880-59x42 2069-65057 2277-61562 2506-37719 2758-01490 3034-81640 3339*29803 3674^22784 4042^65062 4447^91568 4893*70725 5384*07798 5923*48578 6516^83435 7169-51779 7887-46957 8677 9545 1 050 1 11552 12708 13980 15379 16918 18611 20474 22522 24775 27254 29980 32979 36278 39907 43899 48290 53120 -21652 -93818 •53199 •68519 95371 •84909 '93399 92739 82013 00215 -40236 •64260 •20686 •62754 -69030 65932 52526 27778 20556 22612 58433 64277 70706 77777 85556 941 13 103525 1 13879 125268 137796 •24873 •57360 •33096 -96406 -76046 •43651 •78016 -35818 -29400 -12340 Present Value 9*92256 9-92960 9*93600 9-94182 9 947 I I 9-95191 9*95629 9 -96026 9-96387 9-96716 9-97014 9-97286 9-97532 9-97757 9-97961 9-98146 9-98315 9-98468 9-98607 9^98734 9-98849 9^98954 9-99049 9-99135 9-99214 9-99285 9-99350 9-99409 9^99463 9-99512 9-99556 9-99597 999633 9-99667 9-99697 9^99724 9^99749 9 '997 7 2 9^99793 9-99812 9-99829 9-99844 9-99859 999871 9-99883 9-99894 9-99903 9-99912 9-99920 9-99927 51 52 53 54 55 56 57 58 59 60 61 62 65 66 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 (84) See also Tables on pp. xx-xxxi. For 15% see p. xl (85) Years 10 20 30 40 50 60 70 80 90 100 10 20 30 40 SO 60 70 80 90 100 10 20 30 40 50 60 70 80 90 100 INTEREST TABLES AMOUNT OF ONE POUND AT END OF YEAB 0/ ^o 1-10462 1-22019 1-34785 I -48886 I 64463 1-81670 2-00676 2-21672 244863 2-70481 U % 1-13227 I -28204 1-45161 I -64362 I -86102 2-10718 2-38590 2-70149 3-05881 3 '46340 U% 1-16054 I -34686 I -56308 I -81402 2-10524 2-44322 2-83546 3-29066 3-81895 4-43205 -3 0/ L4 /o 1-18944 1-41478 I -68280 2-00160 2-38079 2-83182 3 36829 4-00639 476538 5-66816 I -21899 1-48595 1-81136 2 -20803 2-69159 3-28103 3-99956 4-87544 5-94313 7-24465 I -24920 I -56051 I -94939 2-43519 3-04205 3-80013 4-74714 5-93015 7-40796 9-25405 1-28008 1-63862 209757 2-68506 3-43711 4-39979 5-63210 7-20957 9 22886 11-81372 1-31165 1 -72043 2 -25660 295987 3-88232 5-09225 6-67926 876085 1 1 -491 18 15-07242 3% 3i% I -34392 I -8061 1 2-42726 3-26204 4-38391 5 89160 7-91782 10-64089 14-30047 19-21863 1-37689 I -89584 2-61037 3-59420 4-94884 6-8,1402 9-38219 12-91828 17-78711 24-49097 3X 0/ 2^ /o I -41060 I -98979 2-80679 3-95926 5-58493 7-87809 1 1 -1 1282 15-67574 22-11217 31-19141 31 0/ ''O 1-44504 2-08815 3-01747 4-36038 6-30094 9-10513 13-15732 19-01290 27-47448 39-70183 For explanation see pp. 8-13 (86) Years 10 20 30 40 50 60 90 100 10 20 30 40 so 60 90 100 10 20 30 40 50 60 70 80 90 100 '? \ INTEREST TABLES AMOUNT OF ONE POUND AT END OF TEAR Years 4% *4 TO 4i% 4f % Years 10 I -48024 I-51621 1-55297 1 1-59052 10 20 2-19112 2-29891 2-41171 2-52977 20 30 3-24340 3-48564 3-74532 4-02366 30 40 4-80102 5-28497 5-81636 639972 40 SO 7-10668 8-01315 9-03264 10-17892 SO 60 10-51963 12-14965 14-02741 16-18982 60 ss 15-57162 18-42148 21-78413 25-75030 70 23-04980 27-93091 33-83009 40-95647 80 90 34-11933 42-34925 52-53710 65-14226 90 100 50 ■50495 64-21055 81-58852 103-61036 100 10 5% 5i% 6% 6i% zo I 62889 I -70814 1-79085 I -87714 20 265330 2-91776 3-20714 352365 20 30 4-32194 4-98395 5-74349 6-61437 30 40 7-03999 8-51331 10-28572 12-41607 40 50 1 1 -46740 14-54196 18-42015 23-30668 SO 60 18-67919 24-83977 32-98769 43-74984 60 z° 3042643 4242992 59-07593 82-12446 £ 80 49-56144 72-47643 105-79599 154-15891 90 80-73037 123-80021 ! 189-46451 289-37746 90 100 131-50126 211-46864 339-30208 543-20127 100 10 7% 8% 9% 10% 10 I -96715 2-15892 2-36736 2-59374 20 3-86968 4-66096 5-60441 672750 ao 30 7-61226 10-06266 1326768 17-44940 30 40 14-97446 21-72452 31-40942 45-25926 40 50 29-45703 46-90161 74-35752 117-39085 SO 60 57-94644 101-25706 176-03129 304-48164 60 70 113-98938 218-60641 416-73009 789-74696 1 70 80 224-23437 471-95483 986-55167 2048-40021 80 90 441-10293 IO18-91509 2335-52658 53 1 3 -0226 1 90 100 867-71623 2199-76126 5529-04079 13780*61234 100 ii M (87) I INTEBEST TABLES THE PEESENT VALUE OF ONE POUND DUE AT END OF YEAE Years 10 20 30 40 50 60 70 80 90 100 10 20 30 40 50 60 70 80 90 100 10 20 30 40 SO 60 70 80 90 100 1 0/ ^o •90529 •81954 74192 •67165 •60804 •55045 •49831 •451 12 •40839 •36971 li"- o •88318 •78001 •68889 •60841 •53734 •47457 •4I9I3 •37017 •32692 '28873 0/ ^o •82035 •67297 •55207 •45289 •37153 •30478 •25003 •20511 •16826 •13803 2i% •80051 •64082 •51298 •41065 •32873 •26315 •21065 •16863 •13499 •10806 3% •74409 •55368 •41 199 •30656 •2281 1 •16973 •12630 •09398 •06993 •05203 3i Ox ^O •72627 •52747 •38309 •27823 •20207 •14676 •10658 •07741 •05622 •04083 For explanation see pp. 8- 13 2 0/ 'X) li% •86167 •74247 •63976 •55126 •47500 •40930 •35268 •30389 •26185 •22563 •84073 •70682 •59425 •49960 •42003 •35313 •29689 •24960 •20985 •17642 2* % •78120 •61027 •47674 •37243 •29094 •22728 •17755 •13870 •10836 •08465 If % •76240 •58125 •44314 •33785 •25758 •19638 •14972 •II414 •08702 •06635 3i% 31 0/ /o •70892 •50257 •35628 •25257 •17905 •69202 •47889 •33140 •22934 •I587I •12693 •10983 •08999 •07600 •06379 1 •05260 •04522 ' •03640 •03206 •02519 Years 10 20 30 40 50 60 70 80 90 100 10 20 30 40 50 60 70 80 90 100 10 20 30 40 SO 60 70 80 90 100 (88) INTEREST TABLES THE PEESENT VALUE OF ONE POUND DUE AT END OF YEAE ~^ Years 10 ao 30 40 SO €0 90 100 zo ao 30 40 SO 60 90 100 zo ao 30 40 SO 60 70 80 90 100 0/ ^o •67556 •45639 •30832 •20829 •1407 1 •09506 •06422 •04338 •02931 •01980 5% •61391 •37689 •23138 •14205 08720 •05354 •03287 •02018 •01239 •00760 .7% •50835 •25842 •13137 •06678 •03395 •01726 •00877 •00446 •00227 •CGI 15 For 15% see p. xl 4i% •65954 •43499 •28689 •18922 ■12479 •08231 •05428 •03580 •02361 •01557 '2 /O •58543 •34273 •20064 •I 1746 •06877 •04026 •02357 •01380 •00808 •00473 8% •46319 •21455 •09938 •04603 •02132 Tta /o •64393 •41464 •26700 •17193 •11071 •07 1 29 •04590 •02956 •01903 •01226 6% •55839 •31 180 •17411 •09722 •05429 •03031 •01693 •00945 •00528 •00295 9% •42241 •17843 •07537 •03184 •01345 •00988 •00568 •00457 •00240 •00212 j •ooioi •00098 •00043 •00045 ■00018 4-^ 0/ 4 /O •62872 •39529 •24853 •15626 •09824 •06177 •03883 •02442 •01535 •00965 6i9 O •53273 •28380 •15119 •08054 •04291 •02286 •OI218 •00649 •00346 •00184 •38554 •14864 •05731 •02209 •00852 •00328 •00127 •00049 •00019 •00007 Years ZO ao 30 40 SO 60 70 80 90 zoo zo ao 30 40 SO 60 70 80 90 zoo zo ao 30 40 SO 60 70 80 90 100 (89) Years 10 30 SO 60 90 100 ID 20 30 40 50 60 70 80 90 100 10 20 30 40 50 60 70 80 90 100 INTEREST TABLES THE AMOUNT OF ONE POUND PEB ANNUM 1% u 0/ ^o 10-46221 22-01900 3478489 48-88637 64-46318 81-66967 100-67634 121 -67152- 144-86327 170-48138 10-58167 22 -56298 36-12907 51-48956 68-88179 88-57451 110-87200 136-11880 164-70501 197-07234 0/ ^o 10-94972 24-29737 40-56808 60-40198 84-57940 1 14-05154 149-97791 I9377I95 247-15665 312-23230 2i 0/ ^o 11-07571 24-91152 42-19526 63-78618 90-75762 124-45043 166-53962 219-11757 28479813 366-84650 0/ ''O 1 1 46388 26-87037 47-57542 75-40126 112-79687 16305344 230-59406 321-36302 443 -34890 607-28773 31 Q O 11-59675 27-56424 49-54980 79-82158 121-50263 178-89303 257-91354 366-71643 516-52651 722-79916 For explanation see pp. 8-13 1^^ O/ 2 /o 1 0/ 2 /O 1 1 -20338 25-54466 43-90270 67-40256 97-48435 135-99159 1 85 -284 1 1 248-38271 329-15425 432-54865 3i % 11-73139 28-27968 5 1 -62267 84-55028 130-99791 196-51688 288-93786 419-30678 603-20503 862-61166 (90) 14 70 10-70272 23-12367 37-53868 54-26789 73-68283 96-21465 122-36375 152-71085 187-92990 228-80304 10-82540 23-70161 39-01715 57-23413 78-90222 104-67522 135-33076 171-79382 215-16462 266-75177 2i% 11-33276 26-19740 45-69461 71-26815 104-81170 148-80914 206-51843 282-21287 381-49757 511-72445 31% 11-86784 29-01739 53-79924 89-61010 141-35837 216-13690 324-19515 480-34408 705-98614 1032-04883 Years 10 20 30 40 50 60 90 100 10 20 30 40 50 60 90 100 10 20 30 40 50 60 70 80 90 100 Years 10 20 30 40 50 60 70 80 90 ZOO 10 20 30 40 SO 60 70 80 90 100 10 20 30 40 50 60 90 100 INTEREST TABLES THE AMOUNT OF ONE POUND PEE ANNUM 4% 4i% 12-0061 1 12-14622 29-77808 30-56250 56-08494 58-48553 95-02552 100-82283 ' 152-66708 165-01525 237-99069 262-34474 364-29046 ' 409-9171 1 551-24498 633-66848 ' 82798333 972-92354 1237-62370 1487-30697 5% 12-57789 33-06595 66-43885 120-79977 209-34800 353-58372 588-52851 971-22882 1594-60730 2610-02516 54 O/ 2 /O 12-87535 34-86832 72-43548 136-60561 246-21748 433-45037 753-27120 1299*57139 2232-73IOI 3826-70246 7% 13-81645 40-99549 94-46079 199-6351 1 406-52893 . 813-52038 1614-13417 3189-06268 6287-18543 12381-66179 8% 14-48656 4576196 113-28321 259-05652 573-77016 1253-21330 2720-08007 5886-93543 12723-93862 27484-51570 41 a 2 /O 12-28821 31-37142 61-00707 107-03032 178-50303 289-49795 461-86968 729-55770 1 145 -26900 1790-85595 6 0/ 13-18079 36-78559 79-05819 154-76197 290-33590 533-12818 967-93217 1746-59989 3I4I -07519 5638-36806 0/ 't) 15-19293 51-16012 136-30754 337-88245 815-08356 1 944 792 1 3 4619-22318 10950-57409 25939-18425 61422-67547 (91) H% 12-43209 32-20563 63-65594 113-67841 193-24036 319-78559 521-05885 841-18887 1350-36345 2160-21801 ii% 13-49442 38-82531 86-37486 175-63192 343-17967 657-68984 1248-06867 2356 29087 4436 57630 8341-55802 10 0/ ^o 15-93742 57-27500 164-49402 442-59256 1 163-90853 3034-81640 7887-46957 204^4-00215 53I20-226I2 1 37796 -1 2340 Years 10 20 30 40 50 60 70 80 90 100 10 20 30 40 50 60 70 80 90 100 10 20 30 40 50 60 70 80 90 zoo li ( INTEREST TABLES THE PEESENT VALUE OF OWE POUND PEE ANNUM DUE AT END OF TEAE Years 1% li% u% 11% Years 10 9-47130 9-34553 9-22219 9-10122 10 20 18-04555 17-59932 17-16864 16-75288 20 30 25-80771 24-88891 24-01584 23-18585 30 40 32-83469 31-32693 29-91585 28-59423 40 50 39-19612 37-01288 34-99969 33-14121 SO 6o 44-95504 42-03459 39-38027 36-96399 60 i;^ 50-16851 46-46968 43-15487 40-17790 70 54-88821 50-38666 46-40732 42-87994 80 90 59-16088 53-84606 49-20985 45-15161 90 zoo 10 63-02888 56-90134 51-62470 47-06147 100 2% 2i% 2\% 21% 8-98258 8-86622 8-75206 8-64008 10 ao 16-35143 15-96371 15-58916 15-22725 20 30 22-39646 21-64533 20-93029 20-24930 30 40 27-35548 26-19352 25-10277 24-07810 40 SO 31-42361 29-83440 28-36231 26-99717 50 60 34-76089 32-74895 30-90866 29-22266 60 70 37-49862 35-08208 32-89786 30-91937 70 80 39-74451 36-94978 34-45182 32-21294 80 90 41-58693 38-44489 35-66577 33-19915 90 100 10 43-09835 39-64174 36-61410 33-95104 100 3% 3i% 3i% 3f % 8-53020 8-42240 8-31661 8-21279 10 20 14-87748 14-53935 14-21240 13-89620 20 30 19-60044 18-98192 18-39205 17-82925 30 40 23-11477 22-20843 21-35507 20-55099 40 SO 25 72976 24-55176 23-45562 22-43449 SO 6o 27-67556 26-25366 24-94474 23-73792 60 70 29-12342 27-48970 26 -00040 2463991 2 8o 30-20076 28-38740 26-74878 25-26411 90 31-00241 29*03937 27-27932 25-69607 90 100 . 31-59891 29-51288 27-65543 25-99499 100 For explanation see pp. 8-13 (92) INTEREST TABLES THE PEESENT VALUE OF ONE POUND PEE ANNUM DUE AT END OF YEAE Years 10 20 30 40 SO 60 70 80 90 100 10 20 30 40 SO 60 70 80 90 100 10 20 30 40 SO 60 70 80 90 zoo 0/ '^ 8-1 1090 1 3 59033 17-29203 19-79277 21-48219 22-62349 23-39452 23-91539 24-26728 24-50500 u /o 7-72173 12-46221 15-37245 17-15909 18-25592 18-92929 19-34268 19-59646 19-75226 19-84791 7% 702358 10-59401 1 2 -40904 I3-3317I 13-80075 14-03918 14-16039 14-22201 14-25333 14-26925 4i% 8-01089 1 3 -29437 16-77902 19-07727 20-59306 21-59278 22-25213 22 -68700 22-97381 23-16297 4i% 7-91272 13-00794 16-28889 18-40158 19-76201 20-63802 21 -2021 1 21-56534 21-79924 21-94985 5* O/ ^O O/ ^o 7-53763 1 1 -95038 14-53375 16-04612 16-93152 17-44985 17-75330 17-93095 18-03495 18-09584 I6-I6I43 16-38454 16-50913 16-57870 16-61755 8 o> ^o 9 ^o 6-71008 9-81815 11-25778 1 1 -92461 12-23348 12-37655 1 2 -44282 12-47351 12-48773 12-49432 6-41766 9-12855 10-27365 10-75736 10-96168 11-04799 1 1 -08445 1 1 -09985 1 1 -10635 11-10910 See also Tables pp. xx-xxxi. For 15% see p. xl (93) 41 0/ ''O 7-81635 12-73067 15-82042 17-76302 18-98437 19-75227 20-23506 20-53861 20-72945 20-84944 6i Oy 2 /O 7-36009 7-18883 1 1 -46992 1 1 01851 13-76483 13-05868 15-04630 14-14553 15-76186 14-72452 15-03297 15-19728 15-28482 15-33145 15-35629 10 0/ ^o 6-14457 8-51356 9-42691 9-77905 9-91481 9-96716 9-98734 9-99512 9 998 I 2 9-99927 Years 10 20 30 40 SO 60 70 80 90 100 10 20 30 40 50 60 70 80 90 100 10 20 30 40 50 60 70 80 90 100 I I !i i INTEREST TABLES THE PBESENT VALUE OF A PERPETUITY OF £1 PER ANKUM At per Cent. £ At percent. £ £ ». d. • £ «. d. 1 or 2 6 800-00000 5f or 5 2 6 19-51220 i , . 5 400-00000 5t » 5 5 19-04762 i . . 7 6 266-66667 ^ 51 » 5 7 6 18-60465 5 . , 10 200-00000 Sk n 5 10 18-18182 .^' , 12 6 160-00000 s\ „ 5 12 6 1777778 f > , 15 ■ 133-33333 5^ M 5 15 17-39130 i . » 17 6 114-28571 Ss '» 5 17 6 17-02128 I , , I 100-00000 6 16-66667 Ik , , I 2 6 88-88889 6^ „ 6 2 6 16-32653 H , ' I 5 80-00000 6i „ 6 5 16-00000 It' *2 > . I 7 6 72-72727 6§ „ 6 7 6* 15-68627 , I 10 66-66667 6| „ 6 10 15-38462 I# , , I 12 6 61-53846 6g „ 6 12 6 15*09434 H , ' I 15 57-14286 6f „ 6 15 14-81481 li » . I 17 6 53-33333 6|» 6 17 6 14-54545 2 , , 2 50 -00000 7 » 7 14*28571 2h , , 2 2 6 47-05882 7* » 7 2 6 1403509 2i , . 2 s 44-44444 1 7i >. 7 5 13-79310 2f , , 2 7 6 42-10526 i n ,, 7 7 6 13-55932 2^- » , 2 10 40-00000 ■ 7i » 7 10 13*33333 2^ , , 2 12 6 38-09524 7^ ,, 7 12 6 13-11475 2i , . 2 15 36-36364 71 ., 7 IS 12-90323 H » , 2 17 6 34-78261 71 ., 7 17 6 12-69841 3 » > 3 33*33333 8 „ 8 12-50000 3^ , » 3 2 6 32 00000 8* „ 8 2 6 12-30769 3i » > 3 5 30-76923 8i „ 8 5 12-12121 3^ , » 3 7 6 29-62963 8f „ 8 7 6 1 1 -94030 3^ » , 3 10 28-57143 81 „ 8 10 1 1 -7647 1 31 . , 3 12 6 27 5862 1 8f „ 8 12 6 1 1 "59420 3f , . 3 15 26-66667 8f „ 8 15 11-42857 3i , » 3 17 6 \ 25 80645 8| „ 817 6 11-26761 4 > , 4 25-00000 9 » 9 ii-iiiii 4^, , 4 2 6 24-24242 9^ ,, 9 2 6 10-95890 4t , > 4 5 23-52941 9i M 9 5 io-8io8i 4i , . 4 7 6 22-85714 -9f » 9 7 6 10-66667 4^ » > 4 10 22-22222 9h „ 9 10 10*53632 4^ , , 4 12 6 21-62162 9^ » 9 12 6 10-38961 4f , . 4 15 21-05263 91 n 9 15 10-25641 Ai . ' 4 17 6 20-51282 9i » 9 17 6 10-12658 5 » » 5 20-00000 10 „ 10 lo-ooooo For explanation see p. 1 3 (94) INTEBEST TABLES THE PRESENT VALUE OF THE REVERSION OF A PERPETUITY OF £1 Years Deferred 1% I 2 3 4 5 6 7 8 9 10 II 12 13 14 15 16 \l 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 39 40 41 42 43 44 45 46 47 48 49 SO 99-00990 98 02960 97-05901 96-09893 95-14657 94*20452 93*27181 92-34832 91*43398 9052870 8963237 88-74492 87-86626 86-99630 86-13495 85-28213 84-43775 83-60173 82-77399 81-95445 81-14302 80-33962 79-54418 78-75661 77*97684 77-20480 76-44039 75*68356 74*93421 74-19229 73*45771 72-73041 72-01031 71-29733 70-59142 69-89250 69-20049 68-51534 67-83697 67-16531 66-50031 65-84189 65 18999 64-54455 63-90549 63-27276 62-64630 62-02604 61-41192 60-80388 u Oy 'X) li Oy ^O .f% Years Deferred 79-01235 78-03688 77-07347 76-12194 75-18217 74-25399 73-33727 72-43188 71*53766 7065447 69-78220 68-92069 68-06982 67-22945 66-39945 65*57971 64-77008 63*97045 63-18069 62-40068 61-63031 60-86944 60-11796 59-37577 58-64273 57*91875 57-20370 56-49748 55*79998 55*i"09 54*43071 53-75^73 53-09504 52-43954 51-79214 51-15273 50-52122 49-89750 49-28148 4867307 48-07216 47-47868 46-89252 46-31360 45-74183 45-17712 44-61938 44-06852 43-52446 42-98712 65-68145 64-71079 63-75447 62-81229 61-88402 60-96948 60-06846 59-18074 58-30615 57-44448 56*59555 55*75916 54*93514 54*12329 53*32344 52-53541 51-75902 50-99411 50-24050 49*49803 48-76653 48-04584 47-33581 46-63626 45-94706 45-26804 44-59905 43-93995 43*29059 42-65083 42 -02052 41-39953 40-78771 40-18494 39-59107 39*00599 38-42954 37-86162 37-30209 36-75082 36-20771 35-67262 35*14544 34-62605 34*11433 33*61018 33*11348 32-62412 32-14199 31-66698 56-16006 55*19416 54-24488 53-31192 52-39500 51*49386 50-60822 49*73781 48-88237 48-04164 47-21537 46-40331 45-60522 44-82085 44-04998 43-29236 42-54778 41*81600 41-09680 40-38998 39-69531 3901259 38-34161 37-68217 37-03408 36*39713 35*77"3 35*15591 34*55126 33-95701 33-37298 32-79900 32-23489 31-68048 31-13561 30-60011 30-07382 29-55658 29-04823 28-54863 28-05762 27-57506 27-10079 26-63469 26-17660 25-72639 25-28392 24-84906 24-42168 24-00165 z 2 3 4 5 6 7 8 9 10 II 12 13 14 IS 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 4 49 50 For explanation see pp. 13, 14. See also Tables on pp. xxxii-xxxix (95) INTEREST TABLES For explanation see pp. 13, 14 (96) THE PEE8ENT VALUE OF THE BEVEE8I0N OF A PERPETUITY OF £1 Years Deferred 9 0/ ^ /o 2i% 2i% 21% Years Deferred I I 49-01961 43-46644 39-02439 35-39040 2 48-05844 42-50997 38-07258 34-44322 2 3 47-II6I2 41-57454 37*14398 33-52138 3 4 46-19227 40-65970 36-23803 32-62421 4 5 45-28654 39-76499 35-35417 31-75106 ■ 5 6 44-39857 38-88996 34-49188 30-90127 6 7 43-52801 38-03419 33-65061 30-07423 I 8 42-67452 37-19726 32-82986 29-26933 9 41-83776 36-37873 32-02913 28-48596 9 10 41-01742 35-57822 31-24794 27-72356 10 II 40-21315 34-79533 30-48579 26-98157 II 12 3942466 34-02966 29-74224 26-25944 12 13 38-65163 33-28084 29-01682 25 55663 13 14 37-89375 32-54850 28-30909 24-87263 14 15 37-15074 31-83227 27-61862 24 20694 15 16 36-42229 31-13181 26-94500 23-55907 16 ^1 3570813 30-44676 26-28780 22-92853 17 18 35-00797 29-77678 25-64664 22-31487 18 19 34-32154 29-12154 25-021 II 21-71764 • 19 20 33-64857 28-48073 24-41084 21 13639 20 21 32-98879 27-85401 23-81545 20-57069 21 22 32-34195 27-24109 23-23459 20-02014 22 23 31*70780 26-64165 22-66789 19-48432 23 24 31-08607 26-05540 22-11501 18-96284 24 25 30-47654 25-48206 21-57562 18-45532 25 26 29-87896 24-92133 21-04939 17-96138 26 27 29-29310 24-37294 20-53599 17-48067 27 28 28-71873 23-83661 20-03511 17-01281 38 29 28-15562 23-31209 19-54645 16-55748 29 30 27-60354 22-79911 19-06971 16-11434 30 31 27-06230 22-29742 18 60460 15-68305 31 32 26-53167 21-80677 18-15082 15-26331 32 33 26-01144 21-32691 17-70812 14-85481 33 34 25-50141 20-85761 17-27621 14-45723 34 35 25-00138 20-39864 16-85484 14-07030 35 36 24-51116 19-94977 16-44375 13-69372 36 % 24-03055 23-55936 19-51078 19-08145 16-04268 15-65140 13-32722 12-97053 39 2309741 18-66156 15-26966 12-62339 39 40 22-64452 18-25092 14-89723 12-28554 40 41 22-20051 17-84931 14-53388 1 1 -95673 41 42 21-76521 17-45654 14-17939 11-63672 42 43 21-33844 1 7 0724 1 13-83355 11-32527 43 44 20-92004 16-69673 13-49615 11-02217 44 45 20-50984 16-32932 13-16698 10-72717 ■ T 45 46 20-10769 15-97000 12-84583 10*44007 46 ^2 19-71342 15-61858 12-53252 10-16065 47 48 19-32688 15-27489 12-22685 9-88871 48 49 18-94792 14-93877 1 1 -92863 9-62405 49 50 18-57639 14-61004 1 1 -63769 936647 SO INTEREST TABLES Years Deferred THE PEESENT VALUE OF THE BEVEESION OF A PERPETUITY OF £1 I 2 3 4 5 6 I 9 10 II 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 3^ 33 34 35 36 37 38 39 40 41 42 43 44 45 46 % 49 50 3% 32*36246 31*41986 30*50472 29*61623 28*75362 27*91614 27*10305 26 3 I 364 25*54722 24*80313 24*08071 23-37933 22*69737 22-03726 21-39539 20*77223 20*16721 19*57982 19-00953 18*45585 17*91831 17*39641 16*88972 16*39779 15*92018 15-45649 15*00630 14*56922 14*14487 13-73289 13-33290 12*94456 12*56754 12*20149 11-84611 11*50108 11*16609 10-84087 10-52511 10-21856 9-92093 9-63197 9-35143 9-07906 8-81462 8-55788 8-30862 806662 7*83167 7-60357 31 0/ 4. /o 29*80071 28*86267 27*95416 27*07425 26*22203 25-39664 24-59723 23*82298 23*07311 22*34683 21-64342 20-96215 20-30233 19-66327 19-04433 18-44487 17-86428 17*30197 16*75735 16*22988 15-71902 15*22423 14*74501 14*28089 13-83137 13*39600 12*97433 12-56594 12-17040 11-78731 11*41628 1 1 -05693 10-70889 10-37181 10-04534 9-72914 9-42289 9*12629 8-83902 8-56080 8*29133 8*03034 7'77757 7*53276 7*29565 7*06600 684359 6*62817 6*41954 6*21747 31 0/ 2 /o 3f% See also Tables on pp. xxxii-xxxix 27*60525 26*67174 25*76979 24*89835 24*05638 23*24288 22*45689 21-69747 20*96374 20*25482 19*56988 18*90810 18*26869 17-65091 1705402 16*47731 15*92011 15*38175 14*86159 14*33903 13*87346 13*40430 12*95102 12*51306 12*08991 11*68108 1 1 *286o6 10*90441 10*53566 10*17938 9*83515 9*50256 9*18122 8-87075 8-57077 8*28094 8*00090 7*73034 7*46893 7*21636 6*97233 6-73655 6*50874 6*28864 6*07598 5*87051 5*67199 5-48018 5-29486 5*11581 25-70281 24-77380 23-87836 23-01529 22-18341 21*38160 20 60877 9-86387 9-14590 8*45388 7-78687 7-14398 6-52431 5-92705 5-35137 4-79650 4-26169 3-74621 3-24936 2-77047 2-30888 1*86398 I -43516 1*02185 0*62347 0*23948 9*86938 9*51266 9*16883 8-83742 8*51800 8-2I012 7-91337 7-62734 7-35166 7-08593 682982 6*58296 6-34502 6-1 1568 5-89463 5-68157 5-47621 5*27828 5*08750 4-90361 4*72637 4*55554 4*39088 4*23218 Years Deferred (97) I 2 3 4 5 6 7 8 9 10 II 12 13 14 15 16 18 19 20 21 22 2Z 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 E ■'I if INTEREST TABLES THE PRESENT VALUE OF THE REVERSION OF A PERPETUITY OF £1 Years Deferred I 2 3 4 5 6 9 10 iz 12 13 14 15 i6 17 i8 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 O/ ^o 24-03846 23-11391 22*22491 21-37010 20-54818 19-75786 18-99795 18-26725 17-56467 16-88910 16-23952 15-61493 15*01435 14-43688 13-88161 13-34770 12-83433 12-34070 1 1 -86606 1 1 -40967 10-97084 10-54888 10-14316 9-75304 9-37792 9-01723 8-67041 8-33694 8-01628 7-70797 7-41151 7-12645 6-85235 6-58880 6-33539 6-09172 5-85742 5-63213 5-41551 5-20723 5-00695 4-81437 4-62920 4-451 16 4-27996 4-II535 3-95706 3-80487 3-65853 3-51781 4^ 2 % 21 '26528 20-34955 19-47326 18-63469 17-83224 17-06435 16-32952 15-62633 14-95343 14-30950 13-69330 13-10364 12-53937 1 1 -99939 1 1 -48267 10-98821 10-51503 10-06223 9-62893 9-21428 8-81750 8-43780 8-07445 7*72674 7-39401 7-07561 6-77092 6-47935 6-20033 5-93333 5-67783 5-43333 5-19936 4-97546 4-76121 4-55618 4-35998 4-17223 3-99256 3 -82064 3-65611 3-49867 3-34801 3-20384 3-06587 2-93385 2 -8075 1 2-68661 2-57092 2-46021 O/ ^o 19-04762 18-14059 17-27675 16-45405 15-67052 14-92431 14-21363 13-53679 12-89218 12-27827 11-69359 1 1 -13675 10-60643 IO-IOI36 9-62034 9-16223 8-72593 8-3I04I 7-91468 7-53779 7-17885 6-83700 6-51143 6-20136 5-90606 5-62482 5-35697 5-10187 4-85893 4*62755 4-40719 4-19732 3-99745 3-80710 3-62581 3-45315 3-28871 3-13211 2-98296 2-84091 2-70563 2-57679 2-45409 2-33723 2-22593 2-11993 2-01899 I -92284 I -83128 I -74408 For explanation see pp. a o 13. 14- See also Tables on pp. (98) 15-72327 14-83328 13-99366 13-20156 12-45431 11-74935 1 1 -08429 10-45688 9-86498 9-30658 8-77980 8-28283 7-81399 7-37169 6-95442 6-56077 6-18941 5-83907 5-50855 5-19675 4*90259 4-62509 4-36329 4-11631 3-88331 3-66350 3-45614 3-26051 3-07595 2-90184 2*73758 2-58263 2*43644 2-29853 2-16842 2-04567 I -92989 I -82067 1-71760 I -62037 I -52865 I -44213 I -36050 I -28349 1-21084 1-14230 I -07764 I -01664 •95910 I -90481 xxxii-xxxix Years Deferred I 2 3 4 5 6 7 8 9 10 II 12 13 14 15 16 19 20 21 22 2Z 24 25 26 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 4 49 50 INTEREST TABLES Tie Present Value of the Perpetuity of One Year's Rent or Fine, Payable for Renewing Estates at Various Intervals and Rates of Interest YEARS' PURCHASE Years Q 0/ /o 4% 12-2549 8-0089 5-8872 4-6157 3-7690 3-1652 2-0823 1-3667 -8395 -7820 -2631 5% 9-7561 6-3439 4-6401 3-6195 2-9403 2-4564 1-5901 I -0205 •6049 •5599 •1656 6% 8% 10% — 4-7619 3021 1 2-1547 1-6380 1-2961 I -0541 -6275 •3575 -1746 •1562 -0226 Years 2 3 4 1 7 10 14 20 21 40 16-4204 10-7839 7-9675 6-2786 5-1533 4-3503 2-9076 1-9509 I -2405 I -1624 -4421 8-0906 5-2350 3-8098 2-9566 2-3894 1-9856 1-2646 •7931 •4531 •4167 •1077 6-0096 3-8504 2-7740 2-1307 1 7039 1-4009 -8629 •5162 -2731 -2479 -0483 2 3 4 7 10 14 ' 20 21 40 Number of Years' Purchase for the Renewal of any Number of Years Expired in a TEN YEARS' LEASE Years I 2 3 4 5 6 7 8 9 10 2% •82034 1*65710 2*51059 3-38115 4-26912 5-17485 6-09870 7-04102 8-00219 8-98258 I 2 3 4 5 6 7 8 9 10 2*% •78119 1-58192 2 -40267 3-24394 4-10623 4-99009 5-89604 6 -82464 7-77645 8-75206 3% •74409 1-51051 2 -29992 3-11301 3-95049 4-81310 5-70159 6-61673 7-55933 8-53020 3i° o -70892 1 -44265 2 -20207 2-98806 3-80156 4-64353 5-51497 6-41692 7-35043 8-31661 Years 4% 4^° o -67557 I -37815 2-10885 2-86876 3-65908 4-48100 5 -33581 6-22481 7-14936 8-11090 •64393 1-31683 2-02002 2*75485 3-52274 4-32519 5-16376 6-04005 6-95578 7-91272 5% 17'95 % -61391 1-25852 1-93536 2-64604 3-39225 4*17578 4-99848 5 -86232 6-76935 7-72173 •1919 •4182 -6851 I -0000 1-3714 1-8094 2-3261 2-9355 3-6543 4-5021 I 2 3 4 5 6 7 8 9 10 I 2 3 4 5 6 7 8 9 10 For explanation see pp. 14-16 (99) £2 INTEREST TABLES Number of Years' Purchase for the Benewal of any Number of Years Expired in a TWENTY YEABS' LEASE Years I 2 3 4 5 6 7 8 9 10 II 12 13 14 IS i6 17 i8 19 20 I 2 3 4 5 6 7 8 9 10 II 12 13 14 IS i6 17 i8 19 20 2% •67297 1 -35940 2 05956 277372 3*50217 4-24518 5-00306 577609 6-56458 7-36885 8-18919 9-02595 9-87944 10-75000 11-63797 12-54370 13-46755 14-40987 15*37104 16-35143 4% •45639 •93103 I -42466 I -93803 2-47194 3-02721 5-60468 4-20526 4-82985 5*47943 6-15500 6-85758 7-58828 8-34819 9*13851 9-96043 10-81524 1 1 -70424 12-62879 13*59033 2i^A •61027 1-23580 I -87696 2-53416 3*20778 3-89825 4-60598 5*33140 6*07495 6-83710 7-61829 8-41902 9*23977 10-08103 10-94333 1 1 -82719 1273314 13-66174 14-61355 15*5^16 4*% •41465 •84795 I -30075 1 -77393 2 -26839 2-78511 3*32509 3-88936 4*47902 5-09522 5*73915 6-41205 7-11524 7 -85007 8-61796 9 •42041 10-25898 11-13527 12-05100 13-00794 For explanation see pp. 14-16 3% *55368 I -12397 1-71136 2-31638 2-93954 3*58141 4*24252 4-92348 5-62486 6-34728 7-09137 7-85779 8-64720 9-46029 10-29777 1 1 -16038 12-04887 12-96401 13-90661 14-87748 •37689 •77262 I^i88i4 I '62444 2-08255 2-56357 3-06864 3*59896 4*15580 4-74048 5-35439 5*99900 6-67584 7*38652 8-13273 8-91626 9*73896 10-60280 1 1 -50983 12-46221 3*% •50256 I '02272 1-56108 2-11828 2-69499 3-29188 3-90966 4-54906 5-21085 5*89579 6-60471 7*33844 8-09786 8-88385 9*69735 10-53932 1 1 -41076 12-31271 13-24622 14-21240 5 % 12-304% -098 '2o8 •332 •471 •628 •803 I'OOO I '221 1*470 1-749 2-062 2-414 2-809 3253 3*751 4*311 4*940 5*646 6-439 7-329 Years I 2 3 4 5 6 2 9 10 II 12 13 14 IS 16 17 18 19 20 z 2 3 4 5 6 7 8 9 10 II 12 13 14 IS 16 18 19 20 INTEREST TABLES Number of Years' Purchase for the Renewal of any Number of Years Expired in a TWENTY-ONE YEARS' LEASE Years I 2 3 4 S 6 9 10 II 12 13 14 IS 16 17 18 19 20 21 I 2 3 4 S 6 I 9 10 II 12 13 14 15 16 17 18 19 20 21 2% -65978 I *33275 2-01918 271934 3-43350 4*16195 4*90496 5-66284 6*43587 7*22436 8-02863 8-84897 9*68573 10-53922 1 1 '40978 1 2 '29775 13-20348 14*12733 15-06965 16-03082 17-01121 2i° o •59539 I -20566 I -831 19 2-47235 3*12955 3*80317 4*49364 5-20137 5-92679 6-67034 7*43249 8-21368 9-01441 9*83516 10-67642 11-53872 12-42258 13*32853 14*25713 15-20894 16-18455 4% •43883 •89522 I 36986 I -86349 2-37686 2-91077 3-46604 4*04351 4*64409 5-26868 5-91826 6*59383 7-29641 8-02711 8-78702 9-57734 10-39926 1 1 -25407 12-14307 13-06762 14-02916 2 /O •39678 •81 143 I -24473 1*69753 2-17071 2-66517 3*18189 3-72187 4-28614 4*87580 5 -49200 6-13593 6-80883 7-51202 8-24685 9-01474 9-81719 10-65576 11-53205 12-44778 13-40472 3% •53754 I -09122 1-66151 2-24890 2-85392 3-47708 4*11895 4-78006 5 46 I 02 6-16240 6-88482 7-62891 8*39533 9*18474 9*99783 10-83531 1 1 -69792 12-58641 13*50155 14-44415 15-41502 5% •35894 *73583 1*13156 1-54708 1*98338 2-44149 2-92251 3*42758 395790 4*51474 5*09942 5*71333 6*35794 7*03478 774546 8 '49 1 67 9*27520 10-09790 10-96174 1 1 -86877 12-82115 3i» o *48557 •98813 I '50829 2-04665 260385 3-18056 3*77745 4*39523 5*03463 5-69642 6-38136 7-09028 7 -82401 8*58343 9-36942 10-18292 1 1 -02489 1 1 -89633 12-79828 13*73179 14*69797 11-564 % -100 •213 •338 •477 633 •806 I'OOO I -216 1*457 1-726 2-026 2-361 2-734 3*151 3-616 4*135 4*713 5*359 6-079 6882 7*779 Years I 2 3 4 5 6 7 8 9 10 II 12 13 14 IS 16 17 18 19 20 21 I 2 . 3 4 S 6 7 8 9 10 II 12 13 14 IS 16 17 18 19 20 21 (100) (lOl) INTEREST TABLES For explanation see pp. 14-16 Number of Tears' Purchase for the Renewal of any Number of Tears Expired in a FOBTT TEARS' LEASE Years 2% 2i% 3% 3i% Years I •45289 •37243 -30655 ■25257 I 2 •91484 •75417 -62231 •51398 2 3 I •sseos I -14545 -94753 -78454 3 4 I •86664 I -54652 I -28252 I -06458 4 S 2-35686 I -95761 I -62755 1-35441 5 6 2-85689 2-37898 I -98293 1-65439 6 7 3-36692 2 81089 2-34898 I -96486 I 8 3-88715 3-25359 2-72600 2 -28620 9 4-41778 3-70737 3-1 1434 2-61879 9 10 4-95902 4-17248 3-51433 2-96302 10 II 5-51110 4-64922 3-92631 3^31930 II 12 6^07421 5-13788 4-35066 3-68805 12 13 6-64858 5-63876 4-78774 4^06970 13 14 7-23444 6-15216 5 -23793 4-46472 14 15 7-83202 6-67839 5-70162 4-87355 IS 16 8-44155 7-21778 6-17923 5-29670 16 'Z 9-06328 7-77066 6-67116 5-73466 17 18 9-69743 8-33736 7-17785 6-18794 18 19 10-34427 8^91822 7-69975 6-65710 19 20 1 1 00405 9-51361 8-23729 7-14267 20 21 1 1 '67702 10-12388 8-79097 7-64523 21 22 12-36345 10-74941 9-36126 8^16539 22 23 1 3^0636 1 11-39057 9-94865 8-70375 23 24 . 13-77777 12-04777 10-55367 9-26095 24 25 14^50622 12-72139 11-17683 983766 25 26 15-24923 13-41186 ir8i87o 10-43455 26 27 16 -007 1 1 14-11959 12-47881 1 1 -05233 27 28 i6^78oi4 1 4^8450 1 13-16077 11-69174 28 29 17-56863 15-58856 13-86215 12-35352 29 30 18^37290 i6^3507i 14-58457 13-03846 30 31 19-19324 17-13190 15-32866 13-74738 31 32 20-03000 17-93263 16-09508 14-481 1 1 32 33 20-88349 18-75338 16-88449 15-24053 33 34 21-75405 19-59465 17-69758 16-02652 34 35 22 -64202 20-45694 18-53506 16-84002 35 36 23-54775 21-34080 19-39767 17-68199 36 37 24-47160 22*24675 20-28616 18-55343 38 25-41392 23-17535 21-20130 19-45538 38 39 26-37509 24-12716 22-14390 20-38889 39 40 27-35548 25-10277 23-11477 21-35507 40 i 11023 INTEREST TABLES Number of Tears' Purchase for the Renewal of anj r Number of Tears Expired in a FORTT TEARS' LEASE Years 4% 4i% 5% 8% Years I -20828 •17192 •14205 •04603 I 2 -42490 •35159 -29120 •09574 2 3 -65019 •53934 -44780 •14943 3 4 •88449 •73554 -61224 •20742 4 5 I^i28i6 •94057 -78490 •27004 5 6 I -38157 I -15482 -96619 •33768 6 7 1-64512 I -37872 I -15654 •41072 1 8 I -91922 1-61269 I -35641 •48961 9 2-20428 I -85719 I -56628 •57481 9 10 2-50074 2-1 1269 I -78664 •66683 10 II 2-80905 2-37969 2-01802 •76620 II 12 3-12971 2-65871 2-26096 -87353 12 13 3^46318 2-95028 2-51606 -98945 13 14 3-81000 3-25497 2-78391 1-11463 14 IS 4-17069 3-57337 > 306515 I ^24983 15 16 4^54581 3-90610 3-36045 1-39585 16 '2 4-93593 4-25381 3-67052 1-55355 \l 18 5-34165 4-61716 3-99609 I -72387 19 5-76361 4-99686 4-33794 I 90781 19 20 6-20244 5-39364 4-69688 2-10646 20 21 6-65883 5-8(5829 5-07377 2-32101 21 22 7-13347 6-24159 5-46950 2-55272 22 23 7-62710 6-69439 5-88502 2-80297 23 24 8-14047 7-16757 6-32132 3-07324 24 25 8-67438 7 -66203 6-77943 336513 25 26 9^22965 8-17875 7 -26045 3-68037 26 27 9^80712 8-71873 7*76552 4-02083 27 28 10^40770 9-28300 8-29584 4-38853 28 29 1 1 '03229 9-87266 8-85268 4-78565 29 30 11-68187 10-48886 943736 5-21453 30 31 12-35744 11-13279 10-05127 5-67772 31 32 1 3 06002 1 1 -80569 10-69588 6-17797 32 33 13-79072 12-50888 11-37272 6-71824 33 34 14-55063 13-24371 12-08340 7-30173 34 35 15-34095 14-01 160 12-82961 7-93190 35 36 16-16287 14-81405 13-61314 8-61248 36 37 17-01768 15-65262 14-43584 9-34751 38 17-90668 16-52891 1 5^29968 10-14135 38 39 18-83123 17-44464 16^2067 1 10-99868 39 40 19.79277 18-40158 17-15909 II -92461 40 (103) INTEREST TABLES The Percentage per Annnm which each Number of Years' Purchase of a Perpetuity allows the Purchaser For explanation see p. i6 Years PEB CENT. PER ANNUM Years £ £ s. d. I 100 100 X 2 50 50 3 3 33 -J 33 6 8 3 4 25 25 4 5 20 20 5 6 166 16 13 4 6 I U'285:^ 14 5 8i I 8 12*5 12 10 9 ii^i II 2 2| 9 10 10 10 10 II 909 9 I 9f XX 12 8-3 8 6 8 X2 13 7-69236 7 13 loj 13 14 7-14285 7 2 loi X4 15 6-6 6 13 4 15 i6 6 25 650 x6 :i 5-88235 S-5 5 17 7f 5 II I: U 19 5 •26316 5 5 3i "9 20 5 500 20 21 4-7619 ■ 4 15 2f 21 22 4-5 4 10 II 22 23 24 4-3478 4^i6 4 6 11^ 4 3 4 23 24 25 4 400 25 26 3-84615 3 16 II 26 27 3-76 3 14 I 27 28 3-5714 3 II 5i 28 29 3-4483 3 8 III 29 30 3-3 368 30 31 3-2258 3 4 6i 31 32 3-125 326 32 33 3-03 3 7j 33 34 2*9412 2 18 10 34 35 ±•85714 2 17 If 35 36 2*7 2 15 6| 36 H ±•76 2 14 of 37 38 2-6316 2 12- 7i 38 39 ±•56416 2 II 3| 39 40 2-5 2 10 40 41 2-4396 2 8 9j 41 42 2-38095 2 7 71 42 43 2-32558 2 6 6J 43 44 2-27 2 5 5i 44 45 2-2 2 4 5i 45 46 2-17391 2 3 5y 46 47 2-12766 2 2 6f 47 48 2-083 2 I 8 48 49 2^0408 2 9| TT 49 50 2-0 200 50 INTEREST TABLES (104) For explanation see p. 16 INTEEEST, AMOUNT, AND DISCOUNT OF £1 IN A YEAR, NINE, SIX, AND THREE MONTHS Interest per Annum Period Interest Amount Discount 1 % M I year 9 months 6 „ I3 M •01 -0075 •005 •0025 I-OI 1-0075 1^005 1-0025 •009901 -007444 •004975 •002494 u% I year 9 months I3 » •015 •01 125 -0075 -00375 1-015 I -01 125 1-0075 I -00375 •014778 •01 1 125 •007444 -003736 If % I year months 6 „ 3 « •0175 •01 3 1 25 •00875 •004375 1-OI75 roi3i25 1^00875 1-004375 •01 7 199 •012955 •008674 -004356 2 % / 1 year 1 9 months 16 „ 3 » •02 •015 •01 •005 I^02 1-015 I-OI 1*005 •019608 •014778 009901 -004975 2i% / 1 year J 9 months 6 „ I3 M -0225 •016875 •01125 •005625 I ^0225 I -016875 I -01 125 I -005625 •022005 •016595 •01 1 125 •005593 2i% / I year 9 months 16 „ (3 » •025 •01875 •0125 •00625 1-025 I -01875 1-0125 1*00625 •024390 -018405 •012346 •006211 2f % i I year 9 months 6 „ 3 » •0275 •020625 •01375 •006875 I ^0275 I ^02062 5 I -01375 I ^006875 •026764 •020208 •013563 •006828 3 % I year 9 months 6 „ 3 » •03 •0225 •0x5 •0075 1-03 I 0225 1-015 1-0075 •029126 -022005 •014778 •007444 3i% / 1 year 9 months 6 „ \3 »» •035 •02625 •0175 •00875 1-035 I ^02625 I -0175 1-00875 •033816 -025579 •017 199 -008674 4 % / 1 year 9 months 6 „ v3 » •04 •03 •02 •01 1^04 I 03 1-02 I-OI 038462 •029126 •019608 •009901 44% / 1 year 9 months 16 „ 13 " •045 •03375 •0225 •01 125 1-045 1-03375 I -0225 I -01 125 •043062 •032648 •022005 •01 1 125 5 % - I year 9 months 6 „ 3 » •05 •0375 •025 •0125 1-05 I -0375 I 025 1-0125 •047619 •036145 -024390 •012346 (105) I INTEBEST TABLES For explanation see pp. i6, 17 SINKING FUND FOE THB EEPAYMENT OF LOANS Years 1% li% li% 11% Years I I'OOOOOO I^OOOOOO I'OOOOOO I 000000 I 2 •497512 •496893 •496278 •495663 2 3 •330022 •329202 •328383 •327567 3 4 •246281 •245361 •244445 •243532 4 5 •196040 •195062 •194089 •193121 1 5 6 •162548 •I6I534 •160525 •159523 6 7 •138628 •137589 •136556 •135531 7 8 •120690 •I 19633 •I 18584 •I 17543 8 9 •106740 •I 0567 1 •104609 •103558 9 10 •095582 •094503 •093434 •092375 10 II •086454 •085367 •084294 •083231 II 12 •078849 •077758 •076680 •075614 12 13 •072415 •07 1 32 1 •070240 •069173 13 14 •066901 •065805 •064723 •063656 14 15 •062124 •061026 •059944 •058877 15 16 •057945 •056847 •055765 •054700 16 'Z •054258 •053160 •052080 •05IOI6 17 18 •050982 •049884 •048806 •047745 18 19 •048052 •046955 •045878 •044821 19 20 •045415 •044320 •043246 •042 19 1 20 21 •043031 •041937 •040866 •039815 21 22 •040864 •039770 •038703 •037656 22 23 •038886 •037897 •036731 •035688 23 24 •037073 •035987 •034924 •033886 24 25 •035407 •034322 •033263 •032230 25 26 •033869 •032787 •031732 •030703 26 27 •032446 •031367 •030315 •029291 27 28 •03 1 1 24 •030049 •029001 •027982 28 29 •029895 •028822 •027779 •026764 ^ 30 •028748 •027679 •026639 •025630 30 31 •027676 •026609 •025574 •024570 31 32 •026671 •025608 •024577 •023578 32 33 •025728 •024668 •023641 •022648 34 •024840 •023784 •022762 •021774 34 35 •024004 •022951 •021934 •020951 35 36 •023214 •022165 •021 152 •020175 36 37 •022468 •021424 •020414 •019443 37 38 1 •021762 •020720 •OI97I6 •018750 38 39 •021092 •020054 •019055 •018094 39 40 •020456 •01 942 1 •018427 •017472 40 41 •019851 •018821 •OI783I •016882 41 42 •019276 •018249 •017264 •01632 1 42 43 •018727 •017705 •016725 •015787 43 44 •018204 •OI7I86 •OI62IO •015278 44 45 •017705 •016690 •015720 •014793 1 ■ 45 46 •017228 •OI62I7 •01 525 1 •014330 46 47 •016771 •015764 •014803 •013888 47 48 •016334 •01 533 1 •014375 •013466 48 49 •01591S •014916 •013965 •OI306I 49 50 ! •015513 •014518 •013572 •012674 50 (106) V INTEREST TABLES SINKING FUND FOE THE EEPAYMENT OF LOANS Years 1% I4 /o li% If % Years SI •015127 •014136 •013195 •012303 51 52 •014756 •013769 •012833 •01 1947 52 53 •014400 •013416 •012485 •01 1605 53 54 •014057 •013078 •012151 •01 1277 54 55 •013726 •012751 •01 1830 •010961 55 1 56 •013408 •012437 •01 1 52 1 •010658 56 P •013102 •012135 01 1223 •010366 •012806 •01 1843 •010937 •010085 58 §2 •012520 •01 1562 •010660 •009814 59 •012244 •01 1290 •010393 •009553 60 61 ^ _ •01 1978 •01 1028 •010136 •009302 61 62 •01 1720 •010774 •009888 009059 62 P. •01 147 1 •010529 •009647 •008825 63 sj •01 1230 •010292 •009416 •008598 64 65 •010997 •010063 •009191 •008379 65 66 •010771 •009841 •008974 •008168 66 67 •01055 1 •009626 •008764 •007964 67 68 •010339 •009417 •008560 •007766 68 ^ 69 •010133 •009215 •008363 •007575 69 70 •009933 •009019 •008172 •007389 70 71 •009739 •008829 •007987 •007210 71 72 •009550 •008645 •007808 •007036 72 73 •009367 •008466 •007634 •006868 73 74 •009189 •008292 •007465 •00670^ 74 75 •009016 •008123 •007301 •006546 75 76 •008848 •007959 •007 141 •006392 76 i U •008684 •007800 •006987 •006243 77 •008525 •007644 •006836 ■006098 78 79 •008370 •007493 •006690 •005958 79 80 •008219 •007347 •006548 •005821 86 , 81 •008072 •007203 •006410 •005688 81 82 •007929 •007064 •006276 •005559 82 J P •007789 •006929 •006145 •005434 83 u •007653 •006797 •006018 •005312 84 85 •007520 •006668 •005894 •005194 85 86 •007390 •006543 •005773 •005078 86 i 87 00 •007264 •006420 •005656 •004966 87 88 •007 141 •006301 •005541 •004857 88 89 •007021 •006185 •005430 •004751 89 90 •006903 •006071 •005321 •004648 90 91 •006789 •005961 •005215 •004547 91 92 •006676 •005853 •0051 12 •004449 92 1 93 •006567 •005747 •00501 1 •004353 93 94 •006460 •005644 •004913 •004260 94 95 •006355 •005544 •004817 •004169 95 96 •006253 •005445 •004723 •004081 • 96 97 •006153 •005349 •004632 •003995 97 98 •006055 •005256 •004543 •00391 1 98 99 •005959 •005164 •004456 •003829 99 100 •005866 •005074 •004371 •003749 100 « < [107) 11 INTEREST TABLES INTEREST TABLES \ SINKING FUND FOE THE EEPAYMENT OF LOANS Years I 2 3 4 5 6 7 8 9 10 II 12 13 14 15 i6 17 i8 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 39 40 41 42 43 44 45 46 47 48 49 50 2% I'OOOOOO ■495049 •326755 •242624 •I92I58 •158526 •I345I2 •I 16509 •1025 1 5 •091326 •082178 •074563 •0681 18 •062602 •057825 '053650 •049970 •046702 •043782 •041 157 •038785 036631 •034668 •032871 •03 1 22 1 •029699 •028293 •026990 •025779 •024650 •023596 •02261 1 •021687 •020819 •020002 •019233 •018507 •01 782 1 •017171 •016556 •015972 •015417 •014890 •014388 •01 39 10 •013453 •01 301 8 •012602 •012204 •01 1823 ■ I'OOOOOO •494438 •325945 •241719 •191200 •157535 •133500 •I 15485 •101482 •090288 •081 136 •073517 •067077 •061562 •056789 •052617 •048940 •045677 •042762 •040142 •037776 •035628 •033671 •031880 •030236 •028721 •027322 •026025 •024821 •023699 •022653 •021674 •020757 •019897 •019087 •018325 •017606 •016928 •016285 •015677 •015101 •014554 •014034 •013539 •013068 •012619 •012191 •01 1782 •01 1392 •011018 2i% 2i% I'OOOOOO •493827 •325137 •240818 •190247 •156550 •132495 •I 14467 •I00457 •089259 •080106 •072487 •066048 •060536 •055766 •051599 •047928 •044670 •041760 •039147 •036787 •034646 •032696 •030913 •029276 •027768 •026377 •025088 •023891 •022777 •021739 •020768 •019859 •019007 •018205 •01 745 1 •01 674 1 •016070 •015436 •014836 •014268 •013728 •01 32 1 7 •012730 •012267 •011826 •01 1407 •011006 •010623 •010258 For explanation see pp. 16, 17 3.0/ 14 /o foooooo •493222 •324332 •239920 •189298 •I5557I •I3I497 •113458 •099441 •088240 •079086 •071469 •065033 •059525 •054759 •050597 •046932 •043681 •040778 •038172 •035819 •033686 •031744 •029969 •028340 •026841 •025458 •024177 •022989 •021884 •020855 •019893 •018993 •OI8I49 •017356 •OI66II •OI59IO •015248 •014623 •014032 •013472 •012942 •012439 •OII96I •01 1507 •01 1075 •010664 •010272 •009898 •009541 Years Z 2 3 4 5 6 7 8 9 10 II 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 $ 49 50 SINKING FUND FOR THE REPAYMENT OF LOANS (108) Years 51 52 53 54 55 56 57 61 62 65 66 % 69 70 71 72 73 74 75 76 77 78 81 82 83 S^ 85 86 U 89 90 91 92 93 94 95 96 97 98 99 100 2% •011459 •01 1 109 •010774 •010452 •010143 •009847 •009561 •009287 •009022 •008768 •008523 •008286 •008058 •007839 •007626 •007421 •007223 •007032 •006847 •006668 •006494 •006327 •006165 •006007 •005855 •005708 '005564 •005426 •005291 •005161 •005034 •0049 1 1 •004792 •004676 •004563 •004454 •004348 •004244 •004144 •004046 •003951 •003859 •003769 •003681 •003596 •003513 •003432 •003354 •003277 •003203 2i% •010661 •010319 •009991 •009677 •009375 •009085 •008807 •008540 •008283 •008035 •007797 •007568 •007347 •007134 •006929 •006731 •006540 •006355 •006177 •006005 •005838 •005677 •005522 •005371 •005226 •005085 •004948 •004816 •004688 •004564 •004444 ^004327 •004214 •004104 •003998 •003895 •003795 •003697 •003603 •003511 •003422 •003336 •003252 'OO3170 •003091 •003014 •002939 •002866 •002795 •002726 2i% •009909 •009574 •009254 •008948 •008654 •008373 •008102 •007842 •007593 •007353 •007123 •006901 •006688 •006482 •006285 •006094 •005910 •005733 •005562 •005397 •005238 •005084 •004936 •004792 •004654 •004519 •004390 •004265 •004143 •004026 •003912 •003803 •003696 •003593 •003493 •003396 •003303 •003212 •003124 •003038 •002955 •002875 •002797 •002721 •002648 •002577 •002507 •002440 •002375 •002312 21% •009200 •008874 •008563 •008265 •007980 •007706 •007444 •007193 •006952 •006720 •006498 •006284 •006079 •005881 005691 005508 •005332 •005163 •005000 •004842 •004690 •004544 •004403 •004267 •004136 •004009 •003886 •003768 •003654 •003543 •003437 •003334 •003234 •003137 •003044 •002954 •002867 •002782 •002700 •00262 1 •002545 •002470 •002399 •002329 •002261 •002196 •002133 •00207 1 •002012 •001954 Years- 51 52 53 54 55 56 57 58 59 60 61 62 63 65 66 $7 68 69 70 71 72 73 74 75 76 79 80 81 82 83 84 83 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 (109) INTEREST TABLES INTEREST TABLi;^ For explanation see pp. i6, 17 SINKING FUND FOE THE REPAYMENT OF LOANS Years 3% 3i% 3i% 3f % Years I I'OOOOOO I'OOOOOO I'OOOOOO I^OOOOOO I 2 •49261 1 •492005 •491400 •490798 2 3 •323530 •322731 •321934 •321 140 3 4 •239027 •238137 •237251 •236369 4 5 •188355 •I874I5 •I8648I •185552 5 6 •154598 •153630 •152668 •I5I7I2 6 7 •130506 •129522 '1 28544 •127574 7 8 •I 12456 •I 1 1463 •II0477 •109498 8 9 •098434 •097436 •096446 •095465 9 10 •087231 •086231 •085241 •084261 10 II •078077 •077079 •076092 •075 "5 II 12 •070462 •069467 •068484 •067512 12 13 •064030 •063039 •062062 •061096 13 14 •058526 •057542 •056571 •055613 14 15 •053767 •052789 •051825 •050876 1 15 16 •04961 1 •048640 •047685 •046745 16 17 •045953 •044990 •044043 •043 II 3 17 18 •042709 •041754 '0408I7 •039897 18 19 •039814 •038868 •037940 •037031 19 20 •037216 •036279 •035361 •034462 20 21 •034872 •033944 •033037 •032149 21 22 •032747 •031829 •030932 •030055 22 23 •030814 •029906 •029019 •028153 23 24 •029047 •028149 •027273 •026419 24 25 •027428 •026539 •025674 •024832 25 26 •025938 •025060 •024205 •023375 26 27 •024564 •023696 •022852 •022033 27 28 •023293 •022435 ■021603 •020795 28 29 •0221 15 •021267 •020445 •019650 29 30 •02IOI9 •020182 •01937 1 •018588 30 31 •019999 •OI9I72 •018372 •017600 31 32 •019047 •018230 •017442 •01 668 1 32 33 •OI8I56 •017350 •016572 •015824 33 34 •017322 •016526 •015760 •015023 34 35 •016539 •015753 •014998 •014273 35 36 •015804 •015028 •014284 •013571 36 H •OI5II2 •014346 •OI36I3 •01 29 1 1 %* 38 •014459 •013704 •012982 '012292 39 •013844 •013099 •012388 •01 1709 39 40 •013262 •012528 •OII827 •01 1 159 40 41 •OI27I2 •01 1988 •on 298 '0 1 0642 41 42 •OI2I92 •01 1478 •010798 '010153 42 43 •01 1698 •010994 •010325 •009691 43 44 •01 1230 •010536 •009878 •009254 44 45 •010785 •OIOIOI •009453 •008841 45 46 •010363 •009688 •009051 •008/J49 46 47 •009961 •009296 •008669 •008078 % 49 SO 48 •009578 •008923 •008306 •007726 49 •009213 •008568 •007962 •007392 so •008866 •008230 •007634 •007074 (no) SINKING FUND FOR THE REPAYMENT OF LOANS Years 3% 3i% •007322 3f % Years 51 •008534 •007908 •006772 51 52 •008217 •007601 •007024 •006485 52 53 •007915 •007308 •006741 •006212 53 54 •007626 •007028 •006471 •005952 54 55 •007349 •006761 •006213 •005704 55 56 •007085 •006506 •005967 •005468 56 57 •006831 'O06261 •005732 •005242 57 58 •006588 'O06028 •005508 •005028 g •006356 '005804 •005294 •004822 59 •006133 •005590 •005089 •004627 60 61 •005919 •005385 •004892 •004440 61 62 •005714 'O05188 •004705 •004261 62 63 ■005517 '005000 •004525 •004090 63 64 •005328 'OO4819 •004353 •003927 64 65 •005146 •004646 •004188 •003771 65 66 •004971 •004479 •004030 •003621 66 S •004803 •004320 •003879 •003478 67 68 •004642 •004166 ■003734 •003341 68 69 •004486 •004019 •003595 •003210 69 70 •004337 •003877 •003461 •003085 70 71 •004193 •003741 ■003333 •002964 71 . 72 •004054 •003610 •003210 'OO2849 72 ! 73 •003921 •003484 •003092 •002738 73 74 •003792 •003363 '002978 •002633 74 75 •003668 •003247 •002869 ■002531 75 76 •003548 •003135 •002764 •002434 76 U •003433 •003027 •002664 •002340 77 78 '003322 •002923 •002567 •002250 78 g '003215 •002823 •002474 •002164 79 '003112 •002727 •002385 •002082 80 81 •003012 •002634 002299 •002003 81 82 •002916 •002545 •002216 •001926 82 83 •002823 •002459 •002137 •001853 83 84 •002733 •002376 •002060 •001783 84 85 '002647 •002295 •001987 •OO1716 85 . 86 •002563 •002218 •001916 •00165 1 86 ; S7 •002482 •002144 •001848 •001589 87 88 •002404 •002072 •001782 •001529 88 89 •002329 •002003 'OO1719 •001472 89 90 '002256 •001936 •001658 •OOI416 90 91 '002185 •001872 •001599 •001363 91 92 •002117 •001809 •001543 OO1312 92 93 •00205 1 •001749 •001488 •001263 93 94 •001987 •001 69 1 •GO 1436 •OOI216 94 95 •001926 •001635 •001385 •001 171 95 96 •001866 •001582 •001337 •001 127 96 97 •001809 •001529 •001290 •001085 % 98 •001753 •001479 'OOI245 'OOIO45 99 '001699 •001430 •00I20I •001006 99 !• 100 •001647 •001384 •001 159 000969 100 (III) »[ I Years Z 2 3 4 5 6 7 8 9 10 II 12 13 M 15 i6 17 i8 19 20 21 22 23 24 25 26 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 .IJTTEREST TABLES SINKING FUND FOB THE BEFATMENT OF LOANS 4% i-oooooo •490196 •320349 •235490 •184627 •150762 •I266IO •108528 •094493 •083291 •074149 •066552 •060144 •054669 •049941 •045820 •042199 •038993 •036139 •033582 •031280 •029199 •027309 •025587 •024012 •022567 •021239 •020013 •018880 •017830 •016855 •015949 •01 5 104 •014315 •013577 •012887 •012240 •01 1632 •011061 •010523 •010017 •009540 •009090 •008665 •008262 •007882 •007522 •007181 •006857 •006550 4i Oy ^O I-OOOOOO •489596 •319559 •234615 •183707 •I498I7 •125652 •107565 •093529 •082330 •073193 •065603 •059203 •053738 •049020 •044910 •041300 •038107 •035264 •032720 •030431 •028362 •026486 •024776 •023215 •021783 •020467 •019255 •OI8I35 •017098 •OI6I37 •015243 •OI44II •013635 •OI29IO •012232 •01 1597 •01 1002 •010444 •009918 •009424 •008959 •008521 •008107 •007717 •007348 •006999 •006669 •006356 •006060 4i% I^OOOOOO •488997 •318773 •233744 •182792 •148878 •I 2470 1 •106609 •092575 •081379 •072248 •064666 •058275 •052820 •0481 14 •044015 •040418 •037237 •034407 •031876 •029601 •027546 •025682 •023987 •022439 •02I02I •OI9719 •O1852I •OI7415 •016392 •015443 •014563 •013745 •012982 •012270 •01 1606 •010984 •010402 •009856 •009343 •008862 •008409 •007982 •007581 •007202 •006845 •006507 •006189 •005887 •005602 /o I^OOOOOO •487805 •317209 •232012 •180975 •I470I7 •122820 •104722 •090690 •079505 •070389 •062825 •056456 •051024 •046342 •042270 •038699 •035546 •032745 •030243 •027996 •025971 •024137 •02247 I •020952 •019564 •018292 •OI7I23 •016046 •01 505 1 •OI4I32 •013280 •012490 •01 1755 •01 1072 •010434 •009840 •009284 •008765 •008278 •007822 •007395 •006993 •006616 •006262 •005928 •005614 •005318 •005040 004777 Years I 2 3 4 5 6 7 8 9 10 II 12 13 M 15 16 \l 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 45 46 47 48 49 50 For explanation see pp. 16, 17 (112) Years 51 52 S3 54 55 56 57 58 60 61 62 P 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 INTEEEST TABLES SINKING FUND FOB THE B^FAYMENT OF LOANS Oy ^O •006259 •005982 •005719 •005469 •005231 •005005 •004789 •004584 •004388 •004202 •004024 •003854 •003692 •003538 •003390 •003249 •0031 15 •002986 •002863 •002745 •002633 •002525 •002422 •002323 •002229 •002139 •002052 •001969 •001890 •OOI8I4 •OOI74I •001672 •001605 •OOI54I •001479 •001420 •001364 •OOI3IO •001258 •001208 •001 160 •001 1 14 •001070 •001028 •000987 •000949 •00091 I •000875 •000841 •000808 41% •005779 •005513 •005261 005021 •004793 •004577 •004371 •004175 •003989 •003812 •003643 •003482 •003329 •003183 •003044 •002912 •002785 •002665 •002549 •002440 •002335 •002234 •002139 •002047 001960 •001877 •001797 •001 72 1 •001648 •001578 •001511 •001448 •001387 •001329 •001273 001219 •001 168 •001 1 19 •001073 001028 •000985 •000944 •000905 •000867 •000831 •000796 •000763 •000732 •000701 •000672 4i% •005332 •005077 •004835 •004605 •004388 •004181 •003985 •003799 •003622 •003454 •003295 •003143 •002998 •002861 •002730 •002606 •002488 •002375 •002267 •002165 •002068 •001975 •001886 •001802 •001 72 1 •001644 •001571 •001 501 •001434 •OOI371 •OOI310 •001252 •OOH97 •001 144 ■001093 •001045 •000999 •000955 •000913 •000873 •000835 •000798 •000763 •000730 •000698 •000667 •000638 •000610 •000584 •000558 Oy "^O •004529 •004295 •004073 •003|^4 003667 •003480 •003303 ■003136 •002978 •002828 •002686 •002552 •002424 •002304 •002189 •002081 •001978 •001880 •001787 •001699 •001616 001536 •00146 1 •001390 •001322 •001257 •00; 196 ■001138 •001082 •001030 •000980 000932 •000887 •000844 •000803 •000764 •000727 •000692 ■000659 •000627 •000597 000568 •000541 •000515 •000490 •000466 •000444 •000423 •000402 •000383 (113) Years 51 52 53 54 55 56 57 58 59 60 61 62 63 ^ 65 66 $7 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 F Sit I '• 'I u INTEREST TABLES SINKING FUND FOB THE BEFATMENT OF LOANS Years 6% 7% 8% 10% Years I I 000000 i-oooooo foooooo I 000000 I 2 •485437 •483092 •480769 •476190 2 3 •314110 •31 1052 •308033 •3021 15 3 4 •228591 •225228 •22 1 92 1 •2I547I 4 5 •177396 •I 73891 • •170456 •163798 5 6 •143363 •139796 •I36315 •129607 6 7 •119135 •II5553 •I 12072 •105406 7 8 •101036 •097468 •094015 •087444 8 9 •087022 •083486 •080079 •073641 9 10 •075868 •072377 •069029 •062745 10 II •066793 •063357 •060076 •053963 II 12 •059277 •055902 •052695 •046763 12 13 •052960 •04965 1 •046522 •040779 13 14 •047585 •044345 •041297 •035746 14 15 •042963 •039795 •036829 •031474 15 i6 •038952 •035858 •032977 •027817 16 ^l •035445 •032425 •029629 •024664 17 i8 •032357 •029413 •026702 •021930 18 19 •02962 I •026753 •024128 •019547 19 20 •027185 •024393 •021852 •01 7460 20 21 •025005 •022289 •019832 •015624 21 22 . •023046 •020406 •018032 •014005 22 23 •021278 •01 87 14 •016422 •012572 23 24 •019679 •01 7 1 89 •014978 •01 1 300 24 25 •018227 •01 581 1 •013679 •01 01 68 25 26 •016904 •014561 •012507 •009159 26 27 •015697 •013426 •01 1448 •008258 27 28 •014593 •012392 •010489 •007451 28 29 •013580 •oii/|/i9 •009618 •006728 29 30 •012649 •010586 •008827 •006079 30 31 •01 1 792 •009797 •008107 •005496 31 32 •01 1002 •009073 •007451 •004972 32 33 •010273 •008408 •006852 •004499 33 34 •009598 •007797 •006304 •004074 34 35 •008974 •007234 •005803 •003689 35 36 •008395 •006715 •005345 •003343 36 37 •007857 •006237 •004924 •003030 38 •007358 •005795 •004539 •002747 38 39 •006894 •005387 •004185 •002491 39 40 •006462 •005009 •003860 •002259 40 41 •006059 •004660 •003562 •002050 41 42 •005683 •004336 •003287 •001860 42 43 •005333 •004036 •003034 •001688 43 44 •005006 •003758 •002802 •001532 44 45 •004701 •003499 •002587 •001391 45 46 •004415 •003260 •002390 •001263 46 ^l •004148 •003037 •002208 •001 147 47 48 •003898 •002831 •002040 •001041 48 49 •003664 •002639 •001886 •000946 49 50 •003444 •002460 •001743 •000859 50 For explanation see pp. 16, 17 ("4) INTEREST TABLES SINKING FUND FOB THE BEFAYMENT OF LOANS Years 51 52 53 54 55 56 57 58 59 61 62 63 ^ 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 99 zoo 6% •003239 •003046 •002866 •002696 •002537 •002388 •002247 •0021 16 •001992 •001876 •001766 •001664 •001567 •001476 •001 39 1 •0013 10 •001235 •001 163 •001096 •001033 •000974 •000918 •000865 •000815 •000769 •000725 •000683 •000644 •000607 •000573 •000540 •000509 •000480 •000453 •000427 •000402 •000380 •000358 •000338 •000318 •000300 •000283 •000267 •000252 •000238 •000224 •0002 1 1 •000199 •000188 •000177 7% 8% •002294 •002139 •001995 •001 86 1 •001736 •001620 •001512 •001411 •001317 •001229 •001 147 •001071 •ooiooo •000934 •000872 •000814 •000760 •000710 •000663 •000620 •000579 •000541 •000505 •000472 •000441 •000412 •000385 •000359 •000336 •000314 •000293 •000274 •000256 •000239 •000223 •000209 •000195 •000182 •000170 •000159 •000149 •000139 •000130 •0001 2 1 •0001 13 •000106 •000099 •000092 •000086 •000081 •001611 •001490 •001377 •001274 •001 1 78 •001090 •001008 •000932 •000862 •000798 •000738 •000683 •000632 •000585 •000541 •000501 •000464 •000429 •000397 •000368 •000340 •000315 •000292 •000270 •000250 •000231 •000214 •000198 •000183 •000170 •000157 •000146 •000135 •000125 •0001 16 •000107 •000099 •000092 •000085 •000079 •000073 •000067 •000062 •000058 •000053 •000049 •000046 •000042 •000039 •000036 10 0/ ^o •000780 •000709 •000644 •000585 •000532 •000483 •000439 •000399 •000363 •000329 •000299 •000272 •000247 •000225 •000204 •000186 •000169 •000153 •000139 •000127 •0001 15 •000105 •000095 •000086 •000079 •000072 000065 •000059 •000054 •000049 •000044 •000040 •000037 •000033 •000030 •000028 •000025 •000023 •000021 •000019 •000017 •000015 •000014 •000013 •000012 •ooooii •ooooio •000009 •000008 •000007 Years 51 52 53 54 55 56 % 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 V\ % ("5) W2 (■■ INTEKEST TABLES For explanation see p. i8 Value of an Annuity Yielding Interest ( >n Capital at £ i and 3^ FEB CENT., and Beplacing Capital when Invested at Lower Sates Yrs. I 3&2% 3&2i% 3i&2% 3i942 97,624 97,245 96,779 96,223 95,614 94,971 94,321 93,683 93,061 92,444 91,826 91,192 90,538 89,865 89,171 88,465 87,748 87,021 86,281 85,524 84,745 83,943 83,122 82,284 81,436 80,582 79,717 77,919 76,969 ^Z 75,973 48 74,932 49 73,850 50 72,726 51 71,566 52 70,373 53 69,138 54 67,852 Number Dying during the Year 490 397 329 288 272 282 318 379 466 556 609 643 650 638 622 617 618 634 654 673 694 706 717 727 740 757 779 802 821 838 848 854 865 887 911^ 950 996 1,041 1,082 1,124 1,160 1,193 1,235 1,286 1,339 Probable Number out of every 100 Alive at the Beginning of a Year who will Survive the Year 4 99*5100 99 6010 99 -668 1 997085 997238 997129 996753 99-6118 99*5208 99-4255 99-3671 993275 99-3156 993236 99-3361 99-3370 99-3315 993096 99-2828 992567 992277 99-2083 99*1895 99*1715 99*1496 99*1226 99-0891 990536 99 "0220 98 9918 98-9694 98*9513 98-9266 98-8873 98-8444 98-7808 98-7060 98-6298 985560 98 4780 98-4050 98*3330 98*2451 98-1400 98-0266 For explanation see pp. 23-25 who will Die during the Year •4900 .3990 *33i9 •2915 •2762 •2871 •3247 •3882 •4792 •5745 •6329 -6725 -6844 -6764 •6639 •6630 •6685 -6904 7172 •7433 •7723 •7917 •8105 •8285 -8504 -8774 -9109 -9464 -9780 1-0082 1-0306 I -0487 I -0734 I'II27 I ''556 1-2192 I 2940 I -3702 1*4440 I -5220 1-5950 1-6670 17549 1-8600 1*9734 Age at Ban- ning of Year 10 II 12 13 14 17 18 19 20 21 22 23 24 u 27 28 29 30 31 32 33 34 36 37 38 39 40 41 42 43 44 46 47 48 49 SO 51 52 53 54 I Age at Be^n- ning of Year 59 60 61 62 64 65 66 69 70 71 72 73 74 ?i 77 78 79 80 81 82 83 84 85 86 89 90 91 92 93 94 95 96 97 INSTITUTE OF ACTUABIES MOBTALITY TABLE Healthy Males (Hm.) Niunber Living at Beginning of Year 66,513 65,114- 63,652 62,125 60,533 58,866 57.119 55.289 53.374 51.373 49.297 47,156 44,960 42,717 40,443 38,124 35,753 33,320 30,823 28,269 25,691 23,164 20,700 18,326 16,068 13,930 11,915 10,032 8,313 6,768 5,422 4,284 3,343 2,570 1.955 1,460 1,052 723 469 274 135 49 9 Number Dying during the Year 1,399 1,462 1,527 1,592 1,667 1,747 1,830 1,915 2,001 2,076 2,141 2,196 2,243 2,274 2,319 2,371 2,433 2,497 2,554 2,578 2,527 2,464 2,374 2,258 2,138 2,015 1,883 1,719 1,545 1,346 1,138 941 773 615 495 408 329 254 195 139 86 40 9 Probable Number out of every 100 Alive at the Beginning of a Year who will Survive the Year who will Die during the Year 4 97*8967 97*7547 97-6010 97*4374 97-2461 97*0322 96-7962 965364 96-2510 95*9590 95-6569 95*3431 95 -on I 94-6766 94 2660 93*7808 93*1950 92-5060 91-7140 90-8805 90-1639 89-3628 88-5314 87-6787 86-6941 85*5348 84-1964 82-8648 81-4147 80-1123 790115 780345 76-8770 76-0700 74-6804 72-0548 68 7263 64-8686 58-4222 49-2700 36-2964 18-3673 00-0000 (134) (135) 2-1033 2*2453 2 3990 2-5626 27539 2-9678 3-2038 34636 3*7490 4-0410 4*3431 4*6569 4-9889 53234 57340 6-2192 6 8050 7-4940 8-2860 9*1195 9-8361 10-6372 1 1 4686 12-3213 13*3059 14-4652 15-8036 17-1352 18*5853 19-8877 20-9885 21-9655 23-1230 23-9300 25-3196 27-9452 31*2737 35*1314 41*5778 50-7300 63*7036 81 6327 100-0000 Age at Begin- ning of Year 55 56 57 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 ?i 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 96 97 MORTALITY TABLES Age at Beginning of Year Number Living at Beginning of Year 10,000 z 8,461 2 7,779 3 7.274 4 6,998 5 6,797 6 6,676 7 6,594 8 6,536 9 6,493 10 6,460 II 6,431 12 6,400 13 6,368 M 6.335 IS 6,300 16 6,261 ^l 6,219 18 6,176 19 6,133 ao 6,090 21 6,047 22 6,005 23 5.963 24 5.921 25 5.879 26 5.836 27 5.793 28 5.748 29 5.698- 30 5.642 31 5.585 32 5.528 a3 5.472 34 5,417 35 5.362 36 5,307 37 5.251 38 5.194 39 5.136 40 5.075 41 5.009 42 4.940 43 4.869 44 4.798 45 4.727 46 4.657 ^l 4.588 48 4,521 49 4,458 CABLISLE TABLE For explanation see pp. 23-25 29 31 32 33 35 39 42 43 43 43 43 42 42 42 42 43 43 45 50 56 57 57 56 55 55 55 56 57 58 61 60 69 71' 71 71 70 69 67 63 61 Number Dying Age at during the ' Begfinning Year of Year 1.539 50 682 51 505 52 276 53 201 54 121 55 82 5^ 58 43 57 33 59 Number Living at Beginning of Year (136) 60 61 62 64 65 66 57 68 69 70 71 72 73 74 75 •76 77 78 79 80 81 82 84 85 86 87 88 89 00 91 92 93 94 95 96 % 99 4.397 4,338 4.276 4,211 4.143 4.073 4,000 3.924 3.842 3,749 3.643 3.521 3.395 3.268 3.143 3,018 2,894 2,771 2,648 2,525 2,401 2,277 2,143 1.997 1,841 1,675 1,515 1.359 • 1,213 1,081 953 837 725 623 529 445 367 296 232 181 142 105 75 54 40 30 23 18 14 II Number Dying during the Year 59 62 65 68 70 73 76 82 93 106 122 126 127 125 125 124 123 123 123 124 124 134 146 156 166 160 156 146 132 128 116 112 102 94 84 78 71 64 51 39 37 30 21 14 10 7 5 4 3 2 t TABLES COMBININQ MORTALITY OF SINGLE LIVES AND INTEREST % \ For explanation see pp. 25-28 (137) MORTALITY TABLES MOKTALlTY TABLES I VALUE OF AN ANNUITY ON A SINGLE LIFE ACCORDING TO THE NOBTHAMPTON TABLE OF MOBTALITY Age 3% 4% 5% 6% Age I l6-02I 13-465 "•563 10-107 I 2 18-599 15633 13-420 11-724 2 3 19-575 16-462 14-135 12-348 3 4 20-2IO 17-010 14-613 12-769 4 5 20473 17-248 14-827 12-962 5 6 20727 17-482 15-041 13-156 6 7 20-853 1 7 -61 1 15-166 13-275 7 8 20-885 17-662 15-226 13-337 w 8 9 20-812 17-625 15-210 13-335 9 lO 20-663 17-523 15-139 13-285 10 II 20-480 17-393 15-043 13-212 II 12 20-283 17-251 14-937 13-130 12 13 20081 17-103 14826 13044 13 14 19-872 16-950 14-710 12-953 14 15 19-657 16-791 14-588 12-857 15 i6 19*435 16-625 14-460 12-755 16 % 19-218 16-462 14-334 12-655 '7 19-013 16-309 14-217 12-562 16 19 18-820 16-167 14-108 12-477 19 20 18-638 16-033 14-007 12-398 20 21 18-470 15-912 13-917 12-329 21 22 18-311 15-797 13-833 12-265 22 23 18-148 15-680 13-746 1 2 200 23 24 17-983 15-560 13-658 12-132 24 25 17-814 .15-438 13-567 12063 25 26 17-642 15-312 13-473 11-992 26 27 17-467 15-184 13-377 11-917 27 28 17-289 15-053 13-278 1 1 -841 28 29 17107 14-918 13-177 11-763 29 30 16-922 14-781 13-072 1 1 682 30 31 16-732 14-639 12-965 11-598 31 32 16-540 14-495 12-854 11-512 32 33 16-343 14-347 12-740 1 1 -423 13 34 16-142 14-195 12-623 11-331 34 35 15-938 14-039 12-502 1 1 -236 35 36 15-729 13-880 12-377 II-I37 36 37 15-515 13-716 12-249 1 1 -035 % 38 15-298 13-548 12-116 10-929 39 15-075 13-375 1 1 -979 10-819 39 40 14-848 13-197 1 1 -837 10-705 40 41 14-620 13-018 1 1 -695 10-589 41 42 14-391 12-838 11-551 10-473 42 43 14-162 12-657 1 1 -407 10-356 43 44 13.929 12-472 11-258 10-235 44 45 13-692 12-283 1 1 -105 lO-IIO 45 v> VALUE OF AN ANNUITY ON A SINGLE LIFE ACCOBDING TO THE NOBTHAMPTON TABLE OF MOBTALITY Age 46 47 48 49 50 51 52 53 54 55 56 P 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 3% 13450 13-203 12-951 12-693 12436 12-183 1 1 -930 1 1 674 1 1 -414 11-150 10-882 io-6ii 10-337 10-058 9-777 9-493 9-205 8-910 8-6II 8-304 7-994 7-682 7-367 7051 6-734 6-418 6-103 5-794 5-491 5-199 4-925 • 4 652 4-372 4-077 3-781 3-499 3-229 2-982 2-793 2-620 2-462 2-312 2-185 2-013 1-794 4% 12*089 II 890 11-685 11-475 1 1 -264 1 1 -057 10-849 10-637 10-421 10-201 9-977 9749 9-516 9-280 9-039 8-795 8-547 8-291 8 030 7-761 7-488 7-211 6-930 6647 6-361 076 790 507 230 962 4-710* 4-457 4197 3921 3-643 3-377 3-122 2-887 2-708 2-543 2-393 2-251 2-131 I 967 1-758 5% 10-947 10-784 io-6i6 10-443 10-269 10-097 9925 9-748 9-567 9382 9-193 8-999 8-8oi 8-599 8-392 8-181 7-966 7-742 7-514 7-276 7-034 6-787 536 281 023 5-764 5-504 5-245 4-990 4-744 6% 9-980 9-846 9707 9563 9-417 9273 9-129 8980 8-827 8670 8-509 8-343 8-173 7-999 7*820 7-637 7-449 7-253 7-052 6-841 6 625 6-405 6-179 5 949 5716 5*479 5-241 5-004 4-769 4-542 4-5II 4326 4-277 4-109 4-035 3-884 3-776 3-641 3-515 3-394 3-263 3-156 3-020 2-926 2-797 2713 2-627 2-551 2-471 2-402 2-328 2-266 2-193 2*138 2-080 2031 1-924 1-882 1-723 1-689 Age 46 47 48 49 50 51 52 53 54 56 56 5Z 58 59 60 61 62 63 64 65 66 % 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 ^o 14-454 14-273 14-088 13-899 13-707 13-510 13*309 13*103 12-891 12-673 12-450 12-219 11-982 11*737 1 1 -484 11-224 10*955 10-676 10-387 10-086 9*783 9*485 9-194 8-900 8-605 8309 8-020 7-736 7-455 7-171 6-886 6-604 6323 6-050 5-788 5-535 5-286 5-050 4-821 4 594 4-376 Oy ^o 12-883 12-743 12-599 12-451 12-300 12-145 11-986 1 1 -822 1 1 -653 11-477 1 1 -298 II-IIO 10-916 10-714 10-506 10-289 10063 9-828 9583 9-326 9-065 8-808 8-556 8-300 8-041 7-781 7-525 7-273 7-023 6-768 6-512 6-257 6-003 5-754 5-515 5-283 5-054 4-836 4-624 4-413 4-210 Age 20 25 30 35 40 41 42 43 44 45 46 % 49 50 51 52 53 54 55 56 57 58 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 2 For explanation see pp. 25-27 (144) MORTALITY TABLES VALUE OF AN ANNUITY ON A SINGLE LIFE ACCOEDING TO THE GOVEKNMENT EXPEBIENCE, 1883 Femalbs Age 20 25 30 35 40 41 42 43 44 45 46 % 49 50 51 52 53 54 55 56 5; 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 IS 2i% 24-479 23-397 22-223 20-939 19-523 19-223 18-915 18-601 18-279 17-950 17-612 17-266 16-91 1 16-552 16-190 15-831 15*465 15-091 14-712 14-329 13-936 13-538 13*138 12-735 12-333 1 1 -925 11-523 1 1 -120 10-713 10-296 9-880 9-463 9-052 8-650 8-260 7-893 7*539 7-196 6-863 6-537 6-220 5-911 5-613 5-323 5*044 3% 22-292 21-415 20-451 19-380 i8-i8o 17-923 17-658 17*386 17-107 16-820 16-525 l6-22I 15-910 15*592 15-271 14*952 14-626 14-292 13*951 13-607 13-252 12-891 12-527 12-160 1 1 -791 11-417 1 1 -046 10-674 10-297 9*909 9-521 9*131 8-745 8-367 8-000 7-654 7-319 6-994 6-677 6-367 6-064 5-769 5*483 5205 4*937 3i? o 20-409 19-695 18-898 18-001 16-980 16-758 16-529 16-294 16-051 15-801 15*543 15-276 15-000 14-719 14-434 14-149 13-859 13-558 13*252 12-942 12-620 12-292 11-960 1 1 -625 11-287 10-943 10-601 10-257 9-907 9*546 9*183 8-818 8-456 8-100 7-754 7-426 7-110 6-801 6-500 6-204 a o 15-904. 15-712 15-514 15-310 15-098 14-879 14-652 14-416 14-173 13-923 13-669 13-415 13-155 12-885 12-609 12-328 12-036 11-738. 11-435 11-128 io-8i8 ► 10-500 10-185 9-866 9-541 9-204 8-865 8-523 8-182 7-847 7-520 7-210 6-910 6-617 6-331 6-048 5*915 5*773 5*633 5-502 5-359 5-240 5-092 4*983 4*834 4*735 5% 14063 13-920 13-769 13-613 13*451 13-281 13-105 12-920 12-727 12-528 12-325 I2-I2I 1 1 -91 1 11*692 1 1 -467 1 1 -236 10-994 10-745 10-492 10-233 9-971 9-700 9-429 9-155 8-873 8-579 8-282 7-980 7-678 7-379 7-087 6-809 6-539 6-274 6-014 5*757 5*504 5-256 5*015 4*777 4*547 Age 20 25 30 35 40 41 42 43 44 45 46 % 49* 50 51 52 53 54 55 56 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 ■"1 (145) MORTALITY TABLES SINGLE PAYMENT TO SECUEE £1 AT DEATH ACCOEDING TO THE CAEUSLE TABLE OF MOBTALITY Age M 111 i(i *■ o I 2 3 4 5 6 7 8 9 10 II 12 13 14 IS • i6 19 20 21 22 23 24 25 26 29 30 31 32 33 34 i 39 40 41 42 43 44 45 46 47 48 49 3% 4% •46641 •38587 •34463 •31021 •29267 •28079 •27633 •27572 •27764 •28125 •28606 •29145 •29681 •30222 •30771 •31315 •31833 •32334 •32841 •33362 •33901 •34455 •35037 •35637 •36252 •36808 •37548 •38218 •38890 •39531 •40129 •40734 •41357 •42010 •42694 •43399 •441 17 •44870 •45624 •46393 •47156 •47893 •48621 •49352 •50108 •50885 •51694 •52542 •53439 •54406 •41224 •32483 •27976 •24173 •22187 •20800 •202 1 1 •20038 •20137 •20419 •20833 •21313 •21789 •22272 •22762 •23249 •23706 •24150 •24590 •25052 •25532 •26031 •26562 •271 15 •27690 •28289 •28901 •29538 •30176 •30781 •31338 •31903 •32491 •331 13 •33771 •34457 •35170 •35901 •36649 •37416 •38178 •3891 1 •39636 •40364 •41 120 •41905 •42734 •43607 •44542 •45565 5% •37700 •28595 •23891 •19886 •17757 •16238 •15548 •15286 •15305 •15514 •15862 •16281 •16695 •17114 •17543 •17967 •18362 •18733 •19110 •19505 •19919 •20352 •20819 •21310 •21824 •22367 •22919 •23500 •24086 •24633 •25129 •25633 •26162 •26729 •27333 •27967 •28633 •29319 •30024 •30752 •31477 •32167 •32852 •33538 •34257 •35010 •35810 •36662 •37586 •38610 6% 7% •35251 •25974 •21 179 ' ^17065 •14857 •13255 •I 249 1 •12*163 •12117 •12264 •12558 •12921 •13277 •13640 •14013 •14381 •1471S •15026 •15343 •15677 •16028 •16402 •16809 •17240 •17692 •18174 •18672 •19198 •19725 •202 II •20642 •21083 •21547 •22051 •22594 •23172 •23783 •244 11 •25062 •25736 •26404 •27038 •27666 •28294 •28957 •29653 •30400 •31204 •32087 •33077 For explanation see pp. 27, 28 •33421 •24079 19258 •15097 •12847 •11198 •10387 •10007 •09916 •1002 1 •10263 •10577 •10891 •11211 •11538 •11859 •12147 •12408 •12677 •12958 •13259 •13579 •13933 •14312 •14711 •15136 •15581 •16052 •16529 •16962 •17335 •17714 •18120 •18564 •19049 •19565 •20115 •20684 •21279 •21894 •22509 •23085 •23648 •24210 •24805 •25440 •26127 •26873 •27697 •28639 8 •32015 •22674 •17867 •13696 •11430 •09748 •08904 •08489 •08363 •08430 •08637 •08919 •09193 •09474 •09763 •10045 •10289 •105 II •10733 •10970 •11222 •I 1496 •I 1807 •12141 •12496 •12874 •13267 •13689 •14119 •14504 •14830 •15155 •15504 •15889 •16319 •16778 •17274 •17793 •18326 •18889 •19444 •19963 •20467 •20971 •21504 •22074 •22696 •23378 •24141 •25030 Age O I 2 3 4 5 6 7 8 9 10 II 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 % 29 30 31 32 33 34 36 37 38 39 40 41 42 43 44 46 '4 49 (146) MORTALITY TABLES SINGLE PAYMENT TO SECTIEE £1 AT DEATH ACCORDING TO THE CARLISLE TABLE OF MORTALITY Age 50 51 52 53 54 57 58 59 60 61 62 63 64 % % 69 70 71 72 73 74 76 77 78 79 80 81 82 83 84 86 87 88 89 90 91 92 93 94 96 97 98 99 100 3% 4% •55429 •56509 •57598 •58699 •59812 •60948 •62096 •63260 •64413 •65512 •66531 •67436 •68325 •69222 •70157 •71112 •72103 •73122 •74168 •75246 •76340 •77465 •78525 •79483 •80334 •81033 •81717 •82352 •82996 •83713 •84374 •85090 •85734 •86392 •87027 •87682 •88253 •88719 •89002 •89325 •89809 •89861 •89582 •89261 •891 18 •89057 •89212 •89633 •90132 •90880 •92185 •46658 •47824 •49003 •5021 1 •51436 •52694 •53977 •55286 •56591 •57833 •58987 •60007 •61012 •62033 •63103 •64203 •65347 •66539 •67770 •69043 •70349 •71701 •72979 •74136 •75161 •76004 •76831 •77597 •78378 •79256 •80066 •80950 •81745 •82561 •83352 ■84173 •84891 •85477 •85833 •86242 •86861 •86929 •86569 •86156 •85962 •85868 •86047 •86569 •87184 •88127 •89797 5% 6% 7% 8% Age 50 •39714 •34164 •29679 •26022 •40905 •35347 •30831 •27126 51 •42124 •36558 •32015 •28267 52 •43371 •37804 •33238 •29459 5,3 •44648 •39089 •34507 •30696 54 •45967 •40431 •35842 •32007 55 •47319 •41812 •37229 •33370 56 •48710 •43243 •38668 •34800 57 •50105 •44687 •401 2 1 •36252 58 •51433 •46062 •41514 •37644 59 •52667 •47336 •42803 •38926 60 •53752 •48445 •43922 •40036 61 •54824 •49549 •45027 •41 133 62 •55914 •50676 •46165 •42259 63 •57067 •51875- •47389 •43481 64 •58262 •53126 •48664 •44763 % •59510 •54440 •50012 •46133 •60824 •55832 •51451 •47593 ?z •62186 i ^57287 •52969 •49141 68 •63605 •58809 •54565 •50793 69 •65067 •60389 •56234 •52519 70 •66595 •62053 •58000 •54371 71 •68043 •63638 •59687 •56134 72 •69357 •65075 •61225 •57748 73 •70524 •66355 •62586 •59178 74 •71481 1 ^67396 •63698 •60333 75 •72419 ■ ^6842 1 •64791 •61481 76 •73291 •69377 •65805 •62548 77 •74181 •70351 •66851 •63645 78 •75191 •71472 •68055 •64919 79 •761 19 •72502 •69167 •66096 80 •77148 •73645 •70410 •67422 81 •78067 •74675 •71529 •68615 82 •79019 •75740 .72693 •69859 83 •79948 •76781 •73838 •71089 84 •80910 ; ^77874 •75042 •72393 55 •81762 1 -78836 •76108 •73548 86 •82452 •79628 •76978 •74496 SZ •82870 1 •80101 .77502 •75067 88 •83357 ; ^80658 •79078 •75733 89 •84103 i -81513 •79196 •76793 90 •84186 81615 •78634 •76926 91 •83752 ' •81111 •77973 •7631 1 92 •83248 •80528 •77633 •75578 93 •83005 i ^80234 •77512 •75185 94 •82876 1 ^80064 •77424 •74941 ?5 •83071 i ^80268 •77626 •75126 96 •83676 •80936 •78352 •75904 97 •84391 •81734 .79216 •76822 98 •85500 •82996 •80609 •78326 99 •87505 •85306 •83193 •81 163 100 I (147) MOETALITY TABLES V II r SINGLE PAYMENT TO SECUBE £1 AT DEATH ACCOEDING TO THE INSTITUTE OF ACTTJAEIES HEALTHY MALES TABLE Age lO II 12 13 14 15 16 17 18 19 20 21 22 23 24 ^ 28 29 30 31 32 33 34 36 37 38 39 40 41 42 43 44 46 47 48 49 50 51 52 53 54 2*% •32361 •32841 •33396 •34012 •34672 •35360 •36060 •36757 •37433 •38072 •38671 •39254 •39830 •40418 •41030 •41668 •42328 •43005 •43691 •44385 •45086 •45794 •46516 •47251 •48002 •48766 •49543 •50329 •51125 •51933 •52755 •53595 •54457 •55340 •56236 •57147 •58064 •58985 •59910 •60842 •61782 •62732 •63695 •64667 •65645 3% •26752 •27198 •27726 •28320 •28962 •29637 •30326 •310J1 •31677 •32302 •32886 •33451 •340 II •34584 •35183 •35812 •36465 •37139 •37824 •38518 •39221 •39934 •40662 •41407 •42170 •42950 •43745 •44553 •45372 •46207 •47060 •47935 •48836 •49762 •50707 •51669 •52642 •53621 •54608 •55605 •56613 •57635 •58676 •59729 •60792 3i% •22378 •22783 •23274 •23836 •24450 •25099 •25764 •26427 •27069 •27670 •28226 •28763 •29294 •29839 •30413 •31019 •31652 •32307 •32975 •33653 •34343 •35044 •35762 •36499 •37256 •38033 •38828 •39637 •40461 •41303 •42165 •43054 •43974 .44921 •45892 •46884 •47889 •48904 •49930 •50970 •52023 •53096 •54191 •55303 •56428 4a o •18937 •19299 •19750 •20276 •20856 •21473 •22109 •22742 •23354 •23924 •24447 •24950 •25446 •25957 •26499 •27074 •27678 •28306 •28947 •29600 •30266 •30943 •31640 •32357 •33097 •33858 •34639 •35437 •36251 •37086 •37943 •38831 •39752 •40706 •41685 •42690 •43712 •44745 •45792 •46856 •47938 •49043 •50174 •51327 •52496 41a 2/0 •16204 •16524 •16937 •17425 •17970 •18553 •19156 •19758 •20337 •20873 •21361 •21827 •22287 •22761 •23267 •23808 •24378 •24973 •25583 •26205 •26840 •27488 •28156 •28847 •29561 •30299 •31057 •31834 •32629 •33446 •34289 •35164 •36076 •37023 •37999 •39004 •40028 •41067 •42122 •43197 •44293 •45416 •46569 •47748 •48947 For explanation see pp. 27, 28 (148) 5% •14015 •14296 •14670 •15122 •15632 •16182 •16752 •17322 •17869 •18371 •18823 •19254 •19676 •20113 •20582 •21087 •2 162 1 •22182 •22758 •23346 •23948 •24563 •25199 •25858 •26542 •27251 •27981 •28731 •29501 •30294 •31 1 14 •31969 •32863 •33796 •34760 •35755 •36772 •37806 •38858 •39934 •41033 •42162 •43326 •44518 •45735 Age 10 II 12 13 14 15 16 19 20 21 22 23 24 25 26 29 30 31 32 33 34 35 36 P 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 MOETALITY TABLES SINGLE PAYMENT TO SECUBE £1 AT DEATH ACCOBDING TO THE INSTITUTE OF ACTUABIES HEALTHY MALES TABLE Age 57 58 59 60 61 62 63 64 % % 69 70 71 72 73 74 79 80 81 82 83 84 u u 89 90 91 92 93 94 2^ 2 % 97 •66627 •67612 •68597 •69583 •70568 •71548 •72522 •73485 •74437 •75375 •76302 •77220 •78132 •79039 •79948 •80849 •81734 •82593 •83415 •84190 •84919 •85628 •86313 •86978 •87628 •88256 •88850 •89394 •89899 •90353 •90778 •91200 •91645 •92113 •92659 •93272 •93899 •94538 •95224 •95899 •96542 •97124 •97561 3% •61863 •62939 •64020 •65103 •66190 •67274 •68353 •69424 •70484 •71532 •72569 •73600 •74626 •75650 •76678 •77700 •78706 •79685 •80623 •81510 •82345 •83159 •83946 •847 1 1 •85461 •86187 •86874 •87506 •88090 •88617 •891 10 •89601 •901 18 •90663 •91 301 •92020 •92756 •93508 •94317 •95116 •95878 •96568 •97087 3i a 2 o •57566 •58712 •59866 •61026 •62193 •63361 •64526 •65685 •66835 •67974 •69104 •70230 •71354 •72478 •73610 •74738 •75852 •76937 •77980 •78967 •79897 •80806 •81686 •82543 •83384 •84200 •84974 •85686 •86345 •86940 •87496 •88050 •88635 •89252 •89977 •90796 •91637 •92498 •93426 •94344 •95222 •96018 •96618 O/ ^o 4i% •53682 •54881 •56090 •57309 •58539 •59773 •61007 •62237 •63461 •64675 •65883 •67089 •68297 •69507 •70729 •71950 •73159 •74339 •75475 •76551 •77567 •78561 •79525 •80466 •81392 •82291 •83145 •83931 •84659 •85317 •85932 •86545 •87194 •87878 •88686 •89600 •90541 •91507 •92549 •93583 •94575 •95475 •96154 5% •50166 •51401 •52651 •53915 •55193 •56478 •57766 •59053 •60337 •61613 •62886 •64159 •65437 •66721 •68021 •69323 •70615 •71879 •73098 •74254 •75347 •76418 •77459 •78476 .79479 •80455 •81383 •82238 •83031 •83747 •84416 •85084 •85792 •86541 •87427 •88432 •89468 •90534 •91687 •92834 •93934 •94933 •95694 Age •46975 •48235 •49513 •50809 •52122 •53446 •54777 •56109 •57441 •58767 •60092 •61421 •62758 I •64105 j •65473 i •66845 •68210 •69549 •70841 •72069 •73231 •74372 •75482 •76569 •77643 •78690 •79686 •80605 •81458 •82228 •82948 •83667 •84430 •85239 •86198 •87290 •88417 •89579 •90840 •92096 •93304 •94405 •95238 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 7| 76 77 78 79 80 81 82 83 84 U 87 88 89 90 91 92 93 94 95 96 97 •i< (149) MORTALITY TABLES Ml 'x ANNUAL PAYMENT DUBING LIFE TO SECURE £1 AT DEATH ACC0BDIN6 TO THE INSTITUTE OF ACTUARIES HEALTHY MALES TABLE Age 10 II 12 14 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 210/ 2 / o •01 167 •OU93 •01233 •01257 ■01295 15 •01334 16 •01376 17 •OI418 18 ■01459 19 •01499 20 •0153^ 21 •01576 22 •OI615 23 •01655 24 01697 25 •01742 26 •01790 27 •01840 28 •01893 29 •01947 •02003 •02061 •02I2I •02185 •02252 •02322 •02395 •0247 1 •02551 •02635 •02723 •02817 •02917 •03022 •03134 •03253 •03377 •03508 •03645 •03790 •03943 •04106 •04279 •04464 •04661 3 0/ /o •01064 •01088 •01 1 17 •01 1 51 •01 188 •01227 •01268 •01309 •01350 •01390 •01427 •01464 'OI50I •01540 •OI58I •01625 •01672 •OI72I •01772 •01825 •01880 •01936 •01996 •02058 •02124 •02193 •02265 •02340 •02419 •02502 •02589 •02682 •02780 •02885 •02996 •031 14 •03238 •03367 •03504 •03648 •03801 •03963 •04136 •04320 •04516 02 /o •00975 •00998 •01026 •01058 •01094 •01 133 •01 174 •OI2I5 •01255 •01294 •01330 •01365 •0140 1 •01438 •01478 •01 52 1 •01566 •OI6I4 •01664 •OI7I5 •01769 •01824 •01883 •01944 •02008 •02076 •02146 •02221 •02298 •02380 •02465 •02557 •02654 •02758 •02868 •02985 •03108 •03237 •03372 •03515 •03667 •03828 •04000 •04184 •04379 For explanation see pp. 27, 28 4% •00899 •00920 ■00947 •0097^ •01014 •01052 •01092 •01 132 •01 1 72 •01210 •01245 •01279 •01313 •01348 •01387 •61428 •01472 •01519 •01567 •01617 •01669 •01723 •01780 •01840 •01903 •01969 •02038 •021 1 1 •02187 •02267 •02352 •02442 •02538 •02640 •02749 •02865 •02987 •031 15 •03249 •03391 •03542 •03702 •03873 •04056 •04250 (i5<^ 4i% 5% •00833 •00852 •00878 •00909 •00943 •00981 •01020 •01060 •01099 •01 1 36 •01 1 70 •01202 •01235 •01269 •01306 •01346 •01388 •01433 •01480 •01529 •01580 •01632 •01688 •01746 •01807 •01872 •01940 •0201 1 •02086 •02164 •02247 •02336 •02430 •02532 •02639 •02754 •02874 •03001 •03134 •03275 •03424 •03583 •03753 •03935 •04129 •00776 •00794 •00819 •00848 •00882 •00919 •00958 •00998 •01036 •01072 •01 104 'Oil 35 •01 166 •01 199 •01234 •01272 •OI3I4 •01357 •01403 •01450 •01499 •01550 •01604 •OI66I •OI72I •01784 •01850 •01920 •01993 •02069 •021 5 1 •02238 •02331 •02431 •02537 •02650 •02769 •02895 •03026 •03166 •03314 •03471 •03640 •03821 •04013 Age 10 II 12 13 14 IS 16 ;i 19 20 21 22 23 24 26 27 28 29 30 31 32 33 34 37 38 39 40 41 42 43 44 46 47 48 49 50 51 52 53 54 MORTALITY TABLES ANNUAL PAYMENT DURING LIFE TO SECUBE £1 AT DEATH ACCOBDINO TO THE INSTITUTE OF ACTUABIES HEALTHY MALES TABLE Age 2i% 55 56 57 59 60 61 62 63 64 65 66 68 ! 69 ! 70 71 72 73 74 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 •04870 •05092 •05328 •05580 •05848 •06134 •06437 •06760 •07102 •07466 •07853 •08268 •08714 •09197 •09725 •10297 •10914 •11572 •12267 •12988 •13734 •14532 •15382 •1629 1 •17275 •18329 •19435 •20559 •21707 •22844 •24009 •25279 •26755 •28485 •30786 •33813 •37537 •42217 •48624 •57035 •68105 •82364 •97561 3% •04725 •04946 •05182 •05434 •05702 •05987 •06291 •06613 •06956 •07319 •07705 •08120 •08566 •09049 •09576 •10148 •10766 •I 1425 •12119 •12840 •13585 •14382 •15230 •16138 •17121 •18174 •19277 •20399 •21543 •22676 •23834 •25096 •26563 •28282 •30570 •33585 •37294 •41954 •48338 •56719 •67748 •81954 •97087 3i% 0/ •04588 •04809 •05044 •05295 •05563 •05848 •061 5 1 •06473 •06815 •07177 •07564 •07978 •08423 •08906 •09433 •10005 •10622 •11281 •I 1976 •12696 •13440 •14236 •15083 •15989 ■16970 •18022 •19123 •20242 •21383 •22510 •23662 •24916 •26373 •28081 •30358 •33360 •37053 •41694 •48055 •56405 •67394 •81546 •96618 'o 41 a 2 /o •04458 •04678 •04913 •05163 •05431 •05715 •06018 •06339 •06680 •07042 •07427 •07841 •08286 •08767 •09294 •09866 •10483 •I 1 142 •I 1836 •12556 •13299 •14094 •14939 •15843 •16823 •17873 •18972 •20089 •21225 •22348 •23493 •24739 •26187 •27884 •30149 •33138 •36816 •41438 •47776 •56095 •67044 •81 144 •96154 5% •04335 •04555 •04788 •05038 •05304 •05588 •05890 •062 1 1 •06551 •06912 •07296 •07709 •08153 •08634 •09160 •09731 •10348 •I 1007 •11701 •12420 •13161 •13954 •14798 •I 5701 •16679 •17727 •18824 •19938 •21071 •22189 •23327 •24565 •26003 •27689 •29943 .32919 •36582 •41 185 •47499 •55789 •66696 •80742 •95694 Age •04219 •04437 •04670 •04918 •05184 •05467 •05768 •06087 •06427 •06787 •07170 •07581 •08025 •08504 •09030 •09601 •IO218 •I1876 •II569 •12287 •13027 •13819 •14660 •15561 •16538 •17584 •18679 •19790 •20920 •22032 •23163 •24393 •25823 •27498 •29740 •32703 •36351 •40935 •47226 •55486 •66354 •80350 •95238 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 77 78 79 80 81 82 83 84 ^§ 86 87 88 89 90 91 92 93 94 % 97 i I ;i (151) r '■. MORTALITY TABLES PKESENT VALUE OF BEVEBSIOIT TO A PEEPETUITY AT DEATH OP A PEESON OP AGE STATED. GOVERNMENT EXPERIENCE, 1883 MALES Age 20 25 30 35 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 2^ o^ 2 /o 17-566 I87I8 19-921 21-178 22 '499 22-773 23-050 23-330 23-613 23-901 24-193 24-489 24-791 25-100 25-412 25732 26-059 26-392 26733 27-081 27-437 27 -802 28-177 28-561 28-946 29-322 29-686 30-052 30-414 30-775 31-125 31-467 31-804 32-142 3^-479 32-809 33-136 ■33-454 33-755 34-045 34-328 34-596 34-855 35-109 35 '353 3% 12-772 13-732 14-745 15-818 16-957 17-195 17-436 17-680 17-929 18-181 18-438 18-700 18-967 19-242 19-520 19-807 20-100 20*400 20-708 21-024 21-347 21 -680 22-023 22-377 22-732 23-079 23-417 23-756 24-094 24-431 24-760 25-081 25-397 25-716 26-034 26-347 26-658 26-960 27-247 27-524 27-795 28-052 28-300 28-545 28-780 For explanation see p. 28 3i% 9635 0-441 1-300 2-2l8 3-206 3413 3-624 3-838 4-057 4-279 4-506 4-738 4-976 5-220 5-468 5-726 5-989 6 260 6-539 6-825 7-120 7-425 7-739 8-393 8-714 9-028 9-343 9-658 9-974 20-282 20-584 20-882 2i*i83 21-484 21-781 22 -076 22363 22-637 22-902 23*161 23408 23-646 23-882 24*108 4% 0-546 0-727 0-912 I-IOI 1-293 1-490 1-691 1-897 2*109 2*'327 2-550 2*781 3-018 3-263 3-516 3-776 4-045 4-324 4-613 4-914 5-217 5-515 5-806 6-100 6*395 6-691 6-980 7-264 7-545 7*829 8*114 8*396 8*677 8-950 9*212 9-465 9*714 9-950 20*179 20-406 20-624 5% 7*117 7257 7-401 7*549 7-700 7-855 8-014 8-178 8-347 8-523 8-702 8-890 9 084 9-286 9-494 9-711 9 937 0-172 0*417 0*674 0935 1*192 1-444 1-700 1-959 2*219 2-475 2*727 2-977 3*232 3*488 3-743 3-997 4*246 4-485 4*717 4-946 5-164 5376 5-587 5*790 Age 20 25 30 35 40 41 42 43 44 45 46 47 48 49 SO 51 52 53 54 55 56 57 58 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 (152) MORTALITY TABLES PRESENT VALUE OF REVERSION TO A PERPETUITY AT DEATH OF A PERSON OF AGE STATED. GOVERNMENT EXPERIENCE, 1883 FEMALES Age 20 25 30 35 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 60 61 62 64 65 66 67 68 69 70 71 72 73 74 75 76 2i9 o 15-521 16-603 17-777 19-061 20-477 20-777 21-085 21-399 21-721 22 -050 22-388 22-734 23-089 23-448 23-810 24-169 24-535 24909 25-288 25-671 26-064 26-462 26-862 27-265 27-667 28-075 28-477 28-880 29-287 29-704 30-120 30-537 30-948 31 350 31740 32-107 32-461 32-804 33-137 33-463 33-780 34-089 34-387 34-677 34-956 a o 1 1 -041 11-918 12-882 13-953 15-153 15-411 15-676 15-947 16-226 16-513 16-808 17-112 17-423 17-741 18-063 18*382 18-707 19-041 19-382 19-726 20-081 20-443 20-806 21-173 21*542 21-916 22-287 22-659 23-036 23-424 23-812 24-202 24-588 24*966 25-333 25-679 26-014 26-339 26-655 26-967 27-269 27-564 27-850 28-128 28*396 3i 2 /O 8-1^2 8-876 9673 10-570 11-591 11*813 12-042 12-277 12-520 12-770 1 3 -028 13-295 13-571 13-852 14-137 14*422 14*712 15-013 15-319 15-629 15-951 16*279 16-61 1 16-946 17*284 17-628 17-970 18-314 18-664 19-025 19-388 19-753 20-115 20-471 20-817 21-145 21*461 21*770 22-071 22-367 22-656 22-938 23-212 23-479 .23-737 a o 9-096 9-288 9-486 9-690 9-902 10*121 10*348 10-584 10-827 1 1 -077 II -331 11-585 11-845 12115 12-391 12-672 12-964 13*262 13-565 13-872 14*182 14*500 14*815 15134 15-459 15-796 16*135 16*477 16-818 17*153 17-480 17*790 18-090 18-383 18-669 18-952 19-227 19*498 19-760 20-017 20-265 5% 5-937 6080 6*231 6-387 6-549 6-719 6-895 7 080 7-273 7-472 7-675 7-879 8-089 8-308 8-533 8-764 9*006 9-255 9-508 9-767 10*029 10*300 10*571 10-845 11-127 11*421 11*718 1 2 -020 12-322 12-621 12-913 13*191 13-461 13-726 13-986 14*243 14-496 14-744 14-985 15*223 15-453 Age 20 25 30 35 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 78 79 80 II ^1 (153) i n: MORTALITY TABLES ! Present Value of Eeversion to a Perpetuity at Death of a Person of Age stated. NORTHAMPTOH TABLE Age 5 lO 15 20 25 30 35 40 45 50 55 60 65 70 75 ?o 85 90 95 Age 5 10 15 20 25 30 35 40 45 50 60 65 70 75 80 85 90 95 3% 1 2 -860 12-670 13-676 14-695 15-519 16-411 17*395 18-485 19-641 20-897 22-183 23556 25 -029 26-599 28-134 29-552 30-713 31-539 33-091 3% 9-640 9-821 10-751 11-639 12-668 13-777 14-900 16-190 17-470 19030 20-925 22 -842 24-416 26-210 27-821 28-968 30104 30-834 30576 4% 7-752 7-477 8-209 8-967 9-562 10-219 10-961 11-803 12-717 13-736 14-799 15-961 17-239 18-639 20-038 21-357 22-457 23-242 24-760 5% 5-173 4-861 5-412 5-993 6433 6928 7498 8-163 8-895 9-731 10-618 11-608 12-724 13-977 15-256 16-485 17-529 18-277 19-762 CABLISLE TABLE 4% 5% 5-406 5-415 6-044 6*637 7-355 8-148 8-959 9 926 10-896 12-131 13-700 15-337 16-693 18-291 19-761 20-817 21-885 22-584 22 -326 3-410 3-331 3-773 4183 4-697 5-277 5-873 6-610 7*352 8-340 9653 11-060 12-235 13664 15-011 15-985 16-991 17-661 17-404 For explanation see p. 28 (154) 6% 3*705 3*382 3-810 4-269 4*604 4*985 5-431 5-962 6*557 7-250 7*997 8-847 9-826 10-951 12*125 13-273 14-265 14-978 16-431 6% 2*342 2-219 2*541 2-832 3-211 3-647 4-094 4*665 5*239 6-036 7*143 8*363 9*386 10-669 11-907 12-809 13*758 14-401 14*145 Age 5 10 15 20 25 30 35 40 45 50 65 70 75 80 85 90 95 Age 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 TABLES COMBINING MORTALITY OF TWO AND THREE LIVES AND INTEREST PREMIUM CONVERSION TABLES For explanation see pp. 29-39 (155) MORTALITY TABLES— TWO LIVES I I i Value of an Anniiity for the Joint Continuance of Two Lives according to the NORTHAMPTON TABLE Ages 3% 15*220 4% 5% Ages 3% 4% 5% 15 15 13-41 1 1 1 -964 35 45 10-622 9-706 8-921 IS 20 14-660 12-961 11-585 35 50 9-912 9-110 8-415 1525 14-230 12-630 1 1 •3?4 35 55 9131 8-448 7-849 15 30 13-734 1 2 -246 1 1 -021 35 60 8-227 7-669 7-174 15 35 13-151 1 1 -787 10-655 3565 7-177 6-747 6-360 1540 12-459 1 1 -234 10-205 35 70 5-971 5-663 5-382 1545 1 1 -687 10-607 9-690 35 75 4-720 4*516 4-327 1550 10-799 9-872 9-076 3580 3-506 3-383 3-268 15 55 9-851 9-077 8-403 40 40 10-764 9-820 9-016 15 60 8-790 8-170 7-622 40 45 10-236 9-381 8-643 15 65 7-597 7-127 6-705 40 50 9-590 8-834 8-177 1570 6-264 5-933 5-631 4055 9-870 8-221 7-651 1575 4-911 4695 4-495 40 00 8-025 7-490 7-015 15 80 3-621 3-492 3-372 40 65 7-030 6-614 6-240 20 20 14-133 12-535 11-232 40 70 5-871 5-571 5-298 20 25 13-741 12-229 10-989 40 75 4-656 4-457 4-272 . 20 30 13-286 11-873 10-707 40 80 3469 3-349 3-236 2035 12-744 11-445 10-363 45 45 9-776 8-990 8-312 20 40 12-096 10-924 9*937 45 50 9-204 8*503 7-891 2045 11-367 10-330 9-448 4555 8-557 7-948 7-411 20 50 10-523 9-630 8-861 45 60 7-781 7-274 6-822 2055 9-617 8-869 8-216 4565 6-850 6-453 6-094 20 60 8-597 7-995 7-463 45 70. 5-749 5-460 5-195 20 65 7 '444 6-986 6-576 45 75 4-580 4-386 4-206 20 70 6-149 5-826 5-532 I 4580 3-426 3-308 3-197 2075 4-831 4-619 4-424 1 50 50 8-714 8-081 7-522 20 80 3-569 3-443 3-325 ; 5055 8-152 7-593 7-098 25 25 13-383 11-944 10-764 5060 7-461 6-989 6-568 25 30 12-966 1 1 -618 10-499 50 65 6-61 1 6-236 5-897 25 35 12-463 11-217 10-175 50 70 5-582 5-306 5-054 25 40 11-854 10-725 9-771 5075 4*472 4-285 4-112 25 45 11-164 io-i6o 9304 50 80 3-362 3-247 3-140 25 50 10-356 9-488 8-739 55 55, 7-681 7-179 6-735 2555 9-484 8-754 8-116 5560^ 7-088 6-659 6-272 25 60 8-495 7-906 7-383 5565 6*334 5-986 5-671 25 6s 7-370 6-920 6-515 55 70 5-391 5-132 4*893 25 70 6-099 5-780 5489 55 75 4*350 4-171 4-006 25 75 4-799 4-589 4-396 55 80 3-291 3-180 3-076 25 80 3-550 3-425 3-308 60 60 6606 6-226 5-888 30 30 12-589 11-313 10-255 60 65 5*970 5-658 5-372 30 35 12-131 10-948 9*954 1 60 70 5*139 4-900 4-580 30 40 1 1 -568 10-490 9*576 ! 60 75 4-189 4-021 3-866 30 45 10-923 9*959 9*135 ! 60 80 3-197 3-092 2-992 30 50 10-160 9-321 8-596 ' 6565 5*471 5-201 4-960 30 55 9-329 8-619 7*999 65 70 4*783 4-573 4-378 30 60 8-378 7-802 7292 65 75 3*958 3 -806 3*665 30 65 7-286 6-844 6-447 6580 3*063 2-965 2*873 30 70 6-043 5-729 5*442 70 70 4-261 4-087 3*930 3075 4-764 4'557 4*365 70 75 3*599 3*471 3*347 3080 3-530 3-406 3*290 70 80 2-843 2-757 2-675 35 35 11-722 IO-6l2 9-680 7575 3*114 3-015 2-917 35 40 1 1 -213 10-196 9*331 7580 2-526 2-448 2-381 For explanation see pp. 29-31 (1 56) MORTALITY TABLES— TWO LIVES Value of an Annuity for the the Joint Continuance of Two Lives according to CABLISLE TABLE Ages 3% 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 5 100 10 10 10 15 10 20 10 25 10 30 10 35 10 40 10 45 10 so 10 55 10 60 10 65 10 70 10 75 10 80 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 10 85 10 90 10 95 10 100 15 IS 15 20 15 25 15 30 15 35 15 40 15 45 15 50 15 §5 15 60 IS 65 Ages IS 70 15 75 IS 80 19-815 19*873 19-288 18-723 18-016 17-218 16-390 15-391 14-381 13-092 1 1 -463 9-773 8-372 6-737 5-244 4-175 3-102 2-405 2-658 1-637 19-964 19-409 18-872 18-189 17-410 16-596 15*605 14-601 13-309 1 1 -667 9*957 8-537 6-874 5-353 4-262 3-167 2-454 2-714 1-668 18-908 18-423 17-793 17-064 16-295 15-348 14-382 13-131 11*528 9-852 8-458 6-818 5*314 4-235 3% 15 8S 15 90 15 95 15 100 20 20 20 2S 20 30 20 35 20 40 20 4S 20 50 20 SS 20 60 20 6s 20 70 20 75 20 80 20 8S i 20 90 j 20 9S 20 100 25 25 25 30 25 35 25 40 25 45 25 50 25 55 25 60 25 65 25 70 25 75 25 80 25 85 25 90 25 95 2S 100 30 30 30 35 30 40 30 45 30 50 30 55 30 60 30 65 30 70 30 75 30 80 30 85 30 90 Ages % 30 95 30 100 35 35 3-149 2-441 2-699 1-663 17-992 1 7 -420 16-748 16-031 15-131 14-207 12-995 1 1 -428 9-782 8-41 1 6-790 5-298 4-225 3-143 2-437 2-696 I -661 16-915 16-311 1 5 -660 14-823 13-954 12-793 1 1 -274 9-668 8-329 6-736 5-263 4-203 3-130 2-428 2-688 1-660 15*783 15-209 14*449 13*649 12-551 11-089 9*529 8-224 6-662 5-213 4-168 3-107 2-411 2-670 1*651 14-720 35 35 35 35 35 35 35 35 35 35 35 35 35 40 40 40 40 40 40 40 40 40 40 40 40 40 45 50 55 60 65 70 75 80 85 90 95 100 40 45 50 60 65 70 75 80 85 90 95 40 100 45 45 45 45 45 45 45 45 45 45 45 45 SO 55 60 65 70 75 80 85 90 95 45 100 SO SO 50 50 50 50 50 50 50 SO 50 55 60 65 70 75 80 85 90 95 Ages SO 100 55 55 55 60 55 6s 14-048 13-331 12-313 10-919 9-410 8-140 6-608 5-179 4-148 3-095 2-403 2-663 1-650 13-482 1 2 -869 11-955 10-658 9-224 8-006 6-515 5-115 4-102 3*065 2-380 2-639 I -641 12-371 1 1 -580 10-400 9-063 7-910 6-465 5-089 4*087 3*056 2-375 2-633 1-637 10-942 9*924 8-729 7-691 6-338 5-022 4*054 3*040 2-365 2-629 1-639 9-103 8-098 7-219 55 55 55 55 55 55 55 60 60 60 60 60 60 60 60 60 65 65 65 65 65 65 65 65 70 70 70 70 70 70 70 75 75 75 75 75 75 80 80 80 80 80 85 85 85 85 90 90 90 95 95 100 70 80 85 i 90 I 95 i 100 I 60 I 65 70 , 75 i 80 85 90 95 100 65 70 75 80 85 90 95 100 70 75 80 85 90 95 100 75 80 85 90 95 100 80 85 90 95 100 85 90 95 100 90 95 100 95 100 100 3% 6019 4*813 3*920 2-961 2-307 2*575 1-625 7*295 6-589 5565 4*497 3*695 2-812 2199 2-458 1-577 6 047 5-193 4-256 3*542 2-719 2-131 2-398 1-555 4-556 3-804 3-228 2-522 1-987 2-248 1-513 3-231 2-790 2-217 1-758 1-993 1-392 2-459 1-993 1-589 1-806 I -316 1-657 1-335 1-509 1-170 1-088 1-217 -979 1-383 1-072 -991 i\ 'I \\ 1 m *• I I For explanation see pp. 29-31 (157) I 2 I I t MORTAIilTY TABLES— TWO LIVES MORTALITY TABLES— TWO LIVES Value of an Annuity for the Joint Continuance of Two Lives according to the GOVERNMEITT EXPERIENCE TABLE, 1883 Ages 20 20 20 25 20 30 20 35 20 40 2045 20 50 2055 20 60 20 65 20 70 2075 20 80 20 85 20 90 20 95 25 25 25 30 2535 25 40 2545 25 50 25 55 25 60 25 65 25 70 25 75 25 80 25 85 25 90 2595 30 30 30 35 30 40 30 45 TWO MALES 2i° o 30 50 3055 30 60 30 65 30 70 30 75 30 80 30 85 30 90 30 95 17-438 16-847 i6-i86 15-445 14-617 13-687 12-632 11-409 9*954 8-204 6-584 5-Hi 3-833 2-786 1-958 1-125 16-321 15-724 15-046 14-277 13-403 12-399 11-226 9-817 8-110 6522 5-102 3 809 2-773 1-950 1-122 15-198 14-593 13-893 13-083 12-139 1 1 -022 9-665 8-005 6-452 5-058 3-783 2758 1-942 I-II8 3% 16-239 15-726 15-151 14-505 13-778 12-957 12-014 10-907 9-569 7-931 6-399 5-021 3*759 2*743 1*933 1*115 15-265 14-743 14-149 13-472 12-697 1 1 -799 10-737 9-441 7-842 6-340 4-983 3*737 2-730 1-926 1-112 14-279 13-745 13-126 12-406 1 1 560 10-547 9-298 7-743 6-273 4-940 3-711 2-715 1-918 1-109 3*% 15*174 14-727 14-224 13-658 13-018 12-289 11-444 10-441 9-209 7*673 6-222 4*905 3-688 2701 1-910 1*105 14-322 13-862 13*339 12-741 12-052 1 1 -247 10-283 9-089 7-589 6-165 4-869 3-666 2-688 1*903 I -102 13-451 12-977 1 2 -428 11-786 1 1 -026 10-106 8*954 7-495 6-IOI 4-828 3*641 2-674 1-895 1-099 TWO FEMALES Ages 20 20 20 25 20 30 20 35 20 40 2045 20 50 20 55 20 60 20 65 25 45 25 50 25 55 Z5 00 25 65 25 70 25 75 25 80 2585 2590 2595 30 30 30 35 30 40 3045 30 50 30 55 30 60 30 65 30 70 30 75 30 80 3085 30 90 30 95 For explanation see pp. 29-3 1 (158) a-2 /o 20 70 ! 2075 20 80 20 85 20 90 20 95 25 25 25 30 2535 25 40 19-906 19-348 18-675 17-867 16-905 15*760 14*394 12-856 1 1 -184 9*335 7*503 5*742 4-263 3-002 2-041 1-266 18-866 18-271 17*537 16-641 15*552 14-233 12-735 11-096 9-274 7-462 5-717 4-248 2-994 2-037 1-265 17-763 17-121 16-310 15-297 14-042 12-595 10-996 9-206 7*418 5-689 4-232 2-985 2-032 1-262 3% 18-384 17-915 17-347 i6-66i 15-835 14*837 13-625 12-241 10-714 8-998 7*275 5*598 4-177 2-953 2-015 1*255 17*505 16-999 16-373 15-601 14-650 13-479 12-129 10-631 8-940 7*236 5-574. 4-163 2-945 2-01 1 1-253 16-564 16-01 1 15-309 14-422 13-306 12-000 10-538 8-876 7-194 5*547- 4-147 2-937 2-006 I -25 1 3i% 17-047 16-651 16-169 15*584 14-872 14-000 12-922 11-673 10-276 8-680 7*058 5-460 4*093 2-906 1-990 1-243 16-300 15-868 15-332 14-664 13-831 12-789 11-570 10-198 8-625 7-021 5-437 4-080 2 899 1-986 1-241 15-493 15-016 14-406 13-627 12-631 11*451 10-112 8-565 6-981 5*412 4*065 2-890 I -981 1-239 Value of an Annuity for the Joint Continuance of Two Lives according to the GOVERNMENT EXPERIENCE TABLE, 1883 TWO MALES Ages 35 35 35 40 35 45 35 50 35 55 35 60 35 65 35 70 35 75 35 80 3585 35 90 35 95 40 40 40 45 40 50 40 55 40 60 40 65 40 70 4075 40 80 40 85 40 90 40 95 45 45 45 50 45 55 45 60 4565 4570 45 75 4580 4585 45 90 45 95 50 50 50 55 50 60 50 65 50 70 50 75 50 80 5085 50 90 2i9 o Oy ^O 14-067 13-449 12-718 11-845 10-792 9-494 7-886 6-373 5-007 3-753 2-740 1-932- 1-114 12-923 12-285 11*501 10-529 9*301 7*753 6-284 4*951 3*718 2-720 I -92 1 i-iio 11*753 1 1 -079 10-210 i 9-074 7-600 I 6-184 4-887 3-680 2-698 1-909 1*105 10-532 9-795 8-781 7*411 6-064 4*813 3*636 2-672 1-895 3i% 13*277 12-727 12-074 11-290 10-334 9-138 7*630 6197 4-892 3-682 2-698 1-909 1-105 12-254 1 1 -681 10-975 10-090 8-957 7*504 6-112 4*837 3*648 2-679 1-898 i-ioo 11-200 10-589 9*795 8-744 7-360 6-016 4*776 3-611 2-657 1-886 1-095 10-088 9-412 8-471 7-181 5-902 4-705 3-568 2-632 1-872 TWO FEMALES 12-559 12-068 1 1 -483 10-777 9-907 8-804 7-389 6-029 4-781 3-613 2-657 1-886 1-095 1 1 -642 11-126 10-487 9-680 8-634 7-269 5-948 4-728 3*581 2-638 1*875 1-091 10-689 10-134 9*407 8-434 7-132 5-856 4-669 3-544 2-617 1*863 I -086 9*675 9-053 8-179 6-963 5*747 4-601 3*503 2-592 1-849 Ages 35 35 35 40 35 45 35 50 35 55 35 60 35 65- 35 70 35 75 35 80 3585 35 90 35 95 40 40 40 45 40 50 40 55 40 63 40 65 40 70 40 75 40 80 40 85 40 90 40 95 45 45 4550 45 55 45 60 45 65 4570 45 75 4580 4585 45 90 45 95 50 50 50 55 50 60 50 65 50 70 50 75 50 80 5085 50 90 2*% 16-582 15-878 14*965 13-797 12-420 10-876 9-127 7-368 5-659 4-214 2-975 2-027 1-260 1 5 -296 14-510 13-459 12-183 10-716 9-025 7*306 5*623 4-194 2-964 2-021 1*258 13-869 12-969 1 1 -830 10-477 • 8-875 I 7*217 5-574 4-168 2-951 2-014 1*255 12-245 1 1 -284 10-092 8-622 7-061 5-484 4-119 2-926 2-003 3% 15-543 14-929 14-127 13-084 11-841 10-427 8-8oi 7-146 5*518 4-130 2-927 2-001 1-248 14-418 13721 12-781 1 1 -623 10-279 •8-706 7-088 5*484 4-110 2-917 1-995 1-246 i3*H9 12-338 1 1 -302 10-059 8-565 7*003 5*437 4*085 2-904 1-989 1*243 11-680 10-801 9-701 8-328 6-856 5*351 4-037 2-880 1-978 34 O/ ^i) 14-608 14-071 13-363 12-431 1 1 -304 io-oo8 8*495 6 936 5-383 4-048 2-881 1-976 1-237 13-619 13-001 12-156 11-105 9-871 8-406 6 -880 5*351 4-029 2-871 1-971 1-235 12-489 11-757 IO-8l2 9-667 8-274 6-801 5-306 4-005 2-858 1-964 1-232 11-157 10-351 9*335 8-052 6-660 5-223 3 959 2-835 1-953 H n (159) i IM m MORTALITY TABLES— TWO LIVES Value of an Annuity for the Joint Continuance of Two Lives according to the GOVEfiNMENT EXFEBIENCE TABLE, 1883 Ages 5095 55 55 55 60 55 65 55 70 55 75 55 80 5585 55 90 55 95 60 60 60 65 60 70 60 75 60 80 60 85 60 90 60 95 6565 65 70 65 75 65 80 6585 65 90 65 95 70 70 70 75 70 80 7085 70 90 70 95 75 75 75 80 7585 75 90 75 95 80 80 80 85 80 90 80 95 8585 85 90 8595 90 90 90 95 95 95 TWO MALES 21 O/ 'o 1-099 9-212 8-361 7-138 5-898 4-717 3-582 2-642 1-879 1-093 7-705 6-685 5-608 4-546 3-491 2-596 I -857 1-085 5 -91 1 5-0^ 4-175 3-262 2-463 1-786 1-058 4-407 3-719 2-963 2-276 1-676 I -on 3-215 2-625 2-063 I -551 -958 2*199 1-773 1-367 •872 1-469 I -164 •772 •949 •655 •485 O/ 'X> 1-090 8-873 8 -080 6-925 5*744 4-612 3-516 2-603 1-856 1-083 7-465 6-497 5-468 4-429 3-428 2-558 1-835 1-076 5-759 4-936 4-091 3-206 2-428 1-765 1-049 4-314 3-649 2-915 2-245 1-657 I -002 3-161 2-586 2-036 1*534 •950 2-169 1-752 1-353 •865 1-453 1-153 -766 -941 •651 -482 3i O/ ''O I -080 8-555 7-814 6-722 5-597 4-512 . 3-453 2-564 1-834 1-074 7-238 6-319 5*335 4*356 3-367 2-520 1*813 1-066 5-614 -4-825 4-010 3*152 2-394 1-745 1-041 4-225 3-582 2-869 2-215 1-638 *994 3*io8 2-548 2-010 1-518 •942 2-141 1-732 1-340 •858 1*438 1*143 •760 •932 -646 •478 60 60 60 65 60 70 6075 60 80 60 85 60 90 60 95 6565 65 70 6575 65 80 6585 65 90 65 95 70 70 70 75 70 80 7085 70 90 7095 75 75 75 80 7585 75 90 75 95 80 80 80 85 80 90 80 95 8585 85 90 8595 90 90 90 95 95 95 For explanation see pp. 29-31 (160) TWO FEMALES Ages 2i% 3% 5095 55 55 5560 55 65 55 70 1-250 10-523 9-534 8-245 6-824 1-239 10-100 9-182 7-974 6630 55 75 5-343 55 80 4-038 5585 2-882 1 55 90 1-979 55 95 1-239 8-771 7-710 6-481 5-143 3-929 2-826 1-952 1-229 6-910 5-927 4-793 3-722 2-713 1-893 1-203 5-206 4-313 3*427 2-549 i-8o6 1-165 3-671 2-997 2-287 1-657 1-094 2-523 1-985 1-478 1-004 I -617 1-243 ■877 -988 •725 •557 5-216 3-959 2-837 1-954 1-228 I 8-471 L 7-472 p 6-306 I 5-025 3-854 2-783 1-928 1-217 6713. 5*777 4-688 3*654 2-673 1-870 1-192 5-086 4-226 3-367 2-512 1-785 I -154 3-604 2-949 2-256 1-639 1-084 2-486 1-960 1-462 -995 1-599 I -231 -870 -979 -719 *554 3* O/ ^o 1-228 9-704 8-852 7-718 6-446 5094 3-883 2-793 1-930 1-217 8-187 7-245 6-138 4-910 3-781 2-740 1-904 I -206 6-526 5-633 4*587 3*587 2-633 1-847 I-I8I 4-971 4-141 3-310 2-476 1*764 1*144 3-539 2-903 2-226 1-620 1-075 2-451 1-936 1-447 -987 I -581 I-2I9 •863 -970 -714 •550 MORTALITY TABLES— TWO LIVES Value of an Annuity for the Joint Continuance of Two Lives according to the GOVERNMENT EXPERIENCE TABLE, 1883. MALE AND FEMALE FEMALE THE ELDER ^» Ages 2"2 % M. F. 20 20 20 25 20 30 20 35 20 40 20 45 20 50 2055 20 60 20 65 20 70 20 75 20 80 20 85 20 90 20 95 2525 25 30 25 35 25 40 2545 25 50 25 55 25 60 2565 25 70 25 75 25 80 2585 25 90 2595 30 30 30 35 3040 30 45 30 so 3055 30 60 30 65 30 70 30 75 30 80 30 85 30 90 30 95 3% 18-580 18-124 17-568 16-890 16-067 15-066 13-842 12-436 10-880 9-129 7-370 5-662 4-218 2-977 2-028 I -261 17-497 17-014 16-411 15-659 14-726 13-566 12*221 10-719 9-016 7-296 5-616 4-190 2-962 2-020 1-257 16-383 15-864 15*197 14-344 13-259 1 1 -981 IO-539 8-889 7-212 5*564 4-160 2*945 2-01 1 1-253 2 /O 17-235 16-848 16-375 15-797 15-087 14-21I 13-122 11-854 10-431 8-803 7-149 5*521 4-133 2-929 2-002 1-249 16-304 15-890 15-372 14-721 13-903 12-870 1 1 655 10-281 8-697 7-078 5-477 4-106 2-915 1-995 1-246 15-337 14-888 14-307 13-557 12-589 11-433 10-112 8-577 6-998 5*427 4-077 2-898 1-986 1-242 MALE THE ELDER 16-047 15*717 15*313 14-817 14-202 13-434 12-463 II-316 10-012 8-497 6-938 5-387 4-051 2-883 1-977 1-238 15-242 14-886 14-439 13-873 13*154 12-232 11-131 9-871 8-396 6-871 5*344 4*025 2-869 1-970 1-234 14*399 14-008 13*501 12-840 11*973 10-925 9-714 8-283 6-794 5-296 3-996 2-853 1-961 I -231 Ages F. M. 20 20 20 25 20 30 20 35 20 40 20 45 20 50 20 55 20 60 20 65 20 70 20 75 20 80 20 85 20 90 20 95 25 25 25 30 25 35 25 40 25 45 25 50 25 55 25 60 25 65 25 70 25 75 25 80 25 85 25 90 25 95 30 30 30 35 30 40 30 45 30 50 30 55 30 60 30 65 30 70 30 75 30 80 30 85 30 90 30 95 210. 2 /o 3% 3i% 18-580 17-887 17-114 16-258 15-311 14-263 13-092 1 1 -761 10-207 8-373 6-694 5-209 3-872 2-809 1-969 1-129 17-497 16-790 15-993 15-097 14-093 12-959 1 1 659 10-133 8-322 * 6 -660 5-187 3*859 2 -801 1-965 I -128 16-383 1 5 -660 14*833 13*887 12-802 1 1 -542 10-049 8-266 6-623 5*164 3*845 2-793 I -961 I -126 17-235 16-638 15*971 15-229 14-402 13-479 12-435 11-233 9-806 8-091 6503 5-086 3-797 2-765 1-945 1-119 16-304 15-689 14-995 14-211 13*324 12-313 11-139 9-736 8-043 6-471 5-065 3-785 2-758 I -941 1-118 15-337 14-704 13-976 13*139 12-169 1 1 -030 9-658 7-990 6-435 5-043 3-771 2-750 1-937 i-ii6 16-047 15*530 14-952 14-304 13-579 12-763 1 1 -831 10-743 9-431 7-825 6*321 4-968 3-725 2722 I -921 i-iio 15-242 14-705 14-098 13-408 12-623 11-719 io-6f5 9-365 7-779 6-291 4-948 3-713 2-715 I -918 I -108 14*399 13-842 13-199 12-456 1 1 -588 IO-555 9-292 7.729 6-257 4-926 3-700 2 708 I 913 i*io6 111 - 11 i» 1 For explanation see pp. 29-31 (i6i) MOKTALITY TABLES— TWO LIVES ^S?i^(»SLl'^'^^'y ^®' *^® ^°i°* Continuance of Two Lives accordinir to the GOVEBNMENT EXPERIENCE TABLE, 1883. MALE AnTfSiALE FEMALE THE ELDEB Ages M. F. 35 35 3540 35 45 35 50 35 55 35 60 35 65 35 70 35 75 35 80 35 85 35 90 35 95 40 40 40 45 40 50 40 55 40 60 40 65 40 70 4075 40 80 4»85 40 90 40 95 45 45 45 50 45 55 45 60 45 65 45 70 45 75 4580 45 85 45 90 45 95 50 50 5055 50 60 50 65 50 70 5075 50 80 50 8s 50 90 2i^/ 15-229 14659 13-904 12-909 11-711 10-338 8-747 7-117 5-505 4-125 2-926 2-OOI 1-249 14-022 13-379 12-497 1 1 -399 10-109 8-587 7-010 5-438 4-085 2-904 1-989 1-244 12-736 11-988 1 1 -017 9-837 8-402 6-889 5-363 4-040 2879 1-976 1-238 10-516 9-482 8-169 6-744 5-276 3-990 2-851 1-961 O/ ^o H-327 13-827 I 13-159 I 12-269 11-183 9-924 8-443 6*907 5-370 4-043 2-880 I -976 1-237 13-258 12-687 11-893 10-895 9-710 8-292 6-806 5-306 4-004 2-858 1-965 1-232 i2-io8 I I -430 10-544 9-457 8-117 6-691 5-234 3-961 2-834 1-952 1-226 10-833 10-084 9-127 7-899 6-553 5-151 3-912 2 -806 1-937 3^ 2 % 13-511 13-071 12-479 11-680 10-694 9-537 8-156 6-708 5-241 3-964 2-835 I -95 1 1-226 12-562 12-052 11-337 10-427 9-337 8-013 6-61 1 5-180 3-926 2-814 I -940 I -221 11-529 10-914 10-103 9-101 7-849 6-502 5-110 3-884 2-790 1-927 1-215 10-370 9-681 8-795 7-643 6-370 5-030 3-837 2-763 1-913 For explanation see pp. 29-31 MALE THE ELDER Ages F. 35 35 35 35 35 M. 35 40 45 50 55 35 60 35 65 35 70 35 75 ! 35 80 I 3585 35 90 35 95 40 40 40 45 40 50 40 55 40 60 40 65 40 70 40 75 40 80 40 85 40 90 4095 45 45 45 50 45 55 45 60 45 65 45 70 45 75 45 80 4585 45 90 45 95 50 50 5055 50 60 50 65 50 70 50 75 50 80 5085 50 90 (162) 2i O/ ^o 15*229 14-488 13-621 12*603 11*399 9-950 8-201 6-582 5-138 3-830 2-784 1*956 1*124 14-022 13-256 12*331 1 1 -205 9-820 8-119 6-531 5-108 3-813 i 2-775 I -951 1*122 12-736 1 1 -932 10-918 9 627 7-999 6*460 5*067 3-791 2763 1-945 1*119 ii'33^ 10*465 9*309 7-795 6-332 4-992 3-749 2-740 1-934 0/ ^o 14-327 13-671 12-901 1 1 -989 10-898 9-566 7-929 6-396 5-018 3757 2-741 1*932 1-114 13-258 12-574 3i% 13-511 12*928 12-242 11-423 10-433 9-206 7-671 6-219 4-902 3-686 2-699 1-909 1-104 12 562 11-949 11*742 II-I99 10*721 10270 9-445 9-093 7-852 7-598 6-348 6-174 4-989 4-875 3-740 3669 2-732 2*690 1*927 1*903 1*112 1*102 12*108 1 1 *529 11*381 10-871 10-458 10-028 9265 8-926 7-739 7-493 6*280 6*109 4-950 4-837 3-718 3649 2*720 2-679 I -921 1-898 I-IIO 1*100 10*833 10-370 10-040 9643 8-970 8-651 7-546 7-311 6-159 5 -994 4-878 4-768 3-678 3-609 2-698 2-658 I -910 1*887 MORTALITY TABLES -TWO LIVES Value of an Annuity for the Joint Continuance of Two Lives according to the OOVEBNMENT EXPERIENCE TABLE, 1883. MALE AND FEMALE FEMALE THE ELDEB iZALE THE ELDER Ages 2i% 3% Qi 0/ U2 /O Ages 2i% 3% 3i% M. F. F. M. 5095 1*231 1*220 1*208 5095 1*116 I •106 1-097 55 55 9*825 9-447 9093 55 55 9*825 9-447 9-093 55 60 8-974 8-656 8-356 55 60 8-845 8-536 8-245 5565 7-830 7-582 7-346 5565 7-487 7*256 7037 5570 6-539 6-358 6*186 55 70 6*138 5-974 5-817 55 75 5580 5-161 5-040 4-925 i 55 75 4-873 4-763 4-658 3927 3-851 3-778 55 80 3679 3-610 3-544 5585 2*8i8 2*774 2-732 5585 2-700 2*659 2*619 5590 1*944 1*920 1-896 55 90 1-912 1*888 1*866 55 95 1-223 1*212 I -201 55 95 1-106 1*097 1*087 60 60 8-20I 7-934 7-681 60 60 8-201 7*934 7 -681 6065 7-279 7-063 6-857 60 65 7-049 6-843 6*647 60 70 6-182 6 -020 5-866 60 70 5-858 5-707 5-564 6075 4-955 4*844 4-737 6075 60 80 4-706 4*603 4-504 60 80 3-8i8 3 '747 3-678 3*586 3-520 3-457 6085 2-766 2-724 2-683 60 85 2*651 2 -61 1 2-572 60 90 1-920 1-897 1-874 60 90 1*887 1*864 1-842 6095 I -214 1-203 1*192 60 95 1-098 I -088 I -079 6565 6-374 6 202 6-038 6565 6-374 6 202 6038 6570 5-528 5-394 5-266 65 70 5*394 5-264 5-140 65 75 4-524 4-428 4-336 6575 4-408 4*316 4*228 6580 3-554 3-491 3*429 65 80 3-408 3-348 • 3289 6585 2-619 2-581 2-543 6585 2-549 2-511 2-475 65 90 1-844 I 822 1-800 65 90 1*832 I -810 1*789 6595 1*182 1-171 1*161 6595 1*076 1*066 1-057 7070 4-781 4-675 4-574 70 70 4-781 4*675 4-574 7075 70 80 4*ooi 3-923 3-848 7075 3-995 3^918 3-843 3-213 3-159 3-107. 70 80 3*152 3*100 3-049 70 85 2-4,15 2*381 2-348 7085 2-399 2*366 2*333 70 90 1-727 1-707 1*688 70 90 1-751 I -731 1*711 70 95 1-125 1*115 1*105 70 95 1-044 1-035 1*027 75 75 3-430 3*370 3*311 75 75 3-430 3*370 3*31 1 7580 2-829 2*785 2-742 7580 2*774 2*731 2-690 7585 2-i8i 2*152 2*124 7585 2*160 2-132 2-104 7590 1-595 1-577 1-560 7590 I -610 1*592 1*575 S'sS 1-063 1-054 1-045 75 95 -984 •976 -968 2-352 2*320 2-288 80 80 2-352 2*320 2*288 8085 1*868 1-845 1-823 8085 1*882 1*859 1-837 80 90 1*402 1-388 1-373 80 90 1*440 1*425 1*410 8095 *962 •954 •946 8095 •908 *900 •893 8585 1-540 1-524 1*507 8585 I '540 1*524 1*507 85 90 1*191 1-179 I -168 8590 1-215 1-203 I -192 85 95 *846 •839 -832 8595 •799 -793 -787 90 90 *968 -960 •951 90 90 •968 •960 -951 90 95 •712 •707 •702 90 95 666 661 •657 95 95 •519 •515 -512 95 95 •519 -515 -512 1 i^J ^1 .1 h (163) II MOBTILITY TABLES— TWO LIVES f Value of 5° ^nuity for the Joint Contiiinance of Two Lives according to the INSTITUTE OF ACTUAEIES HEALTHY MALES TABLE Ages 3% 3* 10 10 21 -0079 10 15 20-4046 10 20 19-6575 10 25 18-9794 10 30 18-1217 1035 10 40 10 45 10 50 1055 10 60 10 65 10 70 10 75 10 80 10 85 10 90 1095 15 15 15 20 15 25 15 30 15 35 15 40 15 45 15 50 1555 15 60 1565 1570 15 75 15 80 15 85 15 90 15 95 20 20 20 25 20 30 20 35 20 40 2045 20 50 17-1325 15-9913 14 '6570 13-1800 11-5676 9-8667 8-1707 6-4997 4-9661 3-6859 2-7056 I -7242 •4129 19-8661 19-1866 18-5708 17-7738 i"6-8405 15-7501 14-4623 13-0271 11-4524 97844 8-1 160 6-4676 4-9502 3-6801 2-7055 17272 •4138 18-5817 18-0385 17-3149 16-4510 15-4240 14-1936 12-8092 20 55 11-2791 O/ '2 /O ; 19-3289 18-8209 18-1842 17-6168 16-8869 16-0360 15-0410 13-8586 12-5312 1 1 -061 1 9-4891 7-9025 6-3206 4-8528 3-6173 2-6652 17062 •4107 18-3635 17-7798 17-2617 16-5811 15-7762 14-8240 13-6816 12-3908 10-9544 9-4122 7-8512 6-2903 4-8378 3-6118 2-6652 1-7092 -41 15 17-2554 16-7952 16-1739 15-4263 14-5274 13-4344 12-1880 10-7916 O/ ^o 17-8656 17-4348 16-8879 16-4103 15-7863 15-0513 14-1806 13-1296 1 1 -9335 10-5905 9-1350 7-6489 6-1498 4-7440 3-5509 2-6259 I -6885 •4084 17-0435 16-5386 16-1006 15-5163 14-8192 13-9848 12-9684 1 1 -8045 10-4915 9-0633 7-6007 6-1213 4-7298 3-5459 2-6260 I -6915 -4093 16-0809 15-6891 15-1533 14-5035 137141 12-7402 1 1 -6153 10-3381 For explanation see pp. 29-3 1 Ages 20 60 20 65 I 20 70 20 75 20 80 20 85 20 90 20 95 25 25 25 30 2535 25 40 2545 25 50 25 55 25 60 25 6s 2570 2575 2580 2585 2590 12595 30 30 3035 30 40 30 45 30 50 3055 30 60 30 65 30 70 30 75 30 80 30 85 30 90 3095 35 35 35 40 35 45 35 50 35 55 35 60 3% 96503 8-0149 6-3944 4-8992 3-6458 2-6828 1-7153 -4122 17-5703 16-9261 16-1390 15-1822 14-0130 12-6787 1 1 -1886 9-5902 7-9774 6-3726 4-8875 3-6400 2-6801 1 7145 •4121 16-3734 15-6810 14-8162 ^3-73^3 12-4690 1 1 -0378 9-4855 7-9071 6-3275 4-8598 3-6234 2-6705 I -7102 -41 15 15-0950 14-3405 13-3625 12-1954 10-8436 9-3536 31 OZ 2 /o 9-2849 7-7544 6-2197 4-7883 3-5784 2*6429 I -6974 -4099 16-3949 15-8382 15-1537 14-3135 13-2723 12-0695 10-7083 9-2291 77I9I 6-1990 4-7771 3-5728 2 -6404 I -6967 •4098 15-3561 14-7501 13-9872 13-0182 11-8779 10-5688 9-1311 7-6525 6-1559 47503 3-5567 2-6310 1-6925 •4092 14-2329 13-5632 12-6859 1 1 -6285 10-3896 9-0080 j Q o 8-9422 7-5079 6-0531 4-6817 3-5132 2-6042 I 6799 •4076 15-3455 14-8621 14-2645 13-5241 12-5945 11-5075 10-2615 8-8904 7-4748 6-0334 4-6710 3-5078 2-6017 I -6792 •4075 U-4399 13-9077 13-2324 12-3645 11-3320 10-1322 8-7984 7-4117 5 -9922 4-6452 3-4922 25925 I -6750 -4070 13-4496 12-8535 12-0644 1 1 '1041 9-9665 8-6833 ^164) ^i i MORTALITY TABLES-TWO LIVES Valne of an Annuity for the Joint Continuance of Two Lives according to the SsTlTUTE OF ACTUAEIES HEALTHY MALES TABLE Ages 3565 3570 35 75 3580 3585 3590 35 95 40 40 40 45 40 50 40 55 40 60 40 65 40 70 40 75 40 80 40 85 40 90 40 95 45 45 45 50 45 55 45 60 4565 4570 45 75 45 80 4585 45 90 45 95 50 50 50 55 50 60 50 65 50 70 50 75 50 80 5085 50 90 5095 55 55 55 60 5565 O/ ^o 3i O/ ^o 7-8211 6-2742 4-8279 3-6051 2-6600 I -7058 •41 10 13-7103 12-8622 11-8177 10-5734 9-1705 7-7034 6-2029 4-7868 3-5821 2-6476 1-7005 -4103 i2-r6i9 11-2685 I 10-1663 8-8855 7-5145 6-0851 47171 3-5425 2-6257 1-6917 -4094 10-5428 9-6109 8-4864 7-2447 5-9148 4-6152 3-4839 2-5929 1-6776 •4076 8-8676 7-9310 6-8562 O/ ^o 7-5714 6-1050 47197 3-5389 2 -6207 I -6881 -4087 1 2 -9996 12-2343 11-2841 10-1406 8-8373 7-4605 6-0372 4-6802 3-5166 2-6085 1-6828 -4080 11-5979 10-7807 9-7638 8-57,09 7-2821 5-9249 4-6132 3-4782 2-5872 I -6742 •4071 IO-II23 9-2481 8-1970 7-0270 ' 57624 4-5152 3-4214 • 2-5551 I -6603 -4053 8-5546 7-6749 6-6590 Ages 7-3350 5-9437 4-6157 3-4749 2-5825 I -6707 -4065 12-3479 11-6557 10-7894 9-7366 8-5241 7-2304 5-8790 4-5777 3-4533 2-5705 I -6655 •4058 I I -0760 10-3270 93873 8-2747 7-0618 57719 4-5132 3-4160 2-5497 1-6570 -4049 97103 8-9078 7 -9240 6-8204 5-6167 4-4189 3-3609 2-5183 I -6433 -4031 8-2598 7-4327 6-4713 O/ ^o 5570 55 75 5580 5585 55 90 55 95 60 60 1 60 651 60 70; 60 75 1 60 80 6085 60 90 60 95 65 65 65 70 6575 6580 6585 65 90 6595 70 70 7075 70 80 7085 70 90 70 95 75 75 1 75 80 7585 7590 75 95 80 80 80 85 80 90 80 95 8585 8590 8595 90 90 90 95 95 95 (i% 5-6627 4-4616 3-3947 2-5429 I -6568 •4051 7-1988 6-3213 5-3013 4-2332 3-2576 2-4634 I -6224 -4010 5-6519 4-8312 3-9266 3-0687 2-3514 I -5719 •3944 4-2226 3-5095 2-8014 2-1880 1-4989 •3854 2-9876 2-4424 I -9508 I -3791 •3684 2-0488 1-6761 1-2319 -3467 I -4025 1-0676 -3172 -8693 -2850 •1321 4% 5-5216 4-3673 3-3349 2-5063 I -6398 •4029 6-9834 6-1504 5-1755 4-1469 3-2018 2-4285 1-6059 •3987 5-5115 4-7242 3-8507 3-0181 2-3190 I -5561 -3922 4-1378 3-4470 2-7580 2-1591 1-4841 •3833 2-9395 2-4077 I 9265 1-3659 -3663 . 2-0225 , I -6569 I -2206 •3448 1-3877 1-0583 •3155 •8625 -283s -1314 5-3865 4-2764 3-2770 2-4706 1-6231 •4007 67787 5-9872 5-0548 4-0638 3-1476 23945 I -5897 -3965 5-3771 4-6213 3-7775 2-9690 2-2873 1-5406 •3901 4-0560 3-3865 27159 2-1309 1-4696 •3812 2-8928 2-3739 1-9028 1-3530 •3643 1-9969 1-6381 1-2096 •3429 1-3732 I -0491 •3138 -8557 •2820 •1308 : H ' 'i \ ■ ' ri 1* '1 i I 'i 116S) 11 MORTALITY TABLES— TWO LIVES* Sin... P.,„.nt to "-/1,-th^ath^^^eU,^^^^^^ xw. Live, aocordin, u, Ages 15 15 15 20 1525 15 30 1535 15 40 1545 15 50 1555 15 60 15 65 15 70 15 75 15 80 15 85 20 20 20 25 20 30 20 35 20 40 2045 20 50 20 55 20 60 20 65 20 70 20 75 20 80 20 85 20 90 2525 2530 25 35 25 40 2545 25 50 25 55 25 60 25 65 25 70 25 75 25 80 2585 2590 2595 30 30 3035 30 40 3045 30 50 0/ ''O •5273 •5439 •5564 •5708 •5878 •6080 •6305 •6563 •6840 •7149 •7496 •7884 •8278 •8654 •8970 •5592 •5706 •5839 •5997 •6186 •6398 •6644 •6908 •7205 •7541 •7918 •8302 •8669 •8980 •9202 •581 1 •5932 •6079 •6256 •6457 •6692 •6946 7234 7562 7932 •83 1 1 •8675 •8983 •9204 •9639 •6042 •6175 •6339 •6527 •6749 Ages 30 55 30 60 30 65 30 70 30 75 30 80 3085 30 90 30 95 35 35 3540 35 45 35 50 35 55 35 60 3565 35 70 35 75 35 80 3585 35 90 35 95 40 40 40 45 40 50 40 55 40 60 40 65 40 70 40 75 40 80 40 85 40 90 40 95 45 45 45 50 45 55 45 60 45 6s 45 70 45 75 4580 4585 45 90 45 95 50 50 5055 5060 5065 5070 3% •6991 •7269 •7587 •7949 •8321 •8681 •8986 •9205 •9639 •6294 •6443 •6615 •6822 •7049 •7312 •7618 7970 •8334 •8688 •8990 •9207 •9639 •6574 •6727 •6915 7125 •7371 •7661 •7999 •8353 •8698 •8996 •9210 •9640 •6861 •7028 •7216 •7442 •7713 •8034 •8375 •87 1 1 •9003 •9213 •9640 •7170 7334 7536 •7783 •8083 For explanation see pp. 29-31 Ages 5075 50 80 5085 50 90 50 95 55 55 55 60 5565 55 70 55 75 55 80 5585 55 90 55 95 60 60 60 65 60 70 ^P 60 80 60 85 60 90 6565 6570 6575 65 80 6585 65 90 6595 70 70 70 75 70 80 70 8s 70 90 70 95 75 75 75 80 7585 75 90 75 95 80 80 80 8s 80 90 85 8s 85 90 8595 90 90 90 95 95 95 3% •8406 •8730 •9013 •9218 •9640 7471 7644 7864 •8138 •8442 •8750 •9025 •9224 •9641 7785 7970 •8212 •8489 •8778 •9040 •9231 •9641 •8115 •8316 •8556 •8817 •9061 •9241 •9642 •8468 •8660 •8881 •9098 •9259 •9643 •8802 •8973 •9154 •9289 •9645 •9091 •9230 •9330 •9648 •9327 •9396 •9654 •9436 •9657 •9691 (166) MORTALITY TABLES -TWO LIVES Single Payment to secore £1 at the Death of either of Two Lives according to the r CAKLISLE TABLE Ages 3% Ages 3% Ages 3% •8246 15 15 •4202 3055 •6479 50 75 15 20 •4343 30 60 •6933 SO 80 •8528 1525 •4526 306s 7313 5085 •8823 1530 •4739 30 70 •7768 50 90 •9020 1535 •4963 3075 •8190 . so 95 •8943 15 40 •5238 30 80 •8495 55 55 7057 15 45 •5520 308s •8804 5560 7350 15 50 •5884 30 90 •9006 55 65 •7606 15 55 •6351 30 95 •8931 55 70 7956 IS 60 •6839 35 35 •5421 55 75 •8307 15 65 7245 3540 •5617 5580 •8567 15 70 7723 35 45 •5826 5585 •8846 1575 15 80 •8161 35 50 •6122 5590 •9037 •8475 35 55 •6528 55 95 •8959 1585 •8792 3560 •6968 60 60 7584 20 20 •4468 3565 •7338 6065 7790 20 2S •4635 3570 •7784 60 70 •8088 20 30 •4831 35 75 •8200 6075 •8399 20 35 •5039 35 80 •8501 60 80 •8632 20 40 •5302 3585 '8807 60 8s •8890 20 45 •5571 35 90 •9009 60 90 •9068 20 50 •5924 35 95 •8933 6095 •8993 20 55 •6380 40 40 •5782 6565 •7948 20 60 •6860 40 45 •5961 6570 •8196 20 6s 7259 40 50 •6227 6575 •8469 20 70 7731 40 55 •6604 6s8o •8677 207s 20 80 •8166 40 (XI •7022 6585 •8917 •8478 40 6s '7377 65 90 ♦9088 20 8s •8793 40 70 •781 1 65 95 •9010 20 90 •8999 40 75 •8219 70 70 •8382 25 2S •4782 40 80 •8514 70 75 •8601 25 30 •4958 408s •8816 7080 •8769 25 35 •5148 40 90 •9015 7085 •8974 25 40 •5391 40 95 •8940 70 90 •9130 25 45 •5644 45 45 •6105 70 95 •9054 25 50 •5983 45 50 •6336 75 75 7580 • -8768 25 55 •6425 . 45 55 •6680 •8896 2S 60 •6893 45 60 •7069 7585 •9063 25 65 •7283 4565 •7405 7590 •9197 2570 •7747 4570 •7826 75 95 •9128 25 75 •8176 45 75 •8226 80 80 •8992 25 80 •8484 4580 •8518 80 8s •9128 25 85 •8797 4585 •8819 80 90 •9246 25 90 •9002 • 4590 •9017 8095 •9183 2595 •8926 45 95 •8942 8s 8s •9226 30 30 •5111 50 50 •6522 8590 •9320 30 35 •5279 5055 •6818 8595 •9269 30 40 •5500 SO 60 •7166 90 90 •9392 30 45 •5733 506s 7469 9095 •9354 3050 •6053 5070 -7863 95 95 •9306 h '■ w l>l 1 For explanation see pp. 29-31 (167) MORTALITY TABLES— TWO LIVES Single Payment to secure £1 at the Death of either of Two Lives according to the INSTITUTE OF ACTUABIES HEALTHY MALES TABLE Ages 3% 3i% •31256 4% Ages 3% 3i% ■75586 4% •72872 10 10 •35900 •27439 20 70 •78463 10 15 •37657 •32974 •29096 20 75 •82818 •80426 •78147 10 20 •39833 •35125 •31200 20 80 •86469 •84518 •82641 10 25 •41808 •37045 •33036 20 85 •89273 •87681 •86138 10 30 •44306 •39514 •35437 20 90 •92091 •90878 •89693 10 35 •47187 •42391 •38263 i 20 95 •95887 •95232 •94586 10 40 •5051 1 •45756 •41612 25 25 •45912 •41 177 •37132 10 45 •54397 ■49754 •45655 25 30 •47788 •43060 •38991 10 50 ■58699 •54243 •50255 25 35 •50081 •45375 •41290 1055 •63396 •59214 •55421 1 25 40 •52868 •48216 •44137 10 6d •68350 •64530 •61019 25 45 •56273 •51737 •47713 10 65 •73289 •69895 •66735 25 50 •60159 •55804 •5i'894 10 70 •78156 •75245 •72500 25 55 •64499 •60407 •56686 1075 •82623 •80208 •77907 25 60 •69155 •65409 •61960 10 80 •86352 •84386 •82496 1 25 65 •73852 •70515 •67404 10 85 •89207 •87606 ■86054 j 25 70 •78527 •75656 •72948 10 90 •92065 •90849 •89659 25 75 •82852 •80464 ■78188 10 95 •95885 •95230 •94583 2580 •86486 •84537 •82662 15 15 •39225 •34520 •30601 25 85 •89281 •87690 •86147 15 20 •41205 •36494 •32543 1 i 25 90 •92094 •90881 •89695 15 25 •42998 •38246 •34228 \ 25 95 •95887 •95233 •94586 15 30 •45319 •40548 •36475 30 30 •49398 •44690 •40615 15 35 •48038 •43270 •39156 30 35 •51415 •46739 •42662 15 40 •51214 •46488 •42365 30 40 •53934 •49319 •45259 15 45 •54965 •50353 •46275 1 3045 •57094 •52596 •48597 15 50 •59145 •54718 •50751 30 50 •60770 •56452 •52569 15 55 •63731 •59575 •55801 30 55 •64939 •60879 •57183 15 60 •68589 •64790 •61295 30 60 •69460 •65741 •62313 15 65 •73449 •70069 •66920 30 65 •74057 •70741 •67647 15 70 •78250 •75347 •72610 30 70 •78658 •75802 •73107 1575 •82669 •80259 •77962 30 75 •82933 •80555 •78287 15 80 •86369 •84405 •82516 30 80 •86534 •84591 •82722 15 85 •89207 •87606 •86054 3085 •89309 •87721 •86183 15 90 •92057 •90839 •89648 30 90 •92106 •90895 •897 1 1 '*'5 95 •95882 •95227 •94580 30 95 •95889 •95235 •94588 20 20 •42966 •38268 •34303 35 35 •53122 •48488 •44424 20 25 •44548 •39824 •35810 35 40 •55319 •50753 •46717 20 30 •46656 ■41925 ■37871 35 45 •58168 •53720 •49752 20 35 •49172 •44453 . ^403 70 35 50 •61567 •57295 •53446 20 40 •52163 •47493 •43407 35 55 •65504 •61485 •57821 20 45 •55747 •51 189 •47152 35 60 •69844 •66157 •62756 20 50 •59779 •55403 •51479 35 65 •74308 j •71015 •67942 20 55 ! •64236 •60126 •56391 1 35 70 •78813 •75974 •73293 20 60 1 •68980 i •65221 •61760 35 75 •83026 •80658 •78401 20 65 •73743 1 •70396 j •67277 j 35 80 •86587 •84651 1 •82789 For explanation see pp. 29-31 (168) MORTALITY TABLES— TWO LIVES Sinele Payment to secure £1 at the Death of either of Two Lives according to the INSTITUTE OJ" ACTUARIES HEALTHY MALES TABLE Ages 0/ ^O 3585 35 90 35 95 40 40 40 45 40 50 40 55 40 60 40 65 40 70 4075 4080 40 85 40 90 40 95 45 45 4550 45 55 45 60 4565 4570 45 75 4580 45 85 45 90 45 95 50 50 5055 50 60 50 65 5070 50 75 SO 80 5085 50 90 50 95 55 55 5560 5565 5570 3i% •89340 •921 19 •95890 •57155 •59625 •62667 •66291 •70377 •74650 •79021 •83145 •86654 •89376 •92135 •95892 •61665 •64267 •67477 •71207 •75201 •79364 •83348 •86770 •89440 •92160 •95895 •66380 •69095 •72370 •75986 •79863 •83645 •86940 •89535 •92201 •95900 •71260 •73988 •77118 •80594 4% •87756 •90910 •95236 •52659 •55247 •58460 •62327 •66734 •71390 •76203 •80792 •84727 •87797 •90928 •95239 •57399 •60162 •63601 •67635 i 71993 •76583 •81018 •84857 •87870 •90957 •95242 •62423 •65345 •68899 •72856 •77132 •81350 •85049 •87978 •91004 •95248 •67690 •70665 ■74100 •77947 •86220 •89728 •94590 •48661 •51324 •54656 •58705 •63368 •68344 •73542 •78547 •82872 •86267 •89748 •94593 •53553 •56434 •60048 •64328 •68993 •73954 •78795 •83015 •86347 •89781 •94596 •58806 •61893 •65677 •69921 •74551 •79158 •83227 •86468 •89833 •94603 •64385 •67566 •71264 •75436 Ages 55 75 5580 55 85 5590 55 95 60 60 60 65 60 70 60 75 60 80 60 85 60 90 60 95 6565 65 70 6575 65 80 65 85 65 90 6595 70 70 70 75 70 80 70 85 70 90 70 95 75 75 75 80 75 85 75 90 75 95 80 80 80 85 80 90 80 95 8585 85 90 8595 90 90 90 95 95 95 O/ ^o 3i9 O •84093 •87200 •89681 •92262 •95908 •76120 •78676 •81647 •84758 •87599 •89913 •92362 •95919 •80626 •83016 •85651 •88150 •90239 •92509 •95939 •84789 •86866 •88928 •90715 •92722 •95965 •88386 •89974 •91405 •93071 •96014 •91 120 •92206 •93499 •96078 •93002 •93978 •96164 •94555 •96257 •96703 0/ •81850 •85341 •88143 •91073 •95256 •73003 •75820 •79II7 •82595 •85791 •88406 •91 188 •95270 •77981 •80643 •83597 •86412 •88776 •91356 •95292 •82626 •84962 •87292 •89317 •91600 •95322 •86678 •88477 •90104 •91999 •95380 •89779 •9IOI5 •92491 •95452 •91926 •93040 •95552 •93702 •95660 •96174 ^o •79706 •83550 •86651 •8991 1 •94613 •70082 •73126 •76712 •80524 •84048 •86944 •90039 •94629 •75472 •78379 •81625 •84734 •87356 •90228 •94653 •80554 •83129 •85708 •87958 •90501 •94688 •85028 •87023 •88835 •90950 •94753 •88473 •89853 •91 501 i. ^94835 '90872 •921 19 •94947 •92863 •95069 •95651 \ .i' (160) i I :i : 1 MORTALITY TABLES— TWO LIVES Annual Payment during the Joint Continuance of Two Lives rvo'TTfri^i^^^Jit ^^ ** ^^® ^^^^ D®ath according to the IHSTITUT E OF ACTUAEIES HEALTHY MALES TABLE Ages 3% 10 10 10 20 10 30 10 40 10 so 10 60 10 70 10 80 10 90 15 20 1525 15 30 1535 15 40 1545 1550 1555 15 60 15 70 IS 80 IS 90 20 20 20 2S 20 30 20 3S 20 40 20 45 20 SO 20 SS 20 60 20 70 20 80 20 90 25 25 25 30 25 3S 2S 40* 2S 4S 2SS0 255s 2S 60 2S 70 2S 80 25 90 30 30 30 35 30 40 304s 30 so -016 -019 •023 •030 -041 -063 -104 •184 -338 -019 •020 -022 •024 •027 •031 •036 •042 •051 •064 •105 -185 •338 -022 •023 •025 •028 -032 ■043 •052 -065 •106 •186 -339 •025 •027 •029 -033 -037 •044 3i% •015 -018 •022 •028 •040 -062 -103 •183 •336 •018 •019 •021 •023 •026 •029 •034 •04 1 -050 •062 •103 •183 •336 -021 •022 -024 •027 •031 •035 •042 -051 -063 •105 •185 -337 -024 •026 •028 -031 -036 •043 4% •053 -052 ■06s -064 •107 -105 -186 -185 -339 •337 •028 •027 •031 . •030 •034 •033 ■039 •038 •045 •044 •015 •017 -021 -027 •039 -060 -loi •181 •333 •017 -019 -020 -022 •025 -028 •033 •040 •049 -061 -102 -181 •333 •020 •021 •023 •026 -029 •034 -041 -050 •062 •103 •183 •335 •023 •025 •027 -030 '03S •041 -050 •063 ■104 •183 •335 ■026 029 •032 -036 •043 Ages 30 55 30 60 30 70 30 80 30 90 35 35 35 40 35 45 35 50 35 55 35 60 35 70 3580 35 90 40 40 4045 40 50 4055 40 60 40 70 40 80 40 90 45 45 4550 45 55 4560 45 70 45 80 45 90 5050 5055 50 60 50 70 SO 80 SO 90 55 55 5560 55 70 55 80 55 90 60 60 60 70 60 80 60 90 70 70 70 80 70 90 80 80 80 90 90 90 For explanation see pp. 29-31 1170) 3 % -054 -066 •107 -187 -340 •033 ■036 •040 •047 •055 •067 •108 •188 •340 •039 •043 •049 •057 •069 •iio •189 •341 -047 •052 -060 •072 •112 -191 •342 -058 -065 •076 •115 •194 •344 •072 •083 '121 •198 •347 2 /O Oy ^O •053 -065 •106 •186 •338 -032 •035 •039 •045 •054 -066 -107 •186 •338 •038 •042 •048 •056 •068 •108 •188 •339. •046 •051 •059 •071 •III •189 •340 •056 -064 -075 -114 -192 •342 •071 •081 -120 •197 •345 •093 -091 •090 •130 -128 -126 -206 -204 -203 •352 •350 •348 •162 •161 •159 •234 •232 •231 •372 •369 •366 299 •297 -295 -419 •416 -4I4> -471 -468 •46s •051 •064 •105 •184 •335 -031 •034 -038 •044 •053 •065 •106 •184 •336 •036 •041 •046 •055 •067 •107 •186 •337 •044 •050 -058 •069 •109 •188 •338 •055 •062 •074 •113 •191 •340 •070 •080 -118 •'95 •343 MOBTALITY TABLES— TWO LIVES Value of an Annuity during the Continuance of either of Two Lives according to the NORTH AM FTON TABLE Ages 3% 4% /o 6% 14-954 Ages 15 15 24-015 20-171 17-216 15 15 15 25 23-241 19-599 16-831 14-665 15 25 1535 22-444 19-043 16-435 14-368 15 35 1545 21-662 18-467 16-003 , 14-027 1545 1555 20-957 17-915 15-567 13-674 15 55 1565 20-364 17-425 15-155 13-343 15 65 1575 19945 17-058 14-837 13-069 15 75 20 20 23-H3 19-531 16-782 14-640 20 20 20 30 22-274 18-941 16-372 14-348 20 30 20 40 21-390 18-306 15-907 14-003 20 40 20 SO 20-551 17-667 15-415 13-620 20 50 20 60 19-818 17-077 14-936 13-228 20 60 20 70 19-223 16-568 14-498 12-852 20 70 20 80 18-850 16-233 14-197 12-578 20 80 25 25 22-245 18-932 16-370 14-382 25 25 25 35 21-289 18-260 15-894 13-979 25 35 2545 20-342 17-561 15-368 13-569 25 45 25 55 19-480 16-885 14-833 13-142 25 55 25 65 18-748 16-279 14-324 12-719 2565 25 75 18-214 15-811 13-915 12-369 25 75 30 30 21-255 18-249 15-889 14-004 30 30 30 40 20-202 17-488 15-333 13-592 30 40 30 SO 19-198 16-724 14-745 13-133 30 50 30 60 18-321 16-018 14-172 12-665 30 60 30 70 17-613 15-413 13-653 I2-2l8 30 70 30 80 17-173 15-018 13-297 11-895 30 80 35 35 20-154 17-466 15-324 13-557 35 35 35 45 19-008 i6-6i6 14-686 13-070 35 45 35 55 17-957 15-792 14-035 12-547 35 55 35 65 17-065 15-053 13-414 12-024 35 65 35 75 16-417 14-485 12-919 11-614 35 75 40 40 18-932 16-574 14-658 13-088 40 40 40 50 17-694 15-627 13-929 12-520 40 so 40 60 16-600 14-746 13-214 11-935 40 60 40 70 15-711 13-987 12-562 "*374 40 70 40 80 15-160 13-491 12-116 10-969 40 80 45 45 17-608 15-576 13-898 12-463 45 45 45 55 16-285 14-536 13-076 11-809 45 55 45 65 15-146 13-591 12-283 11*252 45 65 45 75 14-311 12-859 11-643 10-594 45 75 SO SO 16-158 14-447 13-016 1 1 -804 SO so SO 60 14^752 13-314 12-093 1 1 -048 SO 60 50 70 13-588 12-319 11-238 10-311 50 70 50 80 12-855 1 1 -660 10-644 9-772 50 80 55 55 14-619 13-223 12-029 10-965 55 55 5565 13-120 1 1 -976 10-983 10-100 55 65 55 75 1 1 -999 10-992 10-120 9*342 55 75 60 60 12-948 11-852 10-896 io-o6i 60 60 60 70 11-372 10-500 9-735 9-058 60 70 60 80 10-361 9-590 8-915 8-315 60 80 11 i 'ii For explanation see pp. 31, 32 4% •0141 •0148 •0158 •0164 •0166 •on 7 •0129 •0141 •0152 •0163 •0172 •0185 •0193 •0196 •0144 •0160 •0175 •0189 •0201 •0220 •0229 •0234 •0180 •0200 •0219 •0237 •0264 •0278 •0284 •0227 •0254 •0279 •0319 •0341 •0351 •0290 •0326 •0388 •0424 •0440 •0376 •0470 •0532 •0561 ■0665 •0838 •0944 •1225 •1577 •2431 lif^ '1 * 1 ■i ■1 i \ MORTALITY TABLES— TWO LIVES 1 Value of the Eeversion to a Perpetuity on the Death of the FIRST of Two Lives Ages 15 IS 20 20 25 25 30 30 35 35 40 40 45 45 5050 55 55 60 60 6565 70 70 75 75 80 80 8585 NORTHAMPTON 3% 18-113 19-200 19-950 20-744 2I-6II 22-569 23-557 24-619 25-652 26-727 27-862 29-072 30-219 31-211 32-024 Oy ''O 1 1 -589 12-465 13056 13-687 14-388 15-180 16-010 16-919 17-821 18-774 19799 20-913 21-985 22-932 23-661 O /o 8-036 8-768 9-236 9-745 10-320 10-984 1 1 -688 12-478 13-265 14-112 15-040 16-070 17-083 17-982 18744 HEALTHY MALES 3% 13-467 14-752 15-763 16-960 18-238 19-623 21-171 22-791 24-466 26-134 27-681 29-111 30-346 31-285 31-931 Q 1 0/ O2 /o 10 -208 11-316 12-176 13-215 14-338 15-572 16-974 18-459 20-017 21-588 23-060 24-434 25-632 26-549 27-184 4% 7-957 8-919 9-654 10-560 11-550 12-652 13-924 15-290 16-740 18-221 19-623 20-944 22-107 23-003 23-627 Ages 15 15 20 20 25 25 30 30 35 35 40 40 45 45 50 50 60 60 6565 70 70 75 75 80 80 8585 Value of the Keversion to a Perpetuity on the Death of the LAST of Two Lives Ages NORTHAMPTON 3% 15 15 20 20 25 25 30 30 35 35 40 40 45 45 50 50 55 55 60 60 6565 70 70 75 75 80 80 8585 9-318 10-190 1 1 -088 12-078 13-179 14-401 15725 17-175 18714 20-385 22-196 24-126 26 -049 27-893 29 -402 a o 4-829 5-469 6-068 6-751 7-534 8-426 9-424 10-553 11777 13-148 14-639 16-365 18-053 19-782 21-253 50Z To 2-784 3-218 3-630 4-111 4-676 5-342 6-I02 6-984 7-971 9-104 10-408 11-884 13-429 14-988 16-314 HEALTHY MALES 3 0/ 6-883 7-830 8-828 9-972 11-254 12-691 14-308 1 6 084 18013 20 060 22-149 24-243 26-198 27-897 29-258 3i% 4% 4-636 5-378 6-169 7-096 8-155 9-366 10-755 12-309 14-029 15-885 17-810 19-769 21-622 23-250 24-564 1 3-210 3-793 4-424 5-178 6-056 7-078 8-275 9-638 11-175 12-861 14-637 16-470 18-228 19-788 21-058 Ages 15 15 20 20 2525 30 30 3S 3S 40 40 45 45 50 50 55 55 60 60 6565 70 70 75 75 80 80 8585 For explanation see p. 32 (i78i MORTALITY TABLES— TWO LIVES Value of an Annuity during the Life of y after the Death of x Age of X 45 45 45 45 45 60 60 60 60 60 Age of y Northampton 20 25 30 35 40 20 30 35 40 50 3% Carlisle 75 30 75 40 75 50 75 60 75 70 7-271 6-650 5-998 5-315 4-612 10-042 8-544 7711 6-822 4-975 12-157 10-191 7-964 5-588 3-135 3% 7-487 6-711 5-906 5-102 4-275 1 1 -91 2 10-027 9-023 7-919 5-574 14-343 12-028 9-281 5-993 3-319 Healthy Males O/ ^o 3i 2% 7-849 7-025 6-136 5-225 4-314 12-392 10-382 9-233 8-006 5-410 15-008 12-389 9-281 6-003 3-147 6-790 6-126 5-397 4639 3-868 10-940 9-284 8-316 7-265 4990 13-665 1 1 -422 8-672 5-688 3-023 O/ -X) 5-904 5-366 4-766 4-132 3-479 9-702 8-332 7-513 6-61 1 4-612 12-486 IO-557 8-II7 5 -395 2-906 Value of an Annuity during the Life of y, who is to be nominated at the Death of x Age of Age of y at X Death of X 10 45 45 25 45 30 45 35 45 40 60 10 60 30 60 35 60 40 60 50 75 10 75 30 75 SO 75 60 75 70 Northampton a o 12-393 10-763 10-253 9-690 9-066 14-863 1 2 -296 11-621 10-873 9-218 17-751 14-685 1 1 -010 8-831 6-338 Carlisle 3% 12*473 1 1 -024 10-460 9-888 9-232 16-308 13-676 12-929 12-071 10-181 19-863 16-657 12-400 9-311 6-582 Healthy Males 3% 12-994 1 1 -387 10-782 10-120 9-391 16-918 14-038 13-177 12-228 10-021 20-708 17-183 12-266 9-252 6-305 3*9 o 10-762 9-564 9-103 8-591 8-018 14-544 12-302 1 1 -610 10-836 8-989 18-340 15-512 11-335 8-657 5968 O/ ^o 8-998 8-094 7 740 7-341 6-888 12-598 10-837 10-279 9*644 8-091 16-348 14-063 10-499 8-113 5657 r I For explanation see p. 33 (179) MORTALITY TABLES -TWO LIVES t- Single Payment to aecnre £1 at the Death of x provided he dies before v, according to the NOSTHAMPION TABLE Ages X V 15 15 20 10 20 20 25 15 25 25 30 10 30 20 30 30 35 15 35 25 35 35 40 10 40 20 40 30 40 40 45 15 45 25 45 35 45 45 50 10 /o •26366 •30838 •27962 •31846 •29054 •36038 •32987 •30210 ■37643 •34755 •31472 •42717 •39579 •36815 •32868 •45053 •42208 •38980 •34306 •50891 Ages X y 50 20 50 30 50 40 50 50 55 15 55 25 55 35 55 45 55 55 60 10 60 20 60 30 60 40 60 50 60 60 65 10 65 15 65 20 65 25 65 30 3% •47767 •45221 •41378 •35853 •53896 •51226 •48319 •43830 •37357 •60306 •57287 •55136 •51734 •46567 •38923 •65695 •64308 •62784 •61920 •60899. Ages X » 65 35 55 40 §5 45 65 50 65 5S i 65 60 1 65 65 i 70 10 ! 70 15 70 20 3% 70 70 70 70 70 25 30 35 40 45 70 50 70 ss 70 60 70 65 70 70 •59587 •57855 •55766 •53073 •49904 •45822 •40576 •71527 •70284 •68822 •68087 •67236 •66139 •64650 •62843 •60461 •57691 •54027 •49029 •42338 Single Payment to secure £1 at the Death of x provided he dies before «, according to the CABLISLE TABLE Ages 15 15 20 10 20 20 25 15 25 25 30 10 30 20 30 30 35 15 35 25 35 35 40 10 40 20 40 30 40 40 45 15 45 25 45 35 45 45 SO 10 3% •2101 •2503 •2234 •2705 •2391 •3190 •2928 •2556 •3427 •3136 •2710 •3959 •3733 •3388 •2891 •4262 •4018 •3636 •3052 •4880 Ages 3% 50 50 50 50 55 55 55 55 60 60 60 60 60 65 65 65 65 65 y 20 30 40 50 15 25 35 45 55 10 20 30 40 60 10 15 20 25 30 •4681 •4400 •3965 •3260 •5409 •521 1 •4931 •4454 •3528 •6147 •5986 •5766 •5472 •4917 •3792 •6673 •6592 •6531 •6439 ■6332 Ages 3% 65 35 •6236 55 40 •6088 65 45 •5940 65 50 i -5644 65 5S •5137 65 60 •4534 65 65 •3973 70 10 •7276 70 15 •7205 70 20 •7161 70 25 •7082 70 30 •6986 70 35 •6908 70 40 •6788 70 45 •6692 70 50 •6475 70 SS •6034 70 60 •5464 70 65 •4956 70 70 •4190 For explanation see p. 34 61 62 63 65 (193) >»* SINGLE PREMIUMS FOR LIFE ASSURANCE FOR £100 Sum Assured Payable Age at Entry Age at Entry In 25 Years In 30 Years In 35 Years In 40 Years f s. (1. £ s. d. £ s. d. £ .'. d. 16 58 3 6 53 48 14 45 4 6 16 17 58 7 53 4 6 48 19 6 45 10 6 17 18 58 10 53 8 49 4 6 45 17 18 19 58 12 6 53 II 6 49 8 6 46 2 19 20 58 14 6 53 14 49 12 6 46 7 20 21 58 16 53 16 6 49 15 6 46 II 6 21 22 58 17 6 53 19 49 19 46 16 22 23 58 19 54 I 50 2 6 47 I 23 24 59 I 54 4 50 6 6 47 6 6 24 25 59 3 54 7 50 10 6 47 12 6 25 26 59 5 6 54 10 6 50 15 6 47 19 26 27 59 8 54 H 6 51 I 48 6 27 28 59 10 6 54 18 6 51 6 6 48 13 6 28 29 59 13 6 55 2 6 51 12 6 49 I 6 29 30 59 16 6 55 7 51 18 6 49 10 30 31 59 19 6 55 II 6 52 5 49 18 6 31 32 60 3 55 16 6 52 12 50 8 32 33 60 6 6 56 2 52 19 6 50 17 6 33 34 60 10 56 7 6 53 8 51 8 34 35 60 14 6 56 14 53 16 6 51 19 35 36 60 19 57 6 54 5 6 52 II 36 37 61 3 6 57 7 6 54 15 53 3 37 38 61 8 6 57 15 55 5 53 16 38 39 61 14 58 3 55 16 54 9 6 39 40 62 58 II 6 56 7 6 55 3 6 4C 41 62 6 59 I 56 19 6 • • • 41 42 62 13 59 II 57 13 • • « 42 43 63 I 60 I 6 58 7 • • • 43 44 63 9 6 60 13 59 I 6 • • • 44 45 63 18 61 5 6 59 17 • • • 45 46 64 7 6 61 18 6 • • • • •• 46 47 64 17 6 62 12 • •• • •• % 48 65 8 63 6 • • • • •• 49 65 19 64 6 • • • ■ • • 49 50 66 10 6 64 16 • • • 50 51 67 3 • • « « • • ■ •• 51 52 67 16 6 • • • • • • • • • 52 53 68 10 6 • •• • •■ • •• 53 54 69 5 6 • • • • • • • • • 54 55 70 I • • • • • • ■ • • 55 POST OFFICE ASSURANCES ANNUAL PBEMIUMS FOB LIFE ASSURANCE FOB £100 Age at Entry Sums Assured Payable at Age at Entry Death Death Age 55 Age 60 Age 65 Premiums Payable Annually till (5 Death Age 50 Age 55 Age 60 Age« £ s. d. £ s. d. £ $. d. £ «. d. £ s. d. i6 I 9 6 I 12 2 I 6 I 17 I 14 x6 'Z I 10 6 I 13 230 I 18 6 I 15 17 i8 I II 6 I 14 6 246 I 19 6 I 16 18 19 I 12 I 15 6 260 2 I I 17 6 19 20 I 13 I 16 6 280 2 2 6 I 18 6 20 21 I 14 I 17 6 296 2 3 6 I 19 6 21 22 I 14 6 I 18 6 2 II 6 2 5 2 6 22 23 I 15 6 I 19 6 2 13 2 6 6 2 2 23 24 I 16 6 2 I 2 15 2 8 2 3 24 25 I 17 6 226 2 17 6 2 9 6 2 4 6 25 26 I 18 6 236 2 19 6 2 II 6 2 6 26 27 I 19 6 2 5 320 2 13 6 2 7 6 27 28 206 270 350 2 15 6 2 9 28 ^ 2 I 6 286 3 7 6 2 17 6 2 10 6 29 30 230 2 10 3 II 2 19 6 2 12 6 30 31 240 2 12 3 14 3 2 2 14 31 32 2 5 6 2 14 3 17 6 3 4 6 2 16 32 33 266 2 16 4 I 6 3 7 6 2 18 6 33 34 280 2 18 6 460 3 10 3 6 34 35 296 3 I 4 10 6 3 13 6 3 3 35 36 2 II 3 3 6 4 15 6 3 17 3 5 6 36 37 2 13 366 5 I 6 4 6 3 8 37 38 2 14 6 396 5 7 6 4 4 6 3 II 38 39 2 16 6 3 13 5 14 6 4 9 3 14 39 40 2 18 3 16 6 626 4 13 6 3 17 6 40 41 300 406 6 II 6 4 19 4 I 41 42 326 450 7 I 6 5 4 6 4 5 42 43 346 4 10 7 13 6 5 II 4 9 43 44 370 4 IS 6 876 5 18 6 4 13 6 44 45 396 5 I 6 936 6 6 6 4 19 45 46 3 12 586 • • a 6 16 5 4 6 46 ^Z 3 15 5 16 a a • 7 6 5 10 6 47 48 3 17 6 650 a a a 7 18 5 17 48 49 4 I 6 IS 6 • • • 8 12 6 4 6 49 SO 440 7 7 6 * • • 9 8 6 6 13 50 51 476 • • • • • • • • • 7 2 6 51 52 4 II • ■ • ... a • • 7 13 52 53 4 15 • • • a • • a • • 8 5 6 S3 54 4 19 6 • • ■ a • a • • m 8 19 6 54 55 540 • • • ... a a a 9 16 6 55 56 57 586 5 13 6 • ■ • I a • • • a ■ • • • • • • • • a a • • • 56 57 54 5 19 ■ • • • • • 58 2 60 646 6 10 6 • • • • • ■ a a a • a • a • • • a a ■ • a 6z 62 63 65 6 17 740 7 II 6 7 19 870 a • • • • • • • m • a a • • a • a • • • • a • • • • • ■ • • • ■• • •• • •• • ••. • •• • • • • • • • •• • • • 61 62 65 For explanation see pp. 39, 40 (194) GOVERNMENT ANNUITIES IMMEDIATE LIFE ANNUITIES Granted through the National Debt Office for £100 of 2^ per Cent. Stock when the Frice of £100 Stock is above £99 lOs. Id. Age of the Nominee 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 Male £ 4 4 4 4 4 4 4 5 6 7 d. O 9 7 5 3 4 8 I 490 4 9 II 4 10 10 4 II 10 4 4 4 4 4 4 4 5 5 5 12 10 13 10 14 II 16 o 17 2 18 19 o 2 3 4 6 10 I 5 5 4 10 564 5 7 10 5 9 4 5 II o 5 12 8 5 14 6 5 16 5 18 6 o 6 2 6 4 6 7 6 9 6 12 5 8 7 3 Female £ 3 3 3 4 4 4 4 4 4 4 4 4 4 4 17 18 7 3 18 10 19 6 o I 10 1 6 2 3 3 o 3 9 4 5 6 7 8 4 9 4 10 4 II 4 12 4 13 4 14 4 15 4 17 4 18 6 4 3 I o o o I 2 4 6 9 o 5 4 19 10 5 5 5 5 S 3 4 6 8 4 o 8 5 4 5 10 4 5 12 6 5 14 9 5 17 I 5 19 8 Age of the Nominee SI 52 53 54 55 56 H 58 59 60 6x 62 63 65 66 % 69 70 71 72 73 74 75 76 78 79 80 Male £ 6 6 7 7 7 i. 15 18 I 4 8 I I 5 10 7 7 12 7 7 16 II 8 I 8 6 8 12 8 10 4 8 18 9 4 9 10 9 17 10 4 10 10 II II 12 12 13 14 14 15 15 16 17 18 19 II 19 8 17 7 17 8 o 13 5 19 13 8 4 I o o 4 I 4 10 9 2 2 o 6 9 7 o 10 7 10 10 10 9 Female £ «. 6 2 6 5 6 8 6 II 6 14 6 18 7 2 7 6 7 10 7 15 8 o 8 5 8 II 8 17 9 4 rf. 3 o o 2 6 2 I 2 7 3 4 8 4 6 3 6 6 9 II 9 19 10 7 II 10 17 o 11 6 6 11 16 3 12 6 6 12 17 4 13 8 9 14 I o 14 14 o 15 7 II 16 2 8 16 18 5 17 15 o Life annuities are payable quarterly at the National Debt Office by warrant on the Bank of England. , ^ ■ v. The warrants may be received at the National Debt Office either on personal demand or by power of attorney, or they can be transmitted by post to the proprietor at his or her own risk. Life annuities are transferable, but cannot be transferred in parts or shares, nor can the original nominee ever be changed. For explanation see p. 40 ' ii ; tl iij n (195) LIFE OFFICES ANNUITIES AND ASSURANCES Age 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 AVERAGE RATES FOR ANNUITIES AND ASSURANCES CHARGED BY BRITISH LIFE OFFICES. Annuity Granted for each £100 of Purchase Money Age Males Females Age Males Females £ s. d. £ s. d. £ «. (f. £ i. d. 40 5 16 7 564 55 7 14 10 705 41 5 18 4 5 7 9 56 7 18 10 740 42 6 I 5 9 3 57 8 3 2 778 43 6 I II 5 10 9 58 8 7 II 7 12 I 44 6 3 II 5 12 5 59 8 13 7 16 6 4| 6 5 II 5 14 2 60 8 18 5 8 I 46 6 8 I 5 16 I 61 9 4 3 863 47 6 10 4 5 18 2 62 9 10 4 8 II 10 48 6 12 10 604 63 9 16 10 8 16 6 49 6 15 6 629 64 10 3 7 938 50 51 6 18 3 7 I 2 6 5 3 6 7 10 % 10 II I 10 18 8 9 10 4 9 18 I 52 7 4 3 6 10 7 % II 6 9 10 5 3 53 7 7 7 6 13 7 11 15 2 10 13 8 54 7 II 2 6 16 10 70 12 14 3 II II 9 Annual Premium for Assurance of £100 at Death With Profits £ s. 1 19 2 O 2 2 2 2 2 2 2 2 I 2 3 4 5 6 7 8 2 10 2 II 2 12 8 2 14 I 2 15 8 2 17 3 2 18 II 308 327 346 6 3 2 I I I 2 6 6 9 o 3 Without Profits £ «. d. I 13 8 I 14 4 I 15 I I 15 II I 16 7 I 17 6. I i8 5 1 19 2 o I Age 5 6 7 2 9 3 II 5 2 6 5 7 9 9 3 2 10 10 2 12 5 2 14 2 2 15 II 2 2 2 2 2 2 2 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 With Profits £ 5. d. 369 388 3 10 II 3 13 3 3 15 3 18 4 I 4 4 4 7 4 II Without Profits 9 5 3 I 8 6 4 14 4 18 5 2 5 7 5 12 5 17 6 2 6 8 6 14 7 o 9 7 9 2 o I 7 4 5 8 £ < rf. 2 17 10 2 19 10 3 I II 342 3 6 3 9 3 II 3 14 3 17 4 o 4 4 4 7 4 II 4 15 II 503 5 5 5 10 5 15 6 I 6 6 7 o 8 5 4 7 2 9 8 o I 5 o 8 Annual Premiums for Endowment Assurance of £100 Age at Years to Entry Matiuritj 25 30 25 35 25 40 30 25 30 30 30 35 35 20 35 25 With Profits £ s. d. 350 2 16 I 2 10 10 400 3 7 2 19 5 2 4 2 5 6 6 9 Without Profits £ *. d. 2 16 9 290 2 3 10 3 9 5 2 18 II 2 II 4 4 II o 3 13 o Age at Entiy 35 40 40 40 45 45 45 Years to Maturity 30 15 20 25 10 15 20 With Profits £ ». d. 3 10 10 702 5 5 10 470 10 13 7 4 5 II Without Profits £ t. d. 322 6 6 I 4 14 2 3 16 9 9 15 10 696 4 19 9 For explanation see p. 40 (196) INCOME TAX TABLES At 5d., 6d.: Id., 8d., and 9d. in the Pound For explanation see p. 40 (197) £1-200 INCOME TAX TABLES For explanation see p. 40 (198) TAX THEEEON AT PER £ t % Income 5d. %d. 7d. Sd. 9rf. £ £ s. d. £ t. d. £ s. d. £ s. d. £ s. d. I 1 005 006 007 008 009 2 10 I I 2 014 I 6 3 I 3 I 6 019 020 023 4 I 8 020 024 028 030 5 021 026 2 II 034 039 6 026 030 036 040 046 I 2 11 036 4 I 048 053 034 040 048 054 060 9 039 046 053 060 069 10 042 050 5 10 068 076 IZ 047 056 065 074 083 12 050 060 070 080 090 »5 6. 3 076 089 10 II 3 20 084 10 II 8 13 4 15 25 10 5 12 6 14 7 16 8 18 9 30 12 6 15 17 6 I I 2 6 35 14 7 17 6 I 5 I 3 4 I 6 3 40 16 8 100 I 3 4 I 6 8 I 10 45 18 9 I 2 6 I 6 3 I 10 I 13 9 50 I 10 I 5 I 9 2 I 13 4 I 17 6 65 70 75 I 2 II I 5 I 7 I I 9 2 I 7 6 I 10 I 12 6 I 15 I 12 I I 15 1 17 II 2 10 I 16 8 200 234 268 213 250 289 2 12 6 I II 3 I 17 6 239 2 10 2 16 3 80 85 I 13 .4 200 268 2 13 4 300 I IS 5 226 297 2 16 8 3 3 9 90 I 17 6 2 5 2 12 6 300 376 95 100 1 19 7 2 I 8 2 7 6 2 10 2 15 5 2 18 4 3 3 4 368 3 II 3 3 15 105 239 2 12 6 3 I 3 3 10 3 18 9 no 2 5 10 2 15 342 3 13 4 426 1 "5 2 7 II 2 17 6 3 7 I 3 16 8 463 120 2 10 3 -o 3 10 400 4 10 125 2 12 I 3 2 6 3 12 II 4 3 4 4 13 9 130 135 140 145 150 2 14 2 2 16 3 2 18 4 3 5 3 2 6 350 3 7 6 3 10 3 12 6 3 15 3 15 10 3 18 9 4 I 8 4 4 7 476 468 4 10 4 13 4 4 16 8 500 4 17 6 5 I 3 5 5 589. 5 12 6 165 170 175 3 4 7 368 389 3 10 10 3 12 II 3 17 6 400 426 450 476 4 10 5 4 13 4 4 16 3 4 19 2 5 2 I 5 3 4 568 5 10 5 13 4 5 16 8 5 16 3 600 639 676 6 II 3 180 185 3 15 3 17 I 4 10 4 12 6 5 5 5 7 II 600 634 6 15 6 18 9 190 3 19 2 4 15 5 10 10 6 6 8 726 195 200 4 I 3 4 3 4 4 17 6 500 5 13 9 5 16 8 6 10 6 13 4 763 7 10 INCOME TAX TABLES £205-450 Income £ 205 210 215 220 225 230 235 240 24s 250 260 265 270 275 280 285 290 295 300 3x0 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 405 410 415 420 425 430 435 440 445 450 TAX THEEEON AT PER £ bd. £ d. I 2 3 4 5 6 7 4 5 5 476 4 9 7 4 II 8 4 13 9 4 15 10 4 17 II 500 5 2 5 4 5 8 5 10 5 12 5 14 5 16 8 5 18 9 6 o 10 6 2 II 650 6 7 6 9 6 II 6 13 6 15 6 17 6 19 7 I 7 3 7 5 10 7 7 II 7 10 o 7 12 7 14 7 16 7 18 8 o 8 2 8 4 8 6 8 8 8 10 10 8 12 II 8 15 o 8 17 8 19 9 I 9 3 9 5 9 7 Qd. I 2 3 4 5 6 7 8 9 I 2 3 4 5 6 7 8 9 d. 6 o 6 o 6 £ t. 5 2 5 5 5 7 5 10 5 12 5 15 5 17 6 o 6 2 6 5 6 7 6 10 6 12 6 15 6 17 7 o 7 2 7 5 7 7 7 10 o 7 12 6 7 15 7 17 8 o 8 2 8 5 8 7 8 10 8 12 8 15 8 17 9 o 9 2 9 5 9 7 9 10 9 12 9 15 9 17 10 o o 6 o 6 o 6 o 6 o 6 o 6 o 6 o 6 o 6 o 6 o 6 o 6 o 6 o 6 o 6 o 6 o 10 2 10 5 10 7 10 10 10 12 6 o 6 o 6 10 15 o 10 17 6 11 o o II 2 6 II 5 o 7d. £ s. 5 19 6 2 6 5 6 8 6 II d. 7 6 5 4 3 2 I o 6 14 6 17 7 o 7 2 II 7 5 10 7 8 9 7 II 7 14 7 17 8 o 8 3 8 6 8 9 8 12 8 15 8 17 II 9 O ID 9 3 9 9 6 9 9 9 12 9 15 9 18 10 I 10 4 10 7 10 10 10 12 II 10 15 10 10 18 9 11 I 11 4 II 7 II 10 II 13 II 16 11 19 12 2 12 5 12 7 II 12 10 10 12 13 9 12 16 8 12 19 7 13 2 6 8 7 6 5 4 3 2 I o 8 7 6 5 4 3 2 I o 8 7 6 5 4 3 2 I o Zd. £ s.d. 6 16 8 700 7 3 7 6 7 10 4 8 7 13 4 7 16 8 8 8 3 4 8 6 8 8 10 8 13 4 8 16 8 9 9 3 4 9 6 8 9 10 9 13 4 9 16 8 10 10 3 4 10 6 8 10 10 o 10 13 4 10 16 8 II II 3 II 6 4 8 II 10. II 13 4 II 16 8 12 12 3 12 6 4 8 12 10 12 13 12 16 4 8 13 13 6 4 8 13 10 13 13 13 16 4 8 14 14 3 4 14 6 8 14 10 14 13 14 16 4 8 15 9^. £ s. 7 13 7 17 8 I 8 5 8 8 8 12 8 16 9 o 9 3 9 7 9 II 9 15 9 18 10 2 10 6 10 IQ 10 13 10 17 II' I 11 5 11 8 II 12 11 16 12 o 12 3 12 7 12 II 12 15 12 18 13 2 13 6 13 10 13 13 13 17 14 I 14 5 14 8 14 12 14 16 15 o 15 3 15 7 15 II 15 15 15 18 16 2 16 6 16 10 16 13 16 17 d. 9 6 3 o 9 6 3 o 9 6 3 o 9 6 3 o 9 6 3 o 9 6 3 o 9 6 3 o 9 6 3 o 9 6 3 o 9 6 3 o 9 6 3 o 9 6 3 o 9 6 M ^1 J? (199) INCOME TAX TABLES INCOME TAX TABLES £455-700 £7051,000 Income 455 460 465 470 475 480 485 490 495 500 505 510 5?5 520 525 530 535 540 545 550 565 570 575 585 590 '5 610 620 625 630 635 640 ^^ 650 660 665 670 675 680 68s 690 695 700 TAX THESEON AT FEB £ 5d. £ s. d. 9 9 7 9 II 8 9 13 9 9 IS 10 9 17 II 10 o 10 2 10 4 10 6 10 8 10 10 10 12 10 14 10 16 10 18 I I I I I I I I I I 12 12 o I 2 3 4 5 6 7 8 9 o 10 2 II 5 o 7 9 II 13 15 17 19 I 3 I 2 3 4 5 6 7 8 9 12 5 10 12 7 II 12 10 12 12 I 12 14 2 12 16 3 12 18 4 13 5 13 2 6 13 4 7 13 6 8 13 8 9 13 10 10 13 12 II 13 15 13 17 I 13 19 2 14 I 3 14 3 4 14 5 5 14 7 6 14 9 7 14 II 8 6d. £ s. II 7 II 10 II 12 II 15 11 17 12 O 12 2 12 5 12 7 12 10 12 12 12 15 12 17 13 o 13 2 13 5 13 7 13 10 13 12 13 15 13 17 14 o 14 2 14 5 14 7 14 10 14 12 14 15 14 17 15 o 15 2 15 5 15 7 15 10 15 12 15 15 15 17 16 o 16 2 16 5 16 7 16 10 16 12 16 15 16 17 17 o 17 2 17 5 17 7 17 10 d. 6 o 6 o 6 o 6 o 6 o 6 o 6 o 6 o 6 o 6 o 6 o 6 o 6 o 6 o 6 o 6 o 6 o 6 o 6 o 6 o 6 o 6 o 6 o 6 o 6 o T'i. £ s. 13 5 13 8 13 II 13 14 13 17 14 o 14 2 14 5 14 8 14 II 14 14 14 17 15 o 15 3 15 6 15 9 15 12 15 15 15 17 16 o 16 3 16 6 16 9 16 12 16 15 16 18 17 I 17 4 17 7 17 10 17 12 17 15 17 18 18 I 18 4 18 7 18 10 18 13 18 16 18 19 19 2 19 5 19 7 19 ID 19 13 19 16 19 19 20 2 20 5 20 8 d. 5 4 3 2 I o II 10 9 8 7 6 5 4 3 2 I o II 10 9 8 7 6 5 4 3 2 I o» II 10 9 8 7 6 5 4 3 2 I o II 10 9 8 7 6 5 4 For explanation see p. 40 8^. d. 4 8 o 4 £ «. 15 3 15 6 15 10 15 13 15 16 8 16 o 16 3 16 6 16 10 16 13 16 16 8 17 o o 17 3 17 6 17 10 o 17 13 4 17 16 8 18 o o 18 3 4 18 6 8 o 4 8 o 4 4 8 18 10 18 18 13 16 4 8 19 19 3 4 19 6 8 19 10 19 19 13 16 4 8 20 20 20 3 6 4 8 20 10 20 20 13 16 4 8 21 21 21 3 6 4 8 21 10 21 13 4 21 16 8 22 22 22 3 6 4 8 22 10 22 13 4 22 16 8 23 o o 23 3 4 23 6 8 9^. £ ». 17 I 17 5 17 8 17 12 47 16 18 o 18 3 18 7 18 II 18 15 18 18 19 2 19 6 19 10 19 13 19 17 20 I 20 5 20* 8 20 12 20 16 21 o 21 3 21 7 21 II 21 15 21 18 22 2 22 6 22 10 22 13 22 17 23 I 23 5 23 8 23 12 23 16 24 o 24 3 24 7 24 II 24 15 24 18 25 2 25 6 25 10 25 13 25 17 26 I 26 5 d. 3 o 9 6 3 o 9 6 3 o 9 6 3 o 9 6 3 o 9 6 3 o 9 6 3 o 9 6 3 o 9 6 3 o 9 6 3 o 9 6 3 o 9 6 3 o 9 6 3 o (200) TAX THEREON AT PER £ Income 5d. 6^. 7d. Sd. 9^. £ 1 £ 1. d. £ s. d. £ s. d. £ s. d. £ «. d. 705 710 715 , 720 725 14 13 9 14 15 10 14 17 II 17 12 6 17 IS 17 17 6 20 II 3 20 14 2 20 17 I 23 10 23 13 4 23 16 8 26 8 9 26 12 6 26 16 3 15 15 2 I 18 21 24 27 18 2 6 21 2 II 24 3 4 27 3 9 730 . 15 4 2 18 5 21 5 10 24 6 8 27 7 6 735 15 6 3 18 7 6 21 8 9 24 10 27 II 3 740 15 8 4 18 10 21 II 8 24 13 4 27 15 w 9 745 15 10 5 18 12 6 21 14 7 24 16 8 27 18 9 750 15 12 6 18 15 21 17 6 25 a 28 2 6 15 14 7 18 17 6 22 5 2S i 4 28 6 3 760 IS 16 8 19 22 3 4 2S 6 8 28 10 765 15 18 9 19 2 6 22 6 3 25 10 28 13 9 770 16 10 19 S 22 9 2 2S 13 4 28 17 6 • • 775 16 2 II 19 7 6 22 12 I 25 16 8 29 I 3 780 16 5 19 10 22 15 26 29 5 785 16 7 I 19 12 6 22 17 II 26 3 4 29 8 9 790 16 9 2 19 15 23 10 26 6 8 29 12 6 795 • 16 II 3 19 17 6 23 3 9 26 10 29 16 3 Si 16 13 4 20 23 6 8 26 13 4 30 805 16 IS S 20 2 6 23 9 7 26 16 8 30 3 9 810 16 17 6 20 5 23 12 6 27 30 7 6 815 16 19 7 20 7 6 23 15 S 27 3 4 30 II 3 820 17 I 8 20 10 23 18 4 27 6 8 30 15 825 17 3 9 20 12 6 24 I 3 27 10 30 18 9 830 17 S 10 20 15 24 4 2 27 13 4 31 2 6 835 17 7 II 20 17 6 24 7 I 27 16 8 31 6 3 840 17 10 21 24 10 28 31 10 845 17 12 I 21 2 6 24 12 II 28 3 4 31 13 9 850 17 14 2 21 5 24 IS 10 28 6 8 31 17 6 855 17 16 3 21 7 6 24 18 9 28 10 32 I 3 860 17 18 4 21 10 25 I 8 28 13 4 32 5 865 18 5 21 12 6 2S 4 7 28 16 8 32 8 9 870 18 2 6 21 15 25 7 6 29 32 12 6 875 18 4 7 21 17 6 25 10 5 29 3 4 32 16 3 880 18 6 8 22 2S 13 4 29 6 8 33 885 18 8 9 22 2 6 25 16 3 29 10 33 3 9 890 18 10 10 22 5 25 19 2 29 13 4 33 7 6 895 18 12 II 22 7 6 26 2 I 29 16 8 33 II 3 900 18 15 22 10 26 5 30 33 IS 910 18 19 2 22 15 26 10 10 30 6 8 34 2 6 920 19 3 4 23 26 16 8 30 13 4 34 10 930 19 7 6 23 5 27 2 6 31 34 17 6 940 19 II 8 23 10 27 8 4 31 6 8 3S S 950 19 IS 10 23 IS 27 14 2 31 13 4 3S 12 6 960 20 24 28 32 36 970 20 4 2 24 S 28 5 10 32 6 8 36 7 6 980 20 8 4 24 10 28 II 8 32 13 4 36 IS 990 20 12 6 24 IS 28 17 6 33 37 2 6 1,000 20 16 8 25 29 3 4 33 6 8 37 10 :l I > (201) INCOME TAX TABLES £1,010-1,500 r TAX THEBEON AT FEB £ Income 5d. 6^. 7^. 8^. ^d. £ £ s. d. £ s. d. £ *. d. £ «. d. £ i. d. 1,010 21 10 25 5 29 9 2 33 13 4 37 17 6 1,020 21 5 25 10 29 15 34 38 5 1,030 21 9 2 25 15 30 10 34 6 8 38 12 6 1,040 21 13 4 26 30 6 8 34 13 4 39 1,050 21 17 6 26 5 30 12 6 35 39 7 6 1,060 22 I 8 26 ID 30 18 4 35 6 8 39 15 1,070 22 5 10 26 15 31 4 2 35 13 4 40 2 6 1,080 22 10 27 C 31 ID 36 40 10 1,090 22 14 2 27 5 31 15 10 36 6 8 40 17 6 1,100 22 18 4 27 10 32 I 8 36 13 4 41 5 1,110 23 2 6 27 15 32 7 6 37 41 12 6 1,120 23 6 8 28 32 13 4 37 6 8 42 1,130 23 10 10 i 5 32 19 2 37 13 4 42 7 6 1,140 23 15 28 10 33 5 38 42 15 1,150 23 19 2 28 15 33 10 10 38 6 8 43 2 6 1,160 24 3 4 29 33 16 8 38 13 4 43 10 . 1,170 1,180 24 7 6 29 5 34 2 6 39 43 17 6 24 II 8 29 10 34 8 4 39 6 8 44 5 1,190 24 15 10 29 15 34 14 2 39 13 4' ^ 12 6 1,200 25 30 35 40 45 1,210 25 4 2 30 5 35 5 10 40 6 8 45 7 6 1,220 25 8 4 30 10 35 II 8 40 13 4 45 15 1,230 25 12 6 30 15 35 r7 6 41 46 2 6 1,240 25 16 8 31 36 3 4 41 6 8 46 10 1,250 26 10 31 5 36 9 2 41 13 4 46 17 6 1,260 26 5 31 10 36 15 42 47 5 1,270 26 9 2 31 15 37 10 42 6 8 47 12 6 26 13 4 32 37 6 8 42 13 4 48 1,290 26 17 6 32 5 37 12 6 43 48 7 6 1,300 27 I 8 32 10 37 18 4 43 6 8 48 15 1,310 27 5 10 32 15 38 4 2 43 13 4 49 2 6 1,320 27 10 33 38 10 44 49 10 1,330 27 14 2 27 18 4 28 2 6 33 5 38 15 10 44 6 8 49 17 6 1,340 1,350 33 10 33 15 39 I 8 39 7 6 44 13 45 4 50 5 50 12 6 1,360 28 6 8 34 39 13 4 45 6 8 51 1,370 28 10 10 28 15 34 5 34 10 39 19 2 40 5 45 13 46 4 51 7 6 51 IS 1,390 28 19 2 34 15 40 10 10 46 6 8 52 2 6 1,400 29 3 4 35 40 16 8 46 13 4 52 10 1,410 29 7 6 35 5 41 2 6 47 52 17 6 1,420 29 II 8 35 10 41 8 4 47 6 8 53 5 1,430 29 15 10 35 15 41 14 2 47 13 4 53 12 6 1,440 30 36 42 48 54 1,450 30 4 2 36 5 42 5 10 48 6 8 54 7 6 1,460 30 8 4 36 10 42 II 8 48 13 4 54 15 1,470 1,480 30 12 6 36 15 42 17 6 49 55 2 6 30 16 8 37 43 3 4 49 6 8 55 10 1,490 31 10 37 5 43 9 2 49 13 4 55 17 6 1,500 31 5 37 10 43 15 50 56 5 For explanation see p. 40 f202> INCOME TAX TABLES £1,510 2,000 TAX ' rHEBEON AT FEB £ Income 5^. 6^. • Id. 8^. 9^;. £ £ s. d. £ s. d. £ $. d. £ s. d. £ .s. rf. 1,510 31 9 2 37 IS 44 lb 50 6 8 56 12 6 1,520 31 13 4 38 44 6 8 50 13 4 57 1,530 31 17 6 38 5 44 12 6 51 57 7 6 1,540 32 I 8 38 10 44 18 4 SI 6 8 57 15 1,550 32 5 10 38 15 45 4 2 51 13 4 58 2 6 1,560 32 10 39 45 10 52 58 10 1,570 32 14 2 39 5 45 IS 10 52 6 8 58 17 6 1,580 32 18 4 39 10 46 I 8 52 13 4 59 5 1,590 33 2 6 39 IS 46 7 6 53 59 12 6 1,600 33 6 8 40 46 13 4 S3 6 8 60 1,610 33 10 10 40 5 46 19 2 S3 13 4 60 7 6 1,620 33 15 40 10 47 5 54 60 15 1,630 33 19 2 40 IS 47 10 10 54 6 8 61 2 6 1,640 34 3 4 41 47 16 8 54 13 4 61 10 1,650 34 7 6 41 s 48 2 6 55 61 17 6 1,660 34 II 8 41 10 48 8 4 55 6 8 62 5 1,670 34 15 10 41 15 48 14 2 55 13 4 62 12 6 1,680 . 35 42 49 56 63 1,690 35 4 2 42 5 49 5 10 56 6 8 63 7 6 1,700 35 8 4 42 10 49 II 8 56 13 4 63 15 1,710 35 12 6 42 IS 49 17 6 57 64 2 6 1,720 35 16 8 43 SO 3 4 57 6 8 64 10 1,730 36 10 43 5 SO 9 2 57 13 4 64 17 6 1,740 36 5 43 10 50 15 58 65 5 1,750 36 9 2 43 IS 51 10 58 6 8 65 12 6 1,760 36 13 4 44 51 6 8 58 13 4 66 1,770 36 17. 6 44 5 51 12 6 59 66 7 6 1,780 37 I 8 44 10 SI 18 4 59 6 8 66 15 1,790 37 5 10 44 IS 52 4 2 59 13 4 67 2 6 1,800 37 ID 45 52 10 60 67 10 X) 1,810 37 14 2 45 5 52 15 10 60 6 8 67 17 6 1,820 37 18 4 45 10 S3 I 8 60 13 4 68 5 1,830 3i \ \ 45 IS S3 7 6 61 68 12 6 1,840 38 6 8 46 S3 13 4 61 6 8 69 1,850 38 ID 10 46 5 S3 19 2 61 13 4 69 7 6 1,860 38 IS 46 10 54 5 62 69 15 1;IS 38 19 2 46 15 54 10 10 62 6 8 70 2 6 39 3 4 47 54 16 8 62 13 4 70 10 1,890 39 7 6 47 5 55 2 6 63 70 17 6 1,900 39 II 8 47 ID 55 8 4 63 6 8 71 5 1,910 39 15 ic 47 IS 55 14 2 63 13 4 71 12 6 1,920 40 48 56 64 72 1,930 40 4 2 40 ^ 1 4iD 12 6 48 s 56 5 10 64 6 8 72 7 6 1,940 48 10 56 II 8 64 13 4 72 15 1,950 48 IS 56 17 6 65 73 2 6 1,960 40 16 8 49 57 3 4 65 6 8 73 ID 1,970 41 10 49 5 57 9 2 65 13 4 73 17 6 1,980 41 5 49 10 57 15 66 74 5 1,990 41 9 2 49 IS 58 10 66 6 8 74 12 6 2,000 j 41 13 -^ 50 * 58 6 8 66 13 4 75 (203) M INCOME TAX TABLES i-i : t i r £2.050 5.000 For explanation see p. 40 (204) TAX . THEREON AT PES £ • Income 1 5^. £ ». d. 6^. £ s. rf. 7^. Sd. £ $. d. 9d. £ £ s. d. £ t. d. 2,050 1 42 14 2 51 5 59 15 10 68 6 8 76 17 6 2,100 43 15 52 ID 61 5 70 78 15 2,150 44 15 10 53 15 62 14 2 71 13 4 80 12 6 2,200 45 16 8 55 64 3 4 73 6 8 82 10 2,250 46 17 6 56 5 65 12 6 75 84 7 6 2,300 47 18 4 57 10 67 I 8 76 13 4 86 5 2,350 48 19 2 58 15 68 10 10 78 6 8 88 2 6 2,400 50 60 70 80 90 2,450 51 10 61 5 71 9 2 81 13 4 91 17 6 2,500 52 1 8 62 10 72 18 4 83 6 8 93 15 2,550 53 2 6 63 15 74 7 6 85 95 12 6 2,600 54 3 4 65 75 16 8 86 13 4 97 10 A65O 55 4 2 66 5 77 5 10 88 6 8 99 7 6 2,700 56 5 67 10 78 15 90 loi 5 2,750 57 5 10 68 15 80 4 2 91 13 4 103 2 6 2,800 58 6 8 70 81 13 4 93 6 8 105 2,850 59 7 6 71 5 83 2 6 95 106 17 6 2,900 60 8 4 72 10 84 II 8 96 13 4 108 15 2,950 61 9 2 73 15 86 10 98 6 8 no 12 6 3,000 62 10 75 87 10 100 112 10 3,050 63 10 10 76 5 88 19 2 loi 13 4 114 7 6 3,100 64 II 8 77 10 90 8 4 103 6 8 116 5 3fiSo 65 12 6 78 15 91 17 6 105 118 2 6- 3,200 66 13 4 80 93 6 8 106 13 4 120 3,250 67 14 2 81 5 94 15 10 108 6 8 121 17 6 3,300 ' 68 15 82 10 96 5 no 123 15 3,350 69 15 10 83 15 97 14 2 III 13 4 125 12 6 3,400 70 16 8 85 99 3 4 113 6 8 127 10 3,450 71 17 6 86 5 100 12 6 115 129 7 6 3,500 72 i8 4 87 10 102 I 8 116 13 4 131 5 3,550 73 19 2 88 15 103 10 ID 118 6 8 133 2 6 3,600 75 90 105 120 135 3,650 76 10 91 5 106 9 2 121 13 1 136 17 6 3,700 77 I 8 92 10 107 18 4 123 6 138 15 3,750 78 2 6 93 15 109 7 6 125 140 12 6 3,800 79 3 4 95 no 16 8 126 13 4 142 10 3,850 80 4 2 96 5 112 5 10 128 6 8 144 7 6 3,900 81 5 97 10 113 15 130 146 5 3,950 82 5 10 98 15 115 4 2 131 13 4 148 2 6 4,000 83 6 8 100 116 13 4 133 6 8 150 4,100 85 8 4 102 10 119 II 8 136 13 4 153 15 4,200 87 10 105 122 10 140 157 10 4,300 89 II 8 107 10 125 8 4 143 6 8 161 5 4,400 91 13 4 no 128 6 8 146 13 4 165 4,500 93 15 112 10 131 5 150 168 15 4,600 95 16 8 115 134 3 4 153 6 8 172 10 4,700 4,800 97 18 4 100 117 10 120 137 I 8 140 156 13 160 4 176 5 180 4,900 102 I 8 120 10 142 18 4 163 6 8 183 15 5,000 104 3 4 125 145 16 8 166 13 4 187 10 THE LOGARITHMS OP NATURAL NUMBERS TOGETHER WITH THOMAN'S LOGARITHMIC TABLES OF COMPOUND INTEREST AND ANNUITIES AND AN EXPLANATION OF THE TABLES (20s) M 1 I . LOGARITHMS OF NATURAL NUMBERS Pages 229-266 contain the logarithms of the natural numbers from I to 10,000. The logarithm of a number is the index of the power to which the base must be raised to be equal to the number. Thus 5 x 5=5S where 5 is raised to the second power, and 2 is the index of the power. Again, 5x5x5 = 5^, where 5 is raised to the third power, and 3 is the index of the power. The base adopted for common logarithms such as are here given is 10, so that the logarithm of 100 is 2 because io'= 10x10 = 100 of 1,000 „ 3 „ 10^=10x10x10 = 1,000 of 10,000 ,, 4 „ 10'*= 10 X 10 X 10 X 10= 10,000 and so on. But we may raise a number to any power we please, without confining ourselves to whole numbers. Thus 10^^ = 4*641 as may be seen from page 244, where 666612 is given as the logarithm 6 666 2 2 of 4*641. Now 10^^ = 10'*^ = I ©3 very nearly, but io3 = V 10' that is the cube root of 100. The cube root of 100 is approximately 4*641, that is to say 4*641 x 4641 x 4641 = 9996, which is very nearly 100. By means of logarithms we may get our results as nearly exact as we please, and the larger number of figures we have in our log- arithms the more exact will our results be. We have said that *6666 is the logarithm of 4*641, but there is nothing in the table to show where the decimal point ought to come. For anythmg that appears in the table to the contrary, 6666 is the log of 4641, or 46*41 or 464*1. The explanation of this is. that only one part of the logarithm, called the mantissa^ is given in the table ; the other part of the logarithm, called the index or charac- teristic, is supplied by inspection, according to certain rules which will be described presently. The rationale of these rules is very easy to follow. The mantissa is the decimal part of the index of the power to which 10 must be raised to equal a given number, and if the index is o, it means that the power to which 10 has to be raised is less than unity, but as 10* or 10 to the first power = 10, it is plain that 10^^ must be less than 10, whence it follows that the natural number corresponding to log *6666 cannot be 46 4 or 464, because these numbers are more than 10. (207) Ii !i! LOGARITHMS OF NATURAL NUMBERS If we want to find the logarithm of 46-41, the complete logarithm must clearly be between i and 2, because i is the logarithm of 10, 2 is the log of 100 and 46 is between 10 and 100. Clearly, therefore, the log of 46 must have i for its index, and, looking in the table for the decimal part of the log corresponding to 4641, we find it to be 6666. There- fore the complete log of 46*41 is 1*6666. This means that 10 must be raised to a power the index of which is i 6666, that is to 16666 5 say 10'^^= io»«»o = io3= ^iqs. Now iqs equals 100,000, and the cube root of this is 46*41, more nearly 46*416, more nearly still 46*4158929. The reason why the index part of the log can be so readily determined by inspection, and why therefore it is unnecessary to tabulate more than the mantissa or decimal part of the logarithm, is based upon the fact that multiplication of numbers can be performed by adding their logarithms together. Now, as we have just seen, the log of 10 is I, the log of 100 is 2, the log of 1,000 is 3, and so on. Hence, if we want to multiply a number by 10, we add i to the log ; to multiply by 100 we add 2 to the logarithm, and tp multiply by 1,000 we add 3 to the logarithm of the number. Hence, 4*641 X 10 46*41 X 10 464*1 X 10 4641 X 10 = log 0*6666 + log I = = log I *6666 + log I = = log 2*6666 + log I log 3*6666 4- log I : log 1*6666 log 2*6666 log 3*6666 log 4*6666 46*41 464*1 4641 46410 This leads us to the rule for determining the index part of the logarithm. If the number whose logarithm is sought contain one or more integral figures the index or characteristic is always one less than the number of integral figures in the number, and is positive. Negative Index Frequently, however, we have to deal with numbers that are less than unity, in which case the index of the logarithm becomes negative, although the decimal part remains positive. Dealing with these negative figures as we previously dealt with the positive ones, we see that 10' =10, therefore i is the log of 10 10" = I IO~'= 'I io~'= -oi IO~3 = •001 if if o — I or I — 2 or 2 -3 or 3 a j» »> >) •I •01 ■00 1. and so on. This leads us to the rule for finding the index of quanti- ties less than unity, which is that the index is the same as the place (208) TO FIND THE LOGARITHM OF A NUMBER from the decimal point which the first significant figure of the num- ber occupies. Thus the first significant figure of *ooi is i, which is in the third place from the decimal point, and the index of the log is consequently 3, while the mantissa is o. This index, as stated above, is minus, the minus sign being written over the index thus 3, not in front of it thus — 3, in order to signify that the index only is minus, the mantissa remaining positive. In dealing with numbers less than unity the mantissa is kept positive, and the index only is made negative for the sake of con- venience in working ; but if there were any advantage in doing so the mantissa as well as the index could, of course, be made negative. We know that the log of 4641 is 06666, while the log of 100 is 2, and we can divide 4641 by 100 by subtracting log 2 from log o*6666. This gives us log i'3334, the whole of which is minus, and is the log of -04641. Log — 1*3334 is exactly the same as log 2*6666, where the index only is minus, and the mantissa is plus. It is, however, found in practice much more convenient to keep the mantissa invariably positive, or plus, letting the index only be minus. Referring again to the example we have already quoted, and applying these two rules, we get the following results : — *ooo464i = log 4*666612. •004641 = log 3*666612. •04641 = log 2*666612. •4641 = log I •666612. 4*641 = log 0*666612. 46*41 =: log 1*666612. 464*1 = log 2 '6666 1 2. 4641 = log 3*666612. The special convenience of logarithms, and it is a very great one, is that by their aid numbers can be multiplied by the addition of their logs, divided „ subtraction „ raised to any power by the multiplication of their logarithms and their roots extracted by the division of their logarithms. To find the Logarithm of a Number Before giving examples of the use of logarithms, however, we must explain how to find the logarithm of a given number, and the number corresponding to a given logarithm. Where the number consists of only four figures it is immediately found from the tables by looking in the first column for the first three figures, and on the same line in (209) 4> )t I«i LOGARITHMS OF NATURAL NUMBERS the column headed with the fourth figure the logarithm of the number will be found. Thus on p. 232 we see that the decimal part of the logarithm of 1501 is 176381. Again on p. 242 we find that the decimal part of the logarithm of 4341 is 637590. If, however, we want to find the logarithm of 43405, which is half way between 4340 and 4341, we must take the logarithm as half way between 637490 and 637590, which = log 637540. In order to facilitate finding the logarithms of numbers containing five or more figures, a column of differences is given on each page of the tables. In the case just given the difference is seen to be 100, which means that there is a difference of -oooioo between the logs of one number and the next. To obtain the logarithm of a number containing five figures we take the logarithm of the first four figures direct from the table, then multiply the difference by the fifth figure of the number, divide the result by 10 and add it to the logarithm of the first four numbers. Thus to repeat the example just given : 4340 the difference 100 x 5 43405 = log 637490 10 = log 50 = log 637540 If we wish to find the logarithm of a number containing six figures we take the first five figures m the way just described, and to obtain the difference for the sixth figure we multiply the difference by the sixth figure and divide the result by 100. Thus to find the log of 434054. 43405 r= log 637540 the difference for 6th figure 100 x 4 — 100 = log 4 434054 = log 637544 The differences in this case are exceptionally simple to calculate because m the example chosen the difference is exactly 100, but the simphcity of the calculation serves to show with special clearness the principle involved. This principle of course is, that to find the difference for the 5th figure of a number we must multiply the differ- ence given in the table by a fraction of which 10 is the denominator and the 5th figure of the number is the numerator. To obtain the 6th figure the difference must be multiplied by a fraction of which me denominator is 106 and the numerator the 6th figure. To find (210) THE NUMBER CORRESPONDING TO A LOGARITHM the difference corresponding to the 7th figure the denominator is 1000 and the numerator the 7th figure and so on, as far as we please. In dealing with these differences it must always be borne in mind that the figures printed in the Table of Differences come at the ex- treme right-hand end of the logarithms in the main part of the table. That is to say, if the difference printed in the last column is 100 it is understood to be really -000100. If the printed difference is 99 it is to be understood as -000099, while obviously the difference corre- sponding to the 5th figure must be in all cases less than the printed difference. If this is remembered there will be no fear of any mistake in taking out the logarithms for numbers containing five or six figures. To find the Number Corresponding to a Logarithm To find a number corresponding to a given logarithm we must look in the table for the nearest logarithm to the one we are dealing with. The first three figures of the logarithms are printed in large type on the top of the page. On the left-hand pages the first three figures of the Jirsf logarithm on the page are given. On the right- hand pages the first three figures of the /as/ logarithm on the page are given, so that we can readily see whether the logarithm with which we are concerned does or does not come on a given page. Now, let us suppose that we wish to find the natural number corresponding to log 735868. From p. 246 we see that log 735838 (which is 30 less than the logarithm we are dealing with) = 5443. The difference printed in the last column on this line is 80, and signifies that 80 corresponds to a difference of i in the 4th figure of the natural numbers, therefore 30 corresponds to a difference of ^ x 10 in the 5 th figure of the natural numbers. 80 This = 375, so that the total number corresponding to log 735868 = 5443375- Thus to find the number corresponding to a logarithm that is not given exactly in the table we must take from the table the nearest logarithm below the given logarithm and obtain the 5th and following figures of the natural number by dividing the difference between these two logarithms by the difference printed in the tables. The numerator of this fraction consisting of the difference between the given logarithm and the nearest logarithm below it printed in the tables, being multiplied by 10 to obtain the 5th figure of the natural number and by 100 to obtain the 6th figure, and so on. (211) il LOGARITHMS OF NATURAL JNUMBERS Multiplication by Logarithms Having seen how to find the logarithm corresponding to a number and the number corresponding to a logarithm, we may now proceed to the practical use of logarithms. Multiplication of numbers is accomplished by the addition of the logarithms of their numbers, thus : log 3-406029 (p. 237) log 3-868233 (p. 254) 2547 = 7383 = 2547 ^ 7383 = log 727426 2 = 18804500. The Index of the log being 7, there must be 8 .figures in the answer. A reference to p. 232 shows that the nearest logarithm to the logarithm of the answer is 274158, giving a difference of 104, which divided by the Tabular Difference of 231 equals very approximately 45 for the 5th and 6th figures of the answer. Other examples of Multiplication by means of logarithms are appended. Multiply 25-75 by 4-217. 2575 = log 1-410777 (p. 237) 4-217 = log 0-625004 (p. 243) 25-75 X 4-217 = lo g 2-035781 = 108-58775 (p. 231) Multiply 3847 by 0632. 3847= log 3-585122 (p. 241) •0632 = log 2800717 (p. 250) 3847 X -0632 = 2-385839 = 243-1302 (p. 234) The exact answer in this case is 243-1304, which is obtained by usmg seven-figure logarithms, as follows : — 3847 = log 3 5851222 -0632= log 2-8007171 3847 X 0632 = 2-3858 393= 243-1304. It must, therefore, be borne in mind that to obtain exact results it is necessary to use a large number of figures in the logarithm, but the six figures given in the tables are suflftcient for most practical purposes. (212) DIVISION BY LOGARITHMS Division by Logarithms The division of numbers is accomplished by subtraction of their logarithms, the logarithm of the divisor being taken from the divi- dend, the remainder being the logarithm of the quotient. Thus to divide 4364 by 2536 we have 4364 = log 3-639885 (p. 242) 2536 = log ^404149 (P- 237) 4364^-2536 = log 0-235736= 1-7208 (p. 232) Divide 426-53 by 32*79. 426-53 = log 2-629950 (p. 243) 32-79 = log 1-515741 (p. 239) 426-53^-32-79 = log 1- 114209 = 13008 (p. 230) m Divide 3279 by 426-53. 32-79 = log 1-515741 (p. 239) 426-53 = log 2-629950 (p. 243) 32-79 -f- 426-53 = log 2-885791 =-076876 (p. 257) Divide 8652 by -0461. 8652 = log 3-937117 (P- 260) -0461 =log 2-663701 (p. 244) 8652 -r- -0461= log 5-273416 =187679 (p. 233) In the last example we are subtracting a negative characteristic, and of course the subtraction of a minus quantity is accomplished by the addition of the corresponding positive or plus quantity. Divide 0461 by 8652. •0461 =log 2-663701 (p. 244) 8652 = log 3-93711 7 (P- 260) •0461 -5-8652 = log 6-726584 = -000005328 (p. 247) In this example we are subtracting a positive characteristic from a negative one, and this involves the addition of the corresponding negative quantity. If, as we have just seen, 8652-^-0461 = 187679 =log 5-273416 and •0461 H- 8652 = -000005328 = log 6-726584 187679 X -000005328 = log 0'000000= I, thus affording an instructive proof of the accuracy of the results by adding the two logarithms together and obtaining the answer. (213) ( LOGARITHMS OF NATURAL NUMBERS Involution by Logarithms To raise a number to any given power we multiply the logarithm of the number by the index of the power. Thus the cube of loo is log 2-000 X 3 = log 6-000 = 1,000,000 = 100 X 100 X 100. Similarly 733' •00733= •007333 :l0g 2*865104 X2 log 3-865104x2; log 3-865104x3; = log 5730208 log 5730208: log 7*595312: 537289 •0000537 -0000003938 In the last two examples we had negative characteristics to deal with, and it will be noticed that after multiplying the decimal part of the log- arithm by 2 there was a positive remainder of i, which is subtracted from twice the negative characteristic. Similarly in the cube there ' was a remainder of 2, which was subtracted from three times the negative characteristic. This treatment of the matter is an obvious consequence of the mantissa being positive and the characteristic negative. Evolution by Logarithms • To find the root of a given number we must divide the logarithm of the number by the exponent of the root. Thus to find the square root of a number we divide the log by 2 ; » cube „ „ „ » 3; „ fourth „ „ „ » 4; and so on. For example : ^537289 = log 5 -730208 -f- 2 = log 2-865 104 = 733 v^i7'43 =log 1*241297 -f-3 = logo-4i3766 = 2-5928 V2560000 = log 6-408240 -J- 4 = log I -602060 = 40 ^•0081 = log3-9o8485 h- 3 = log i -302828 = -20083 ^•00081 = log 4-908485-^3 = log 2 -969495 = -0932 1 7 In this last instance we had a negative characteristic to deal with, and the most convenient way of treating it was to add — 2 to the 4 of the index, so obtaining a number, 6, which is exactly divisible by 3. To compensate for thus dealing with the index we must prefix an index of + 2 to the mantissa, and divide this result also by 3. The process thus becomes : log 4 -f 2 . . . . = log 6 this -f- 3 = log 2 log 908485 + 2 = log 2-908485 this -j- 3 = log 0-969495 log 4-908485 -h 3 = log 2-969495 (214) — — EVOLUTION BY LOGARITHMS 'f his produces the same result as if we had stated our entire log- arithm as negative, divided it by 3, and subsequently converted it into a logarithm with a negative index and a positive mantissa. Thus : is the same as log — 4-000000 log + 0908485 log-3-091515 when both index and mantissa are negative. This divided by 3 = log- 1030505, the whole of which is still negative. But this equals log 2-969495, where the index is negative and the mantissa positive, and this is the result obtained by dividing 4-908485 by 3. , .^ ^ Thus the rule for dividing a logarithm with a negative mdex if the index is not exactly divisible by the divisor, is to add such a negative number to it as will make it exactly divisible, and prefix to the frac- tional part of the logarithm a positive integer equal to the negative integer added to the negative index. Of course, by adding a minus quantity to one part of the logarithm and a corresponding plus quantity to another part of it, the value of the logarithm is unaltered. :ti («5) COMPOUND INTEREST The Amount of i in any Number of Periods Pages 269-316 contain M. Thoman's logarithmic tables of the amount of ;^i at the end of any number of years and the logarithm of the annuity which £1 will purchase. The great value of these tables, and the various uses to which they may be put, will be at once apparent when the use of logarithms is understood. On p. 9 we showed that the amount of ^i in any number of years— or, more generally, the amount of i in any number of periods— is the amount of I in I period raised to the nih. power. This is expressed as (1 + if, where / is the rate of interest and n the number of years. M. Thoman uses the symbol r as the equivalent of i +/, which means the amount of I in I period, but the modern practice is to use / for the rate of interest and 1+/ for the amount of i in i period. Now, as a number may be raised to any power by multiplying the logarithm of the number by the index of the power, we can obviously obtain the amount of ^^i in any number of years with very little trouble. Thus, if we want to know the amount of ^i in 25 years at 4 %, we have to find the value of ro^'^K The log of 1*04 is seen from p. 230 to be 0-017033. This multiplied by 25 equals log 0*425825, which, from p. 237, we find to be 2-6658, which agrees with the result given in the interest table on p. 70. On turning to Thoman's table on p. 291 the logarithm is seen to be 04258335, and taking the natural number corresponding to this logarithm we get 266584, which agrees with the 5 places of decimals in the interest table of p. 70. It thus appears that to obtain the amount of i at the end of any number of periods we must multiply the log of i -f / at the end of I period by the number of periods. The natural number correspond- ing to the logarithm thus obtained gives the required result. Further examples are appended. What is the amount of £1 at the end of 73 years at 5I % per annum ? Turning to M. Thoman's table on p. 306 we find in "the column headed log r" year 73, log 1-8099199, which is the logarithm of the answer. From the logarithmic table on p. 251 we find that this corresponds to 64*5535. (216) AMOUNT OF 1 IN ANY NUMBER OF PERIODS What is the amount oi £1 at the end of 27 years at 3!% per annum ? This rate of interest is not tabulated, so we must take the log of (1+/)^'. Now, as / = 3i% or -032, the value of i 4- / = 1032, = log 00 1 368, which is the logarithm given on p. 230. Multiplying this by 27, we obtain as our answer log 36936 = 2-3408. It will be seen that by means of logarithms enormous calcula- tions may be made with the greatest ease. Thus suppose we want to know the amount to which id. will accumulate at 5 % compound interest in 1900 years ; our answer in pence is 1-05^^ = log 0*02 11 893 X 1900 = log 40-25967. To obtain the answer in pounds we sub- tract the log of 240, namely 2-38021, thus leaving log 3787946 = ;^7 5, 763,500,000,000,000,000,000,000,000,000,000,000. If we wish to extend the calculation and show what income would be yielded from such an amount as this at 5 % interest every second to every man, woman, and child on the face of the earth, we have simply to divide by 20 to find the annual income from this sum, then by 365^ to find the daily income, by 24 to find the income hourly, by 60 to find the income per minute, by 60 again to find the income per second, and finally by (say) 1,483 millions to find the income in each second for every individual in the world. These divisions are readily accomplished by adding the logarithms of the numbers together and subtracting the total from the logarithm of the amount of id. at the end of 1900 years. Thus, 1-05^500 = log 40259670 240 = log 2 3802 1 1 20 = log 1*301030 365-25 = log 2-562590 24 —log! -3802 1 1 • 60 = log 1778151 60 =logi778i5i 1,483,000,000 = log 9-17 1 141 log 20-351485 log 19-908185 which gives us £80,944,000,000,000,000,000 per second as the income for every man, woman, and child in every second from the accumulations of id. at 5% compound interest for 1900 years. We often require to know, not so much what £1 will amount to in any number of times, but what various other amounts will come to. This is arrived at by the help of logarithms with very great ease. We have only to add the logarithm of the amount to the logarithm of the amount of £1 in the given number of years to at once obtain the logarithm of the answer. (217) h I COMPOUND INTEREST What will £4372 amount to in 46 years at 4 % ? 1-04^ = log 07835336 (p. 291) 4372 = log 3-6406802 (p. 242) 1-04^ X 4372 = log 4^242x38=^26,559. Again, what will £987 amount to at the end of 22 years at 3^^ = 3*583, so that I +/= I -03583 = log 0-0152899 (p. 320) i'o3583'' = log 0*0152899 X 22 = log '3363778 987 = log 2-9943172 =log 2-9943172 (p. 264) 103583- X 987 = log 3^306^95^ = £2141-4. Present Value of £1 On p. 10 we showed that v= - '— ., where v is the present value I +/ of £1, and z;"=(— -— J , where n represents the term. Hence to obtain the present value of £1 due at the end of any number of years we subtract the log of (1+/)" from the log of i". Thus, suppose we require to know the present value of £1 due at the end of 20 years at 5%, w^e have (i -f /)" = 1-05^= log -021 189 x 20 = log 0-42378 to be subtracted from i" = log 0-000000. Now log o'oooooo — log 0-42378 = log 1*57622 = -3769, this agreeing with the result given in the interest tables on p. 74. The log of (i +/")'* is obtained from the columns headed log r" on p. 299, and by sub- tracting the logarithm there given from the log of i we obtain the logarithm of the present value of i due at the end of n years. Further examples are appended. What is the present value of £1 due at the end of 22 years at 44%? From p. 298 we see that log (i + /)" = log r" = 0*4547834. «=^-~-.j =log 0*0000000 - log o-4547834 = log 7-5452166 = -£•35093- / V What is the present value of j£i due at the end of 47 years at o.T 0/ ;> ^s /o ' This equals log 0-0000000 — log 0-4791140 (p. 278)=log r52o886o = -33i8i- What is the present value of ;£i due at the end of 30 years at 3^%? (218) ANNUITY WHICH ;^i WILL PURCHASE This rate of interest is equivalent to 3 0625, and is not tabulated, so we must find from the table on p. 230 the logarithm of 1-030625, multiply by 30, and subtract it from the logarithm of i. I = log O'oooooo 1*0306253° = log -0131007 X30 = log -393021 i-o3o6253° =^Qg 1^606979 =^-40456 What is the present value of ;^i due at the end of 25 years at 3*%? _ This rate of interest also is not tabulated, but the logarithm corresponding to i + / when i is at the rate of 3I % is given in the column log r, p. 320. It is there seen to be 0-0163368. Multiplying this by 25 we have log 04084 2, which, subtracted from log I, leaves log i -591 58, corresponding to -39046. Annuity which £1 will Purchase On pp. 16 and 17 we explain the Sinking Fund Tables given on pp. 106-115. It is there shown that the Sinking Fund is obtained by dividing unity by the amount of jQ\ per annum. It is, however, further explained (p. 17) that in this table no provision is made for paying interest on the capital. If this has to be done, the amounts given in the Sinking Fund Table must be increased each year by the annual interest on £\. Thus, if the Sinking Fund required to replace £^\ in ten years at 4 % is ;^ -083291 per annum, we must add the annual interest on ;^i = *o4 to this amount, in order to obtain the annuity which jQ\ will purchase for ten years at 4 %. The result of this addition is (-083291 +-04=) -123291, the logarithm of which is 1*090931, which is the logarithm given in the column headed «" on p. 291. M. Thoman uses the symbol a" to represent this quantity, but in modern notation it is more usually expressed by the symbol — . It will, moreover, be noticed that in M. Thoman's tables the index of the logarithm is given as 9 instead of i, as given above. The reason of this is that some people think it more convenient to avoid the negative characteristics of logarithms by adding 10 to the index, subtracting the negative index, when it occurs, from this 10, and so always dealing with a positive index. The 10 that has been added is subsequently deducted from the index, and thus the same result is arrived at. The more usual and, we think, the more convenient plan is not to employ this artifice, but to (219) N COMPOUND Interest deal with negative characteristics, whenever they occur, in the manner already explained. Another point to be noticed in M. Thoman's logarithmic tables is that he puts a comma between the index and mantissa, and a decimal point between the 5th and 6th decimal places'. It is more in accordance with modern English custom to put the decimal point between the index and mantissa of the logarithm, while there is nothing to be gained by putting any mark at all between the 5th and 6th decimal places. Thus 0,1 7033*34 in Thoman=o'i 703334 in modern notation ; and in regard to negative characteristics 9,09093- 1 2 in Thoman = 1-09093 12 in modern notation, and so on throughout wherever the index is seen by inspection, as it readily can be, to have had 10 added to it. From what has already been said, it will be seen that in dealing with annuities there are four things to be considered. One is the sum to which an annuity will amount in any number of years ; another is the present value of an annuity for any number of years ; the third is the annuity for any number of years which i or any other given amount will purchase ; and the fourth is the sinking fund which will redeem a debt in a given number of years. The third and fourth of these only differ by the amount of the interest on the debt for one year or one period, as has just been explained. It is the third of these for which the logarithm is given in M. Thoman's tables on pp. 269-316 in the column headed a". The fourth is tabulated in natural numbers under the head of Sinking Fund on pp. 106-115. Dealing with the third of these first, namely the annuity which ^i will purchase for any number of years, we have to notice that it is the reciprocal of the present value of ^i per annum tabulated in natural numbers on pp. 50-85. Obviously if the present value of an annuity of ^i per annum for 20 years at 4 % is 1 3*59033 (p. 70) an annuity for 20 years at 4 %, of which the present value is j£i, is equivalent to of;£'i. This i3'59033 equals ^'0735817, the logarithm of which is 2*866770, thus agreeing with the logarithm given on p. 291, where, however, the logarithm is stated as 8,86677*02. This difference in the method of stating the logarithm has already been explained. As another example we may take the present value of an annuity for 26 years at 2| %. This is ^18*40226 (p. 64), and taking the reciprocal of this amount we have -054341 15 = log 2735129, which agrees wath the logarithm given on p. 281. Thus to find the annuity which i will purchase, we have only to take the natural number corresponding to the logarithm given on pp. 269-316 under the heading log a". f220) ANNUITY WHICH £1 WILL PURCHASE A few examples may be added. What annuity for 27 years will £1 buy at 3} % ? Ans. (p. 285) log 2*7497045 = *o56i96. For 86 years at 5i % ? Ans. (p. 300) log 2-7i56373=*o5i956. For 7 years at 3 % ? Ans. (p.283) log r-2054922 = *i6o5o6 =-130506-1; -03 (5 reckoning interest at 4^ % ? 5737=log 3758685 (p. 249) The annuity which i will buy=log 2*675548 (p. 295) >j »» 5737 >> =log 2-434233=^271-79. The annuity that may be bought for i at rates not given in the table may be calculated from the formula ^ — ^ — =log />log(i + /)"-log [(i +/)"-!]. a (I +/)«-! What annuity for 30 years will £1 purchase at 5%? / = -05 = log 2-6989700 (p. 318) (i + /)«= I -053° = log 0-02 1 1 893 X 30 = log 06356790 = 4-32 194 / (i 4. /)« = -05x1 -053° = log I -3346490 (i-f /)"-!= 4'32i94-i =log 0*5213918 _L(i_±it= '05 X 1-053 ° (l +/)«-! 3*32194 "^^ =log2-8i32572= -065051 This is the figure given on p. 299, save that the last figures of the logarithm are 70 instead of 72, a difference that is inappreciable. (221) N 2 ^\ r II ! i I! I i COMPOUND INTEREST What annuity for lo years will ;^683 purchase at 4-1 %? /*= -041= log 2-6127839 (p. 319) (i 4-/)'*= I -041'° = log 0-01745073 X 10 = log o-i 745073 = 1-49454 /(!+/)*= -041x1041'° =log2"-78729i2 (i +/)^— 1 = 1-49454— I = log I -69420 14 ^'(i + /)" __ -041 X 1-041^° :: ~~ 683 = log 2-8344207 ^ Annuity ^683 will buy for 10 years = log 1-9275 105 = 84-6273 Present Value of j£i per Annum We have just seen that the present value of an annuity is the reciprocal of the amount of the annuity which i will purchase for the same period at the same rate of interest. In other words, the annuity which i will purchase and the present value of an annuity multiplied together produce unity — the period and the rate of interest, of course, being the same in both cases. The logarithms of the annuity which i will purchase are given in the column headed a'\ on pp. 269-316. By subtracting this tabulated logarithm from o, which is the log of I, we obtain the logarithm of the present value of an annuity of i. What is the present value of an annuity of ;^i per annum for 43 years at 3 J % ? I =logo-ooooooo Annuity i will purchase for 43 years at 3I % = log 2-6824736 (p. 290) Present value of ^^i per annum for 43 years at 3J % . . . =log i-3i75264 = ;^2o-7743 What is the present value of ;^i per annum for 30 years at 5 % ? I =log o -0000000 The annuity which i will purchase for 30 years at 5 % . . . ^ log 2-8132570 (p. 299) Present value of £^\ per annum for - 30 years at 5% . . .=log i'i86743o ==;^i5-37245 This result may be seen m the table on p. 74. Although the present values of annuities are given in natural numbers on pp. 50-85, it is often convenient to have the logarithms of the values rather than the natural numbers. Thus, suppose we want to know (222) PRESENT VALUE OF £\ PER ANNUM the present value of an annuity of ;^47-25 per annum for 30 years at 5 %. To obtain the result we must multiply the value of £\ per annum by 47*25, and this, as has been already explained, can be most readily done by the addition of the logarithms of the two numbers. Present value of £,\ per annum for 30 years at 5 % 47-25 i5'37245 X 47*25 = log 1-186743 (p. 299) = log 1-674402 (p. 245) = log 2-861 145=;£726-35» which is the present value of an annuity of ^47-25 per annum for 30 years at 5%. What is the present value of an annuity of ^8642 for 68 years at2j%? 8642 Value of annuity of J[,\ (log o -log 2-5269372) Value of annuity of ;^8642 for 68 years at 2 J % = log 3-9366143 (p. 260) = log I 4730628 (p. 282) = log5-409677i=;^256849. The value of an annuity for some other rate of interest than is given in the tables may sometimes be needed, and we must therefore explain how the value may be arrived at. We have already shown (p. 221) that the present value of an annuity is the reciprocal of the annuity that i will purchase, and that the annuity which i will purchase may be obtained from the formula ^^^^^^^ , Hence the formula for finding the (i+/)"-i present value of an annuity is (^-tOj^ =log[(i -I- /)"-T]--log / -log(i+/)«. We may repeat the example already dealt with. What is the present value of j£i per annum for 30 years at 5 % ? (i +/)«= i-o53° = log 0-0211893 X 30 = log 0-6356790=4-32194 (i +/)"— i=4*32i94- I =3'32^94 =log 05213918 tz= -05 =log 2*6989700 (i -I- /)" = 1-053° =log 0-6356790 /(i -!-/)«= -05 X I -053° = log i-3346490=log 1-3346490 (L± 0" - I ^4'32 194 — I t{i-\-iy -05 XI -053° £ =log i-i867428=i5*372 (223) COMPOUND INTEREST If the logarithm here found is added to the logarithm found in the converse problem on p. 221, we have log I '1867428 log 2-8132572 log 0*0000000=1 ' thus showing that the answers are reciprocals of each other. What is the present value of ;^i per annum for 75 years at 37%? 1-03775 1-03775. •037 1-03775 = log 0-0157788x75 = log 1-1834100=15-255 1= _ 14-255 =log 1-1539672 — log 2*5682017 = log 1-1834100 log r75i6ii7 I -03775 _ I •037 X 1-037 75 = log 1-4023555 = ;£25-2555. The Amount of £1 per Annum Another calculation that we sometimes require to make is the sum to which an annuity will amount in a given number of years at a specified rate of interest.. If we know the present value of the annuity, and if we know also the sum to which ^i will amount in the given period, we can, by multiplying the present value by the amount of ^i, obtain the sum to which the annuity will amount in the period. Thus, suppose we wish to ascertain the amount of ^i per annum for 20 years at 5 %. Turning to p. 74, we see that the present value of ;^i per annum is 12*46221, and on the same page we see that the amount of ^i in 20 years is 2-6533. Multiplying these two amounts together we have 33*066, which agrees with the amount of ;£i per annum given on the same page. The reason of this connection is plain, for since the possession "of an annuity of ^i for 20 years at 5% is mathematically equi- valent to having ^12-46221 in hand now, and as the sum to which ;^i 2-4622 1 will amount in 20 years is the amount of ^i in 20 years multiplied by 12-46221 (=2-6533 x 12-46221 = 33-066), this must also be the sum to which an annuity of ;^i will amount in 20 years at 5 %• This result may very easily be obtained by logarithms from the tables on pp. 269-316. In the column headed «" we have, as already explained, the reciprocal of the present value of an annuity, and in the column headed r" we have the amount of ;;^i, and we (224) SINKING FUND make use of these two tables in the following way to obtain, as in the example just given, the amount of £1 per annum in 20 years at 5 %. Turning to p. 299, we have Value of annuity = (log o - log 2-9044049=) log 1*0955951 Amount of ^i = l^S 0^4237860 Amount of annuity in 20 years at 5% = log i'5^93^^^ = ^33066, thus agreeing with the result previously obtained. Some additional examples are appended. What is the amount of £1 per annum at the end of 63 years at3i%? , «x Value of.annuity =log 1-4259707 (P- 285) Amount of £1 = log 0-87507 38 (p. 285) Amount of annuity =log 2-3010445 = 200007. * What is the amount of ^735 per annum at the end of 34 years at 2i % ? Value of annuity = log 1-3327200 (p. 282) Amount of £1 =log 0*4185348 (p. 282) 735 = log 2*8662^73 (p. 254) Amount of £nS P-a. in 34 years = log 4*6175421 =£4iAS^'^^' It will be noticed that the logarithm of the annual payment is added to the other two logarithms, thus conveniently effecting the necessary multiplication. i Sinking Fund A reference to the remarks on pp. 16, 17, and 219 will show the connection between the sinking fund and the annuity which ^i will purchase ; it will be seen that it is only necessary to deduct the rate of interest from the annuity which £1 will purchase to obtain the sinking fund. Thus the sinking fund which will redeem a debt of ^i in 25 years at 4 % is obtained by taking trom p. 291 the annuity which i will purchase = log 2*8062612 = -064012, and subtracting from this amount the rate of interest -04 ..whence we have •024012, which is the sinking fund given on p. 112. Further examples as obtained by logarithms are appended. What annual payment will redeem a debt of £1 in 65 years at 4i%? (225) COMPOUND INTEREST III The annuity i will purchase (p. 292) Subtract the interest for i year Sinking fund = 2-6479998 = -044463 = •04125 = •003213 What is the annual sinking fund that will amount to ;^337 in 43 years at 2f % ? Annuity i will buy = log 2-5918772 (p. 280) 337 =log 2-5276299 (p. 238) Annuity 337 will buy =log i'iT9507i = 13-16760 Deduct interest on 337 for i year =33 7 x ~^^ — = 8-8462 c 8 X 100 ^ Sinking fund to redeem 337 in 43 years == 4-32135 Or the calculation may be made in a slightly different way : Annuity i will buy =±log "2-5918772= '039073 Sinking fund to redeem i = '039073 - '02625 = log 2-1079896 = -012823 337= log 2-5 276299 Sinking fund to redeem 337 = log 0-6356195 =^4-32135 Annuities for which the Rate of Interest on Capital is Different from the Rate for Sinking Fund As explained on p. 18, we require for this calculation to know the annual sinking fund that will amount to ;^i in a given period at the lower rate of interest, and to know also the annual interest upon ;^i. The present value of an annuity equal to the addition of these two is I, and the present value of an annuity of i is the reciprocal of the present value just mentioned. What annuity must be paid during 29 years to repay a debt of ;^i by accumulation at 3 J % and to pay interest on the loan at 4^ %? The annuity which will amount to ;£■! in 29 years at 3^% is obtained by multiplying the annuity which i will purchase for 29 years by the present value of i due at the end of 29 years. Annuity /^i will purchase (p. 285) = log 2-7305144 Present value of^i (p. 285) = log 1-5971883 Annuity to amount to ;^i in 29 years - log 2-3277027 = -021267 Annual interest on ^i . = *o4S Annual payment required = log 2-8212973 = 066267 (226) LOGARITHM OF THE RATE OF INTEREST If, on the other hand, we want to know the present value of an annuity of ;£i for 29 years on the condition that interest on the loan is being paid at 4^ %, and the principal is being replaced by accumulation at 3J %t we must take the reciprocal of the above amount. This is log 0-0 - log 2^-82 12973 = 1*1787027 = ;£i 5*0905. What is the value of an annuity of ^i for 50 years yielding interest on capital at 5 %, and replacing capital when invested at 3%? • Annuity;^! will purchase (p. 283) = log 2-5895642 Present value of ^i (p. 283) = log 1-3581388 Annuity to amount to £1 in 50 years = log 3-9477030 = "0088655 Annual interest on £1 = '050 Annuity to pay ^i and interest = log 2-7698608 = -0588655 Required value of annuity = log 0*0 — log 2-7698608 = log 1*2301392 = ^16-98788, which agrees with the amount given on p. 120. As in other cases, the values or amounts of annuities other than £1 may be obtained by the addition of the logarithms. Logarithm of the Rate of Interest The Tables on pp. 318-320 give the logarithm of the rate of inte- rest under the heading /. This is in modern notation represented by the symbol i. On p. 318 this is given to 10 places of decimals for every rate given in M. Thoman's first Table (pp. 269-316). On p. 319 it is given for every J^th % up to 10 % and on p. 320 for every ^V^h % also up to 10 %. This Table is convenient for such calculations as the present value of ^i per annum, as may be seen from the first example on p. 222. It has several times been pointed out that the more decimals are taken in the logarithm the more nearly exact will be the results. This is especially the case when the logarithm has to be multiplied. Logarithm of the Amount of i in i Period This logarithm is given to 7 places of decimals on pp. 269-316 in the column r", but on p. 318 the logarithm is given to 10 places of decimals. As has just been said, the use of to places gives more nearly exact results than 7 places, though for most purposes 7 places are sufficient. (227) 1 1 COMPOUND INTEREST As an example of a fairly large difference, as differences go, take the amount of ^^i for 90 years at 2| % :— 1-028759° {see p. 2i6) = log 0-0123098482 (p. 318^ x go = log 1-1078863380=12-8199544. 1-028759° = log 0-0123098 X 90 = log 1-1078820=12-8198265. This only gives a difference of 25 shillings in the amount of ^10,000 in 90 years, thus showing that 7 places are usually ample. Even this difference does not occur if we take the logarithm from p. 282, where it is seen to be log 1-1078863= 12-8199533, giving a difference of ;^i in the amount of one million pounds in 90 years. The lo-figure logarithms are useful, however, for the construction of a table of (1+/)" (or /-"), as in pp. 269-316, where the multiplica- tion is worked to 10 places, and the nearest 7 places are printed. This accounts for the smaller variation when (H-/)9° is taken from p. 282. The tables on pp. 319 and 320 give log (1+/), or log /-, as M. Thoman called it, for every ^^^th and ^Vth %, and it is more convenient to take these logarithms from this table than from the table of logarithms on pp. 230-266. The Logarithms of Log r Under the heading of Mog2 r' we have the logarithm of 'log n' Thus at ^ % 'log /-' = 0-00216606 ; and from p. 235 we see that this number = log 3-33567, which agrees with the value of 'log^ r' on p. 318. We sometimes find it convenient to multiply a logarithm by taking the logarithm of the logarithm and adding the logarithm of the multiplier. This gives us a logarithm of the second order, as it were (log-), and the number corresponding to this log^ is the log we require. Thus to get the logarithm of (i ^tj^ when / = -04, we have log2 r= log 2-2312998 (p. 318) 87= log 1-9395^93 log (i -|-/)87 = log2 0-1708191 = log 1-48190, thus agreeing with the figure given on p. 291 and with log (i -f-/) X87 by ordinary multiplication. (228) I TABLE OF THE LOGARITHMS OP THE NATURAL NUMBERS From 1 to 10,000 For explanation see pp. 207-215 (229) I \ t llf : 111 Log. 000. No. 100. LOGARITHMS No. 100 lOI 102 103 104 105 106 107 108 109 no III 112 "3 114 116 117 118 119 120 121 122 123 124 126 '^ 128 129 130 132 133 134 136 137 138 139 140 141 142 143 144 146 147 148 149 OCXXX)0 004321 008600 012837 017033 021 189 025306 029384 033424 037426 041393 045323 049218 053078 056905 060698 064458 068186 071882 075547 079I8I 082785 086360 089905 093422 096910 00371 03804 07210 10590 13943 I727I 20574 23852 27105 30334 33539 36721 39879 43015 46128 49219 52288 55336 58362 61368 64353 67317 70262 73186 000434 004751 009026 013259 01 745 1 021603 025715 029789 033826 037825 041787 045714 049606 053463 057286 061075 064832 068557 072250 075912 079543 083144 086716 090258 093772 097257 1007 1 5 104146 107549 1 10926 1 14277 1 17603 120903 124178 127429 130655 133858 ^37037 140194 143327 146438 149527 152594 155640 158664 161667 164650 167613 170555 173478 2 000868 005181 009451 013680 017868 022016 026125 03019s 034227 038223 042182 046105 049993 053846 057666 061452 065206 068928 072617 076276 079904 083503 087071 090611 094122 097604 101059 104487 107888 1 1 1263 114611 1 1 7934 121231 124504 127753 130977 134177 137354 140508 143639 146748 149835 152900 155943 158965 I 6 1967 164947 167908 170848 173769 001301 005609 009876 014100 018284 022428 026533 030600 034628 038620 042576 046495 050380 054230 058046 061829 065580 069298 072985 076640 080266 083861 087426 090963 094471 097951 101403 104828 108227 I "599 1 14944 1 18265 121560 124830 128076 131298 134496 1 3767 1 140822 14395 1 147058 I 50142 153205 156246 1 59266 162266 165244 168203 171141 174060 001734 006038 010300 014521 018700 022841 026942 031004 035029 039017 042969 046885 050766 054613 058426 062206 065953 069668 073352 077004 080626 084219 087781 091315 094820 098298 101747 105169 108565 "1934 1 15278 1 18595 121888 125156 128399 131619 134814 137987 141136 144263 147367 150449 153510 156549 159567 162564 165541 168497 I 7 1434 I 7435 I Diif. 433 429 425 421 416 412 409 405 401 397 393 390 387 383 380 377 374 370 367 364 361 358 355 352 349 347 344 341 338 336 333 330 328 326 323 321 319 316 314 312 310 307 305 303 301 299 297 295 293 291 OF NUMBERS Log. 175. No. 149. No. 100 lOI 102 103 104 105 106 107 108 109 no III 112 "3 114 "5 116 V^ 119 120 121 122 123 . 124 128 129 130 131 132 133 134 136 137 138 139 140 141 142 143 144 145 146 147 148 149 002166 006466 010724 014940 OI9II6 023252 027350 031408 035430 039414 043362 047275 05II53 054996 058805 062582 066326 070038 073718 077368 080987 084576 088136 091667 095169 098644 I 0209 I I055IO 108903 1 12270 II 561 I II 8926 I222I6 I 2548 I 128722 I3I939 I35I33 138303 I4I450 144574 147676 150756 I538I5 156852 159868 162863 165838 168792 I7I726 17464 1 002598 006894 01 1 147 015360 019532 023664 027757 03I8I2 035830 03981 I 043755 047664 051538 055378 059185 062958 066699 070407 074085 077731 081347 084934 088490 092018 095518 098990 102434 I0585I 10924*1 1 1 2605 I I 5943 I 19256 122544 125806 129045 003029 007321 011570 015779 019947 024075 028164 032216 036230 040207 044148 048053 051924 055760 059563 063333 067071 070776 074451 078094 081707 085291 088845 092370 095866 09933s 102777 106191 109579 I 12940 I 16276 1 19586 122871 126131 129368 8 132260 132580 I 3545 I 135769 138618 138934 141763 142076 144885 145196 147985 148294 151063 151370 154120 154424 157154 157457 160168 160469 163161 163460 166134 166430 169086 169380 172019 172311 174932 175222 003461 007748 011993 016197 020361 024486 028571 032619 036629 040602 044540 048442 052309 056142 059942 063709 067443 07 I 145 074816 078457 082067 085647 089198 092721 096215 099681 103119 I0653I 109916 11327s 116608 II99I5 I23I98 126456 129690 132900 136086 139249 142389 145507 148603 151676 154728 I577S9 160769 163758 166726 169674 172603 175512 9 003891 008174 012415 016616 020775 024896 028978 033021 037028 040998 044932 048830 052694 056524 060320 064083 067815 071514 075182 078819 082426 086004 089552 093071 096562 100026 103462 10687 1 I 10253 1 13609 116940 120245 123525 126781 130012 DiflE. 431 427 423 419 415 411 407 403 399 396 392 389 385 382 379 375 372 369 366 363 360 357 354 351 348 345 343 340 337 335 332 329 327 325 322 I332I9 320 136403 318 139564 315 142702 313 145818 3" 148911 309 151982 306 155032 304 158061 302 161068 300 16405s 298 167022 296 169968 294 172895 292 175802 290 For explanation see pp. 207-215 (230) (331) LOGARITHMS Log. 176. No. 150. No. 1 1 76381 2 3 4 Dili. 150 I7609I 176670 176959 177248 289 151 178977 179264 179552 179839 I 801 26 287 152 I8I844 I82I29 182415 182700 182985 285 153 I 8469 I 184975 185259 185542 185825 283 154 I8752I 187803 188084 188366 188647 281 155 190332 I906I2 190892 191171 191451 279 156 I93I25 193403 I 9368 I 193^59 194237 278 '57 195900 I96I76 196453 196729 197005 276 158 198657 198932 199206 I 9948 I 199755 274 159 201397 201670 201943 202216 202488 273 160 204120 204391 204663 204934 205204 271 161 206826 207096 207365 207634 207904 269 162 209515 209783 210051 210319 210586 268 163 2I2IS8 212454 212720 212986 213252 266 164 214844 2I5I09 215373 215638 215902 264 '5§ 217484 217747 218010 218273 218536 263 166 220108 220370 220631 220892 221153 261 \% 222716 222976 223236 223496 223755 260 225309 225568 225826 226084 226342 258 169 227887 228144 228400 228657 228913 257 170 230449 230704 230960 231215 231470 255 171 232996 233250 233504 233757 23401 I 254 172 235528 235781 236033 236285 236537 252 173 238046 238297 238548 238799 239049 251 174 240549 240799 241048 241297 241546 249 'Z§ 243038 243286 243534 243782 244030 248 176 245513 245759 246006 246252 246499 246 177 247973 248219 248464 248709 248954 245 178 250420 250664 250908 251151 251395 244 179 252853 253096 253338 253580 253822 242 180 255273 255514 255755 255996 256237 241 181 257679 257918 258158 258398 258637 240 182 260071 260310 260548 260787 261025 238 183 262451 262688 262925 263162 263399 237 184 264818 265054 265290 265525 265761 236 185 267172 267406 267641 267875 2681 10 234 186 269513 269746 269980 270213 270446 233 187 271842 272074 272306 272538 272770 232 188 274158 274389 274620 274850 275081 231 189 276462 276692 276921 277151 277380 229 190 278754 278982 27921 1 279439 279667 228 191 281033 28I26I 281488 281715 281942 227 192 283301 283527 283753 283979 284205 226 193 285557 285782 286007 286232 286456 225 194 287802 288026 288249 288473 288696 224 195 290035 290257 290480 290702 290925 222 196 292256 292478 292699 292920 293141 221 197 294466 294687 294907 295127 295347 220 198 296665 296884 297104 297323 297542 219 199 298853 299071 299289 299507 299725 218 For explanation see PP- 207-215 (232) OF NUMBERS Log. 300 , No. 199. No. 5 6 7 8 9 Diff. 150 177536 177825 178113 I 78401 178689 288 151 180413 180699 180986 181272 181558 286 152 183270 18355s 183839 184123 184407 284 153 . 186108 I 8639 I 186674 186956 187239 283 154 188928 189209 189490 189771 19005 1 281 155 191730 192010 192289 192567 192846 279 156 194514 194792 195069 195346 195623 277 157 197281 197556 197832 198107 198382 275 158 200029 200303 200577 200850 201124 274 159 202761 203033 203305 203577 203848 272 160 205475 205746 206016 206286 206556 270 161 208173 208441 208710 208979 209247 269 162 210853 211121 211388 211654 211921 267 163 213518 213783 214049 214314 214579 265 164 216166 216430 216694 216957 217221 264 165 218798 219060 219323 219585 219846 262 166 221414 221675 221936 222196 222456 260 167 224015 224274 224533 224792 225051 259 168 226600 226858 227115 227372 227630 257 169 229170 229426 229682 229938 230193 256 170 231724 231979 232234 232488 232742 254 171 234264 234517 234770 235023 235276 253 172 236789 237041 237292 237544 237795 251 173 239299 239550 239800 240050 240300 250 174 241795 242044 242293 242541 242790 249 175 244277 244525 244772 245019 245266 247 178 246745 246991 247237 247482 247728 246 177 249198 249443 249687 249932 250176 244 178 251638 251881 252125 252368 252610 243 179 254064 254306 254548 254790 255031 242 180 256477 256718 256958 257198 257439 240 181 258877 259116 259355 259594 259833 239 182 261263 261501 261739 261976 262214 238 183 263636 263873 264109 264346 26458* 236 184 265996 266232 266467 266702 266937 235 'M 268344 268578 268812 269046 269279 234 270679 270912 271144 271377 271609 233 \U 273001 273233 273464 273696 273927 231 27531 1 275542 275772 276002 276232 230 189 , 277609 277838 278067 278296 278525 229 190 279895 280123 280351 280578 280806 228 191 282169 282396 282622 282849 283075 226 192 284431 284656 284882 285107 285332 225 193 286681 286905 287130 287354 287578 224 194 288920 289143 289366 289589 289812 223 195 291147 291369 291591 291813 292034 222 196 293363 293584 293804 294025 294246 221 197 295567 295787 296007 296226 296446 220 198 297761 297979 298198 298416 298635 218 199 299943 300161 300378 300595 300813 217 (233J LOGARITHMS i I Log. 301. No. 200. No. 1 2 3 4 Difl. 217 200 301030 301247 301464 301681 301898 201 303196 303412 303628 303844 304059 216 202 305351 305566 305781 305996 3062 I I 215 203 307496 307710 307924 308137 308351 214 204 309630 309843 310056 310268 3 1048 I 213 205 31 1754 31 1966 312177 312389 312600 212 206 313867 314078 314289 314499 314710 211 207 315970 316180 316390 316599 316809 210 208 318063 318272 318481 318689 318898 209 209 320146 320354 320562 320769 320977 208 210 322219 322426 322633 322839 323046 207 2X1 324282 324488 324694 324899 325105 206 212 326336 326541 326745 326950 327155 205 213 328380 328583 328787 328991 329194 204 214 330414 330617 330819 331022 331225 203 215 332438 332640 332842 333044 333246 202 216 334454 334655 334856 335057 335257 201 217 336460 336660 336860 337060 337260 200 218 338456 338656 338855 339054 339253 199 219 340444 340642 340841 341039 341237 198 220 342423 342620 342817 343014 343212 197 221 344392 344589 344785 344981 345178 196 222 346353 346549 346744 346939 347135 195 223 348305 348500 348694 348889 349083 194 224 350248 350442 350636 350829 351023 194 225 352183 352375 352568 352761 352954 193 226 354108 354301 354493 354685 354876 192 227 356026 356217 356408 356599 356790 191 22!i 357935 358125 358316 358506 .358696 190 229 359835 360025 360215 360404 360593 190 230 361728 361917 362105 362294 362482 189 231 363612 363800 363988 364176 364363 188 232 365488 365675 365862 366049 366236 187 233 367356 367542 367729 367915 368101 186 234 369216 369401 369587 369772 369958 185 235 371068 371253 371437 371622 371806 185 236 372912 373096 373280 373464 373647 184 237 374748 374932 375115 375298 375481 183 238 376577 376759 376942 377124 377306 182 239 378398 378580 378761 378943 379124 182 240 38021 I 380392 380573 380754 380934 181 241 382017 382197 382377 382557 382737 180 242 383815 383995 384174 384353 384533 179 243 385606 385785 385964 386142 386321 179 244 387390 387568 387746 387923 388101 178 24s 389166 389343 389520 389698 389875 ^77 246 390935 391 I 12 391288 391464 391641 176 247 392697 392873 393048 393224 393400 176 248 394452 394627 394802 394977 395152 175 249 396199 396374 396548 396722 396896 174 OF NUMBERS Log. 397. No. 249. For explanation see pp. 207-215 (234) No. 200 aoi 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 21 21 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 237 239 240 241 242 243 244 249 3021 14 304275 306425 308564 310693 312812 314920 317018 319106 321 184 323252 325310 327359 329398 331427 333447 335458 337459 339451 341435 343409 345374 347330 349278 351216 353147 355068 356981 358886 360783 362671 364551 366423 368287 370143 371991 373831 375664 377488 379306 381115 382917 384712 386499 388279 390051 391817 393575 395326 397071 6 302331 304491 306639 308778 310906 313023 315130 317227 319314 321391 323458 325516 327563 329601 331630 333649 335658 337659 339650- 341632 343606 345570 347525 349472 351410 353339 355260 357172 359076 360972 362859 364739 366610 368473 370328 372175 374015 375846 377670 379487 381296 383097 384891 386677 388456 390228 391993 393751 395501 397245 302547 304706 306854 308991 311118 313234 315340 317436 319522 321598 323665 325721 327767 329805 331832 333850 335859 337858 339849 341830 343802 345766 347720 349666 351603 353532 355452 357363 359266 361 161 363048 364926 366796 368659 370513 372360 374198 376029 377852 379668 381476 383277 385070 386856 388634 390405 392169 393926 395676 397419 8 302764 304921 307068 309204 31 1330 313445 315551 317646 319730 321805 323871 325926 327972 330008 332034 334051 336059 338058 340047 342028 343999 345962 347915 349860 351796 353724 355643 357554 359456 361350 363236 3651 13 366983 368845 370698 372544 374382 376212 378034 379849 381656 383456 385249 387034 388811 390582 392345 394101 395850 397592 9 302980 305136 307282 309417 31 1542 313656 315760 317854 319938 322012 324077 326131 328176 330211 332236 334253 336260 338257 340246 342225 344196 346157 348110 350054 351989 353916 355834 357744 359646 361539 363424 365301 367169 369030 370883 372728 374565 376394 378216 380030 381837 383636 385428 387212 388989 390759 392521 394277 396025 397766 Difl. 2J6 215 214 213 212 211 210 209 208 207 206 205 204 203 202 201 200 199 199 198 197 196 19s 194 193 192 192 191 190 189 188 187 187 186 185 184 183 183 182 181 180 180 179 178 177 177 176 175 175 174 (235) LOGAKITHMS :\ Log. 397. No. 250. No. 397940 1 2 3 398461 4 Diff. 250 3981 14 398287 398634 173 251 399674 399847 400020 400192 400365 173 252 40I40I 401573 401745 401917 402089 172 253 403I2I 403292 403464 403635 403807 171 254 404834 405005 405176 405346 405517 171 256 • 406540 406710 406881 407051 407221 170 408240 408410 408579 408749 408918 169 257 409933 410102 410271 410440 410609 169 258 41 1620 41 1788 41 1956 412124 412293 168 259 413300 413467 413635 413803 413970 167 260 414973 415140 415307 415474 415641 167 261 4I664I 416807 416973 417139 417306 166 262 4I830I 418467 418633 418798 4 I 8964 165 263 419956 420121 420286 420451 420616 165 264 421604 421768 421933 422097 422261 164 265 423246 423410 423574 423737 423901 163 266 424882 425045 425208 425371 425534 163 267 4265 I I 426674 426836 426999 427161 162 268 428135 428297 428459 428621 428783 162 269 429752 429914 430075 430236 430398 161 270 431364 431525 431685 431846 432007 160 271 432969 433130 433290 433450 433610 160 272 434569 434729 434888 435048 435207 159 273 436163 436322 436481 436640 436799 159 274 437751 437909 438067 438226 438384 158 275 439333 439491 439648 439806 439964 157 440909 441066 441224 441381 441538 157 277 442480 442637 442793 442950 443106 156 278 444045 /]/]/\?,Ol 444357 444513 444669 156 279 445604 445760 445915 446071 446226 15s 280 447158 447313 447468 447623 447778 155 281 448706 448861 449015 449170 449324 154 282 450249 450403 450557 4507 1 1 450865 154 283 451786 451940 452093 452247 452400 153 284 453318 453471 453624 453777 453930 153 285 454845 454997 455150 455302 455454 152 286 456366 456518 456670 456821 456973 152 287 457882 458033 458184 458336 458487 151 288 459392 459543 459694 459845 459995 151 289 460898 461048 461 198 461348 461499 150 290 462398 462548 462697 462847 462997 149 291 463893 464042 464191 464340 464490 149 292 465383 465532 465680 465829 465977 148 293 466868 467016 467164 467312 467460 148 294 468347 468495 468643 468790 468938 147 295 469822 469969 4701 16 470263 470410 147 296 471292 471438 471585 47 '732 471878 146 297 472756 472903 473049 473195 473341 146 298 474216 474362 474508 474653 474799 146 299 475671 475816 475962 476107 476252 145 OF NUMBERS No. For explanation see pp. 207-215 (236) 250 251 252 253 2S4 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 276 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 299 398808 400538 402261 403978 405688 407391 409087 410777 412461 414137 415808 417472 419129 420781 422426 424065 425697 427324 428944 430559 432167 433770 435367 436957 438542 440122 441695 443263 444825 446382 447933 449478 451018 452553 454082 455606 457125 458638 460146 461649 463146 464639 466126 467608 469085 470557 472025 473487 474944 476397 6 Log. 476. No. 299. 398981 4007 1 1 402433 404149 405858 407561 409257 410946. 412629 414305 415974 417638 419295 420945 422590 424228 425860 427486 429106 430720 432328 433930 435526 4371 16 438701 440279 441852 443419 444981 446537 448088 449633 45II72 452706 454235 455758 457276 458789 460296 461799 463296 464788 466274 467756 469233 470704 472I7I 473633 475090 476542 8 399154 400883 402605 404320 406029 407731 409426 411114 412796 414472 416141 417804 419460 421 1 10 422754 424392 426023 427648 429268 430881 432488 434090 435685 437275 438859 440437 442009 443576 445137 446692 448242 449787 451326 452859 454387 455910 457428 458940 460447 461948 463445 464936 466423 467904 469380 470851 472318 473779 475235 476687 9 399328 401056 402777 404492 406199 407901 409595 41 1283 412964 414639 416308 417970 419625 421275 422918 424555 426186 42781 1 429429 431042 432649 434249 435844 437433 439017 440594 442166 443732 445293 446848 448397 449941 451479 453012 454540 456062 457579 459091 460597 462098 463594 465085 466571 468052 469527 470998 472464 473925 475381 476832 399501 401228 402949 404663 406370 408070 409764 411451 413132 414806 416474 418135 419791 421439 423082 424718 426349 427973 429591 431203 432809 434409 436004 437592 439175 440752 442323 443889 445449 447003 448552 450095 451633 453165 454692 456214 457731 459242 460748 462248 463744 465234 466719 468200 469675 471145 472610 474071 475526 476976 Diff. 173 173 172 171 171 170 169 169 168 167 167 166 165 165 164 163 163 162 162 161 160 160 159 159 158 157 157 156 156 155 155 154 154 153 153 152 152 151 150 150 149 149 148 148 147 147 146 146 146 145 (237) OS LOGABITHUS Log. 477. No. 300. No. 1 2 3 4 Diff. 300 477I2I 477266 47741 1 477555 477700 145 301 478566 47871 1 478855 478999 479143 144 302 480007 4801 5 I 480294 480438 480582 144 303 481443 481586 481729 481872 482016 143 304 482874 483016 483159 483302 483445 143 305 484300 484442 484585 484727 484869 142 306 485721 485863 486005 486147 486289 142 307 487138 487280 487421 487563 487704 141 308 488551 488692 488833 488974 4891 14 141 309 489958 490099 490239 490380 490520 140 310 491362 491502 491642 491782 491922 140 3" 492760 492900 493040 493179 493319 139 312 494155 494294 494433 494572 4947 1 1 139 313 495544 495683 495822 495960 496099 138 314 496930 497068 497206 497344 497483 138 315 4983 1 1 498448 498586 498724 498862 138 310 499687 499824 499962 500099 500236 137 317 501059 501 196 501333 501470 501607 137 318 502427 502564 502700 502837 502973 136 319 503791 503927 504063 504199 504335 136 320 505150 505286 505421 505557 505693 136 321 506505 506640 '06776 50691 1 507046 13s 322 507856 507991 J08126 508260 508395 135 323 509203 509337 509471 509606 . 509740 134 324 510545 510679 510813 510947 511081 134 335 51 1883 512017 512151 512284 512418 133 320 513218 513351 513484 513617 513750 133 327 514548 5 1468 I 514813 514946 515079 133 328 515874 516006 516139 516271 516403 132 329 517196 517328 517460 517592 517724 132 330 518514 518646 518777 518909 519040 131 331 519828 519959 520090 520221 520353 131 332 521138 521269 521400 521530 521661 131 333 522444 , 522575 522705 522835 522966 130 334 523746 ' 523876 524006 524136 524266 130 ^^5 525045 525174 525304 525434 525563 129 330 526339 526469 526598 526727 526856 129 337 527630 527759 527888 * 528016 528145 129 338 528917 529045 529174 529302 529430 128 339 530200 530328 530456 530584 530712 128 340 531479 531607 531734 531862 531990 128 341 532754 532882 533009 533136 533264 127 342 534026 534153 534280 534407 534534 127 343 535294 535421 535547 535674 535800 126 344 536558 536685 53681 I 536937 '537063 126 fji 537819 537945 538071 538197 538322 126 539076 539202 539327 539452 539578 125 347 540329 540455 540580 540705 540830 125 348 541579 541704 541829 541953 542078 125 349 542825 542950 543074 543199 543323 124 For explanation see pp. 207-215 (238) OF NUMBERS Log. 543 L No. 349. No. 5 6 7 8 9 Diff. 300 477844 m 477989 478133 478278 478422 H5 301 479287 479431 479575 479719 479863 144 302 480725 480869 481012 481 156 481299 144 303 482159 482302 482445 482588 482731 143 304 483587 483730 483872 484015 484157 143 305 48501 I 485153 485295 485437 485579 142 300 486430 486572 486714 486855 486997 142 ^ 487845 487986 488127 488269 488410 141 489255 489396 489537 489677 489818 141 309 490661 490801 490941 491081 491222 140 310 • 492062 492201 492341 492481 492621 139 3" 493458 ' 493597 493737 493876 494015 139 312 494850 494989 495128 495267 495406 139 313 496238 496376 496515 496653 496791 '3! 314 497621 497759 497897 498035 498173 138 ^'5 310 498999 499137 499275 499412 499550 138 500374 5°°5" 500648 500785 500922 137 317 501744 501880 502017 502154 502291 137 318 503109 503246 503382 503518 503655 136 319 504471 504607 504743 504878 505014 136 320 505828 505964 506099 506234 506370 136 321 507181 507316 507451 507586 507721 135 332 508530 508664 508799 508934 509068 135 323 509874 510009 510143 510277 510411 134 324 511215 51 1349 51 1482 511616 511750 134 ^ 512551 512684 512818 512951 513084 133 • 326 513883 514016 514149 514282 514415 133 327 515211 515344 515476 515609 515741 133 328 516535 516668 516800 516932 517064 132 329 517855 517987 518119 518251 518382 132 330 519171 519303 519434 519566 519697 131 331 520484 520615 520745 520876 521007 131 332 521792 521922 522053 522183 522314 131 333 523096 523226 523356 523486 523616 130 334 524396 524526 524656 524785 524915 130 135 525693 525822 525951 '526081 526210 129 330 526985 527114 527243 527372 527501 129 337 528274 528402 528531 528660 528788 129 338 529559 529687 529815 529943 530072 128 339 530840 530968 531096 531223 531351 128 340 5321 17 532245 532372 532500 532627 128 341 533391 533518 533645 533772 533899 127 342 534661 534787 534914 535041 535167 127 343 535927 536053 536180 536306 536432 126 344 537189 537315 537441 537567 537693 126 340 538448 538574 538699 538825 538951 126 539703 539829 539954 540079 540204 125 ^l 540955 541080 541205 541330 541454 125 348 542203 542327 542452 542576 542701 125 349 543447 543571 543696 543820 543944 124 (239) LOGABITHMS H;' Log. 544. No. 350. No. 1 2 3 4 Diff. 350 544068 544192 544316 544440 544564 124 351 545307 545431 545555 545678 545802 124 352 546543 546666 546789 546913 547036 123 353 547775 547898 548021 548144 548267 123 354 549003 549126 549249 549371 549494 123 355 550228 550351 550473 550595 550717 122 356 551450 551572 551694 551816 551938 122 357 552668 552790 55291 I 553033 553155 121 358 553883 554004 554126 554247 554368 121 359 555094 555215 555336 555457 555578 121 ^ 556303 556423 556544 556664 556785 • 120 361 557507 557627 557748 557868 557988 120 362 558709 558829 558948 559068 559188 120 363 559907 560026 560146 560265 560385 119 364 561 lOI 561221 561340 561459 561578 119 365 562293 562412 562531 562650 562769 119 366 563481 563600 563718 563837 563955 119 367 564666 564784 564903 565021 565139 118 368 565848 565966 566084 566202 566320 118 369 567026 567144 567262 567379 567497 118 370 568202 568319 568436 568554 568671 117 371 569374 569491 569608 569725 569842 117 372 570543 570660 570776 570893 571010 117 373 571709 571825 571942 572058 572174 116 374 572872 572988 573104 573220 573336 116 375 574031 574147 574263 574379 574494 116 376 575188 575303 575419 575534 575650 115 377 576341 576457 576572 576687 576802 115 378 577492 577607 577722 577836 577951 "5 379 578639 578754 578868 578983 579097 114 380 579784 579898 580012 580126 580241 114 381 580925 581039 581 153 581267 581381 114 382 582063 582177 582291 582404 582518 114 383 583199 583312 583426 583539 583652 "3 384 584331 584444 584557 584670 584783 113 355 585461 585574 585686 585799 585912 "3 386 586587 586700 586812 586925 587037 112 387 58771 I 587823 587935 588047 588160 112 388 588832 588944 589056 589167 589279 112 389 589950 590061 590173 590284 590396 112 390 591065 591 176 591287 591399 591510 III 391 592177 592288 592399 592510 592621 III 392 593286 593397 593508 593618 593729 III 393 594393 594503 594614 594724 594834 no 394 595496 595606 595717 595827 595937 no 395 596597 596707 596817 596927 597037 no 396 597695 597805 597914 598024 598134 no 397 598791 598900 599009 599119 599228 109 3^ 599883 599992 600101 600210 600319 109 399 600973 601082 601191 601299 601408 109 For explanation see pp. 207-215 (240) OP NUMBERS Log. 601. No. 399. No. 5 6 7 8 9 Dlfif. 350 544688 544812 544936 545060 545183 124 351 545925 546049 546172 546296 546419 124 352 547159 547282 547405 547529 547652 123 353 548389 548512 548635 i 548758 548881 123 354 , 549616 549739 549861 549984 550106 123 356 550840 550962 551084 551206 551328 122 552060 552181 552303 552425 552547 i 122 ii 553276 553398 553519 553640 553762 121 554489 554610 554731 554852 554973 121 359 555699 555820 555940 556061 556182 ^ 121 360 556905 557026 557146 557267 557387 120 361 558108 558228 558349 558469 558589 120 362 559308 559428 559548 559667 559787 120 363 560504 560624 560743 560863 560982 119 3^ 561698 V 561817 561936 562055 562174 1 119 365 562887 563006 563125 563244 563362 : 119 366 564074 i 564192 56431 1 564429 564548 119 367 565257 565376 565494 565612 565730 118 368 566437 56655s 566673 566791 566909 118 369 567614 567732 567849 567967 568084 118 370 568788 568905 569023 569140 569257 117 371 569959 570076 570193 570309 570426 117 372 57II26 571243 571359 571476 571592. 117 373 . 572291 572407 572523 572639 572755 116 374 573452 573568 573684 573800 573915 116 375 574610 574726 574841 574957 575072 116 . 376 575765 575880 575996 5761 II 576226 115 576917 577032 577147 577262 577377 115 578066 578181 578295 578410 578525 "5 379 579212 579326 579441 579555 579669 114 380 580355 580469 580583 580697 58081 I 114 381 581495 581608 581722 581836 581950 114 382 582631 582745 582858 582972 583085 114 383 583765 583879 583992 584105 584218 113 384 584896 585009 585122 585235 585348 113 385 586024 586137 586250 586362 586475 113 386 587149 587262 587374 587486 587599 112 iH 588272 588384 588496 ; 588608 588720 112 589391 589503 589615 589726 589838 112 389 590507 590619 590730 590842 590953 112 390 59I62I 591732 591843 591955 592066 III 391 592732 592843 592954 593064 593175 III 392 593840 593950 594061 5941 7 I 594282 III 393 594945 595055 595165 595276 595386 no 394 596047 596157 596267 596377 596487 no 395 597146 597256 597366 597476 597586 no 396 598243 598353 598462 598572 598681 no 599337 599446 599556 599665 599774 109 398 600428 600537 600646 600755 ! 600864 109 399 601517 601625 601734 1 601843 j 6OI95I 109 1! (.a4i> LOGAKITHMS Log. 602. No. 400. No. 400 401 402 403 404 406 409 410 411 412 414 410 418 419 420 421 432 423 424 420 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 AA9. 443 444 445 446 447 448 449 602060 603144 604226 605305 606381 607455 608526 609594 610660 611723 612784 613842 614897 615950 617000 618048 619093 620136 621 176 622214 623249 624282 625312 626340 627366 628389 629410 630428 631444 632457 633468 634477 635484 636488 637490 638489 639486 640481 641474 642465 643453 644439 645422 646404 647383 648360 649335 650308 651278 652246 1 602169 603253 604334 605413 606489 607562 608633 609701 610767 61 1829 612890 613947 615003 616055 617105 618153 619198 620240 621280 622318 623353 624385 625415 626443 627468 628491 629512 630530 631545 632559 633569 634578 635584 636588 637590 638589 639586 640581 641573 642563 643551 644537 645521 646502 647481 648458 649432 650405 651375 652343 602277 603361 604442 605521 606596 607669 608740 609808 610873 61 1936 612996 614053 615108 616160 617210 618257 619302 620344 621384 622421 623456 624488 625518 626546 627571 628593 629613 630631 631647 632660 633670 634679 635685 636688 637690 638689 639686 640680 641672 642662 643650 644636 645619 646600 647579 648555 649530 650502 651472 652440 602386 603469 604550 605628 606704 607777 608847 609914 610979 612042 613102 614159 615213 616265 617315 618362 619406 620448 621488 622525 623559 624591 625621 626648 627673 628695 629715 630733 631748 632761 633771 634779 635785 636789 637790 638789 639785 640779 641771 642761 643749 644734 645717 646698 647676 648653 649627 650599 651569 652536 602494 603577 604658 605736 606811 607884 608954 610021 611086 612148 613207 614264 615319 616370 617420 618466 619511 620552 621592 622628 623663 624695 625724 626751 627775 628797 629817 630835 631849 632862 633872 634880 635886 636889 637890 638888 639885 640879 641871 642860 643847 644832 645815 646796 647774 648750 649724 650696 651666 652633 Diflf. For eif^lanation see pp. 207-215 108 108 108 108 107 107 107 107 106 106 106 106 105 105 105 los 104 104 104 104 103 103 103 103 102 102 102 102 101 101 101 101 100 100 100 100 100 99 99 99 98 98 98 98 98 97 97 97 97 97 (242) OF NUMBERS . Log. 653. No. 449. No. 5 6 7 8 9 Diff. 400 602603 602711 602819 602928 603036 108 401 1 603686 603794 603902 604010 604118 108 402 604766 604874 604982 605089 605197 108 403 605844 605951 606059 606166 606274 108 404 606919 607026 607133 607241 607348 107 405 400 607991 608098 608205 608312 608419 107 609061 609167 609274 609381 609488 107 407 610128 610234 610341 610447 610554 107 408 6x1 192 611 298 611405 611511 611617 106 409 612254 612360 612466 612572 612678 106 410 613313 613419 613525 613630 613736 106 411 614370 614475 614581 614686 614792 106 412 615424 615529 615634 615740 615845 105 413 616476 616581 616686 616790 616895 105 414 617525 617629 617734 617839 617943 105 4x6 618571 618676 618780 618884 618989 105 619615 619719 619824 619928 620032 104 417 620656 620760 620864 620968 621072 104 418 621695 621799 621903 622007 622 no 104 419 622732 622835 622939 623042 623146 104 420 623766 623869 623973 624076 624179 103 421 624798 624901 625004 625107 625210 103 422 625827 625929 626032 626135 626238 103 423. 626853 626956 627058 627161 627263 103 424 627878 627980 628082 628185 628287 102 425 628900 629002 629104 629206 629308 102 426 629919 630021 630123 630224 630326 102 427 630936 631038 631 139 631241 631342 102 428 631951. 632052 632153 632255 632356 lOI 429 632963 633064 633165 633266 633367 101 430 633973 634074 634175 634276 634376 101 431 634981 635081 635182 635283 635383 lOI 432 . 635986 636087 636187 636287 636388 100 433 636989 637089 637189 637290 637390 100 434 637990 638090 638190 - 638290 638389 100 435 638988 639088 639188 639287 639387 100 436 639984 640084 640183 640283 640382 100 437 640978 641077 641 177 641276 641375 99 438 641970 642069 642168 642267 642366 99 439 642959 643058 643156 643255 643354 99 440 643946 644044 644143 644242 644340 98 441 644931 645029 645127 645226 645324 98 442 645913 646011 6461 10 646208 646306 98 443 646894 646992 647089 647187 647285 98 444 647872 647969 648067 648165 648262 98 t^ 648848 648945 649043 649140 649237 97 649821 649919 650016 650113 650210 97 447 650793 650890 . 650987 651084 65II81 97 448 651762 651859 651956 652053 652150 97 449 652730 652826 652923 653019 6531 16 97 (243) LOGARITHMS '■ r, Log. 653. No. 450. No. 450 1 2 3 4 Difl. 653213 653309 653405 653502 653598 96 451 654177 654273 654369 654465 654562 96 452 655138 655235 655331 655427 655523 96 453 656098 656194 656290 656386 656482 96 454 657056 657152 657247 657343 657438 96 455 65801 I 658107 658202 658298 658393 95 456 658965 659060 659155 659250 659346 95 457 659916 66001 1 660106 660201 660296 95 458 660865 660960 661055 661 1 50 661245 95 459 66I8I3 661907 662002 662096 662191 94 460 662758 662852 662947 663041 663135 94 461 663701 663795 663889 663983 664078 94 402 664642 664736 664830 664924 665018 94 463 665581 665675 665769 665862 665956 94 464 666518 666612 666705 666799 666892 94 ^ 667453 667546 667640 667733 667826 93 668386 668479 668572 668665 668759 93 467 669317 669410 669503 669596 669689 93 468 670246 670339 670431 670524 670617 93 469 67II73 671265 671358 671451 671543 93 470 672098 672190 672283 672375 672467 92 471 673021 673II3 673205 673297 673390 92 472 673942 674034 674126 674218 674310 92 473 674861 674953 675045 675137 675228 92 474 675778 675870 675962 676053 676145 92 476 676694 676785 676876 676968 677059 91 677697 677698 677789 677881 677972 91 A77 678518 678609 678700 678791 678882 91 478 679428 679519 679610 679700 679791 91 479 680336 680426 680517 680607 680698 91 480 68I24I 681332 681422 681513 681603 90 481 682145 682235 682326 682416 682506 90 482 683047 683137 683227 683317 683407 90 483 683947 684037 684127 684217 684307 90 484 684845 684935 685025 6851 14 685204 90 ^ 685742 685831 685921 686010 686100 90 686636 686726 686815 686904 686994 89 487 687529 687618 687707 687796 687886 89 488 688420 688509 688598 688687 688776 89 489 689309 689398 689486 689575 689664 89 490 690196 690285 690373 690462 690550 89 491 69I08I 691170 691258 691347 691435 88 492 691965 692053 692142 692230 692318 88 493 692847 692935 693023 6931 I I 693199 88 494 693727 693815 693903 693991 694078 88 495 694605 694693 694781 694868 694956 88 496 695482 695569 695657 695744 695832 87 497 696356 696444 696531 . 696618 696706 87 498 697229 697317 697404 697491 697578 87 499 698IOI 698188 698275 698362 698449 87 For explanation see pp. 207-215 (244) OF NUMBERS Log. 698. NO. 499. No. 450 451 452 453 454 455 456 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 476 477 478 479 480 481 482 483 484 487 488 489 490 491 492 493 494 495 496 497 498 499 653695 654658 055619 656577 657534 658488 659441 660391 661339 662286 663230 664172 6651 12 666050 666986 667920 668852 669782 670710 671636 672560 673482 674402 675320 676236 677151 678063 678973 679882 680789 681693 682596 683497 684396 685294 686189 687083 687975 688865 689753 690639 691524 692406 693287 694166 695044 695919 696793 697665 698535 6 653791 654754 655715 656673 657629 658584 659536 660486 661434 662380 663324 664266 665206 666143 667079 668013 668945 669875 670802 671728 672652 673574 674494 675412 676328 677242 678154 679064 679973 680879 681784 682686 683587 684486 685383 686279 687172 6S8064 688953 689841 690728 691612 692494 693375 694254 695131 696007 696880 697752 698622 8 9 653888 654850 655810 656769 657725 658679 659631 660581 661529 662475 663418 664360 665299 666237 667173 668106 669038 669967 670895 671821 672744 673666 674586 675503 676419 677333 678245 679155 680063 680970 681874 682777 683677 684576 685473 686368 687261 688153 689042 689930 690816 691700 6^2583 693463 694342 695219 696094 696968 697839 698709 653984 654946 655906 656864 657820 658774 659726 660676 661623 662569 663512 664454 665393 666331 667266 . 668199 6691 31 670066 670988 671913 672836 673758 674677 675595 67651 I 677424 678336 679246 680154 681060 681964 682867 683767 684666 685563 686458 687351 688242 689131 690019 690905 691789 692671 693551 694430 695307 696182 697055 697926 698796 654080 655042 656002 656960 657916 658870 659821 660771 661718 662663 663607 664548 665487 666424 667360 668293 669224 670153 671080 672005 672929 673850 674769 675687 676602 677516 678427 679337 680245 681 151 682055 682957 683857 684756 685652 686547 687440 688331 689220 690107 690993 691877 692759 693639 694517 695394 696269 697142 698014 698883 Diff. 96 96 96 96 96 95 95 95 95 94 94 94 94 94 94 93 93 93 93 92 92 92 92 92 92 91 91 91 91 91 90 90 90 90 90 90 89 89 89 89 89 88 88 88 88 88 87 87 87 87 ill o 775246 775319 775392 775465 775538 73 597 775974 776047 776120 776193 776265 73 598 776701 776774 776846 776919 776992 73 599 777427 777499 777572 777644 777717 72 OF NUMBERS Log. 778. No. 599. No. 5 6 7 740915 8 9 Diff. 550 740757 740836 740994 741073 79 551 741546 741624 741703 741782 741860 79 552 742332 74241 I 742489 742568 742647 79 553 7431 18 743196 743275 743353 743431 78 554 743902 743980 744058 744136 744215 78 555 744684 744762 744840 744919 744997 78 556 745465 745543 745621 745699 745777 78 557 746245 746323 746401 746479 746556 78 1 558 747023 747101 747179 747256 747334 78 559 747800 747878 747955 748033 7481 10 78 560 748576 748653 748731 748808 748885 77 561 749350 749427 749504 749582 749659 77 562 750123 750200 750277 750354 750431 77 563 750894 750971 751048 751125 751202 77 564 751664 751741 751818 751895 751972 77 551 752433 752509 752586 752663 752740 77 566 753200 753277 753353 753430 753506 77 567 753966 754042 7541 19 754195 754272 77 568 754730 754807 754883 754960 755036 76 569 755494 755570 755646 755722 755799 76 570 756256 756332 756408 756484 756560 76 571 757016 757092 757168 757244 757320 76 572 757775 757851 757927 758003 758079 76 573 758533 758609 758685 758761 758836 76 574 759290 759366 759441 759517 759592 76 575 760045 7601 2 I 760196 760272 760347 75 576 760799 760875 760950 761025 761101 75 577 761552 761627 761702 761778 761853 75 578 762303 762378 762453 762529 762604 75 579 763053 763128 763203 763278 763353 75 580 763802 763877 763952 764027 764101 75 581 764550 764624 764699 764774 764848 75 582 765296 765370 765445 765520 765594 75 583 766041 7661 1 5 766190 766264 766338 74 584 766785 766859 766933 767007 767082 74 585 767527 767601 767675 767749 767823 74 586 768268 768342 768416 768490 768564 74 587 769008 769082 769156 769230 769303 74 588 769746 769820 769894 769968 770042 74 589 770484 770557 770631 770705 770778 74 590 771220 771293 771367 771440 771514 74 591 771955 772028 772102 772175 772248 73 592 772688 772762 772835 772908 772981 73 593 773421 773494 773567 773640 773713 73 594 774152 774225 774298 774371 774444 73 595 774882 774955 775028 775100 775173 73 775610 775683 775756 775829 775902 73 597 776338 77641 1 776483 776556 776629 73 598 777064 777137 777209 777282 777354 73 599 777789 777862 777934 778006 778079 72 '■\\ (249) LOGARITHMS Log. 778. No. 600. OF NUMBERS Log. 812. No. 649. i 'M No. 600 6oi 602 603 604 605 606 607 608 609 610 6x1 612 613 614 615 616 617 618 619 620 621 622 623 624 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 778I5I 778874 779596 780317 781037 781755 782473 783189 783904 784617 785330 786041 786751 787460 788168 788875 789581 790285 790988 79I69I 792392 793092 793790 794488 795185 795880 796574 797268 797960 798651 799341 800029 800717 801404 802089 802774 803457 804139 804821 805501 806180 806858 807535 80821 1 808886 809560 810233 810904 81 1575 812245 778224 778947 779669 780389 78II09 781827 782544 783260 783975 784689 785401 7861 12 786822 787531 788239 788946 789651 790356 791059 79176I 792462 793162 793860 794558 795254 795949 796644 797337 798029 798720 799409 800098 800786 801472 802158 802842 803525 804208 804889 805569 806248 806926 807603 808279 808953 809627 810300 810971 81 1642 812312 For explanation see pp. 207-215 778296 779019 779741 780461 781181 781899 782616 783332 784046 784760 785472 786183 786893 787602 788310 789016 • 789722 790426 791 129 791831 792532 793231 793930 794627 795324 796019 796713 797406 798098 798789 799478 800167 800854 801541 802226 802910 803594 804276 804957 805637 806316 806994 807670 808346 809021 809694 810367 81 1039 811709 812379 778368 779091 779813 780533 781253 781971 782688 783403 7841 18 784831. 785543 786254 786964 787673 788381 789087 789792 790496 791199 791901 792602 793301 794000 794697 795393 796088. 796782 797475 798167 798858 799547 800236 800923 801609 802295 802979 803662 804344 805025 805705 806384 807061 807738 808414 809088 809762 810434 811106 81 1776 812445 778441 779^63 779885 780605 781324 782042 782759 783475 784189 784902 785615 786325 787035 787744 788451 789157 789863 790567 791269 791971 792672 793371 794070 794767 795463 796158 796852 797545 798236 798927 799616 800305 800992 801678 802363 803047 803730 804412 805093 805773 806451 807129 807806 808481 809156 809829 810501 811173 81 1843 812512 Diff. 72 72 72 72 72 72 72 71 71 71 71 71 71 71 71 71 70 70 70 70 70 70 70 70 70 69 69 69 69 69 69 69 69 69 69 68 68 68 68 68 68 68 68 67 67 67 67 67 67 67 ^^ (250) No. 5 6 7 8 9 Diflf. 4 72 600 778513 778585 778658 778730 778802 601 779236 779308 779380 779452 ! 779524 72 602 779957 780029 780101 780173 780245 72 603 780677 780749 780821 780893 780965 72 604 781396 781468 781540 781612 781684 72 ^ 7821 14 782186 782258 782329 782401 72 782831 782902 782974 783046 783117 72 6^ i 783546 783618 783689 783761 I 783832 71 784261 784332 784403 784475 784546 71 609 784974 785045 785116 785187 , 785259 7' 610 785686 785757 785828 785899 ! 785970 71 611 786396 786467 786538 786609 i 786680 71 612 787106 787177 787248 787319 ' 787390 71 613 787815 78788s 787956 788027 788098 71 614 788522 788593 788663 1 788734 ! 788804 71 615 789228 789299 789369 789440 789510 71 61$ 789933 790004 790074 : 790144 790215 70 617 61& 790637 790707 790778 790848 790918 70 791340 791410 791480 791550 7Q1620 70 619 792041 7921 1 1 792181 792252 792322 70 620 792742 792812 792882 792952 793022 70 621 793441 79351 1 793581 793651 793721 70 622 794139 794209 794279 794349 794418 70 623 794836 794906 794976 795045 7951 15 70 624 795532 795602 795672 795741 79581 1 70 620 796227 796297 796366 796436 796505 69 796921 796990 797060 797129 797198 69 627 797614 797683 797752 797821 797890 69 628 798305 798374 798443 798513 798582 69 629 798996 799065 799134 799203 799272 69 630 799685 799754 799823 799892 799961 69 631 800373 800442 8005 1 1 800580 800648 69 632 801061 801 129 801 198 801266 801335 69 633 801747 801815 801884 801952 80202 1 69 634 802432 802500 802568 802637 802705 69 63s 8031 16 803184 803252 803321 803389 68 636 803798 803867 803935 804003 804071 68 637 638 804480 804548 804616 804685 804753 68 805 161 805229 805297 805365 805433 68 639 805841 805908 805976 806044 8061 12 68 640 806519 806587 806655 806723 806790 1 68 641 807197 807264 807332 807400 807467 68 642 807873 807941 808008 808076 808143 1 68 643 808549 808616 808684 808751 808818 67 644 809223 809290 809358 809425 809492 67 645 809896 809964 810031 810098 810165 67 646 810569 810636 810703 810770 810837 67 647 81 1 240 81 1307 i 811374 , 811441 81 1508 67 648 811910 81 1977 812044 812111 812178 67 649 812579 1 812646 812713 812780 812847 67 ii] (251) LOGARITHMS Log. 812. No. 650. OF NUMBERS Log. 845. No. 699. III! u Mi llllIM! I Hi! li I !|!!! If' IV ■' No. 650 652 654 657 658 659 660 661 662 663 664 66$ 667 668 669 670 672 673 674 675 676 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 812913 813581 814248 814913 815578 816241 816904 817565 818226 818885 819544 820201 820858 821514 822168 822822 823474 824126 824776 825426 826075 826723 827369 828015 828660 829304 829947 830589 831230 831870 832509 ^33H7 833784 834421 835056 835691 836324 836957 837588 838219 838849 839478 840106 840733 841359 841985 842609 843233 843855 844477 812980 813648 814314 814980 815644 816308 816970 817631 818292 818951 819610 820267 820924 821579 j 822233 822887 823539 824191 824841 825491 826140 826787 827434 828080 828724 829368 83001 I 830653 831294 831934 832573 83321 1 833848 834484 835120 835754 836387 837020 837652 838282 813047 813714 814381 815046 815711 816374 817036 817698 818358 819017 819676 820333 820989 821645 822299 822952 823605 824256 824906 825556 826204 826852 827499 828144 828789 829432 830075 830717 831358 831998 832637 833275 833912 834548 835183 835817 836451 837083 837715 838345 838912 838975 839541 839604 840169 840232 840796 840859 841422 841485 842047 8421 10 842672 842734 843295 843357 843918 843980 844539 844601 For explanation see pp. 207-215 813114 813781 814447 815113 815777 816440 817102 817764 818424 819083 819741 820399 821055 821710 822364 823018 823670 824321 824971 825621 826269 826917 827563 828209 828853 829497 830139 830781 831422 832062 832700 833338 833975 83461 1 835247 835881 836514 837146 837778 838408 839038 839667 840294 840921 841547 842172 842796 843420 844042 844664 813181 813848 814514 815179 815843 816506 817169 817830 818490 819149 819807 820464 821 120 821775 822430 823083 823735 824386 825036 825686 826334 826981 827628 828273 828918 829561 830204 830845 831486 832126 832764 833402 834039 834675 835310 835944 836577 837210 837841 838471 839101 839729 840357 840984 841610 842235 842859 843482 844104 844726 Diff. 67 67 67 66 66 66 66 66 66 66 66 66 66 65 65 65 65 65 65 65 65 65 65 64 64 64 64 64 64 64 64 64 64 64 63 63 63 63 63 63 63 63 63 63 63 62 62 62 62 62 (252) No. 650 652 653 654 65s 656 657 658 659 660 661 662 663 664 66s 666 667 668 669 670 671 672 673 674 676 677 678 679 680 681 682 683 684 685 686 68 681 689 690 691 692 693 694 695 696 697 698 699 813247 813914 814581 815246 815910 816573 817235 817896 818556 819215 819873 820530 821186 821841 822495 823148 823800 824451 825101 825751 826399 827046 827692 828338 828982 829625 830268 830909 831550 832189 832828 833466 834103 834739 835373 836007 836641 837273 837904 838534 839164 • 839792 840420 841046 841672 842297 84292 1 843544 844166 844788 6 813314 813981 814647 815312 815976 816639 817301 817962 818622 819281 819939 820595 821251 821906 822560 823213 823865 824516 825166 825815 826464 8271 1 1 827757 828402 829046 829690 830332 830973 831614 832253 832892 833530 834166 834802 835437 836071 836704 837336 837967 838597 839227 839855 840482 841 109 841735 842360 842983 843606 844229 844850 813381 814048 814714 815378 816042 816705 817367 818028 818688 819346 820004 820661 821317 821972 822626 823279 823930 824581 825231 825880 826528 827175 827821 828467 8291 1 1 829754 830396 831037 831678 832317 832956 833593 834230 834866 835500 836134 836767 837399 838030 838660 839289 839918 840545 841172 841797 842422 843046 843669 844291 844912 8 813448 814114 814780 815445 816109 816771 817433 818094 818754 819412 820070 820727 821382 822037 822691 823344 823996 824646 825296 825945 826593 827240 827886 828531 829175 829818 830460 831102 831742 832381 833020 833657 834294 834929 835564 836197 836830 837462 838093 838723 839352 839981 840608 841234 841860 842484 843108 843731 844353 844974 9 813514 814181 814847 815511 816175 816838 817499 818160 818820 819478 820136 820792 821448 822103 822756 823409 824061 824711 825361 826010 826658 827305 827951 828595 829239 829882 830525 831166 831806 832445 833083 833721 834357 834993 835627 836261 836894 837525 838156 838786 839415 840043 840671 841297 841922 842547 843170 843793 844415 845036 Diff. 67 67 67 66 66 66 66 66 66 66 66 66 66 65 65 65 65 65 65 65 65 65 65 64 64 64 64 64 64 64 64 64 64 64 63 63 63 63 63 63 63 63 63 63 63 62 62 62 62 62 (253) p 2 I I ] It '1 LOGABITHMS Log .845. No. 700 • No. 1 2 3 4 Dili. 700 845098 845160 i 845222 845284 845346 62 701 845718 845780 845842 i 845904 845966 62 702 846337 846399 846461 846523 846585 62 703 846955 847017 847079 847 141 847202 62 704 847573 847634 847696 847758 847819 62 705 848189 848251 848312 848374 848435 62 706 1 848805 848866 848928 848989 849051 61 707 1 S49419 849481 849542 849604 849665 61 708 850033 850095 850156 i 850217 850279 61 709 850646 850707 850769 850830 850891 61 710 851258 851320 851381 851442 851503 61 711 851870 i 851931 851992 852053 8521 14 61 712 852480 1 852541 852602 852663 852724 61 713 853090 853150 8532 1 1 853272 853333 61 714 853698 853759 853820 853881 853941 61 71S 854306 854367 854428 854488 854549 61 716 854913 854974 855034 855095 855156 61 717 718 855519 855580 855640 855701 855761 61 856124 856185 856245 856306 856366 60 719 856729 856789 856850 856910 856970 60 720 857332 857393 857453 857513 857574 60 721 857935 857995 858056 858116 858176 60 722 858537 858597 858657 858718 858778 60 723 859138 859198 859258 859318 859379 60 724 859739 \ 859799 859859 859918 859978 60 72s 860338 1 860398 860458 860518 860578 60 726 860937 ! 860996 861056 861 1 16 861 176 60 727 861534 i 861594 861654 861 7 14 861773 60 728 862131 862191 862251 862310 862370 60 729 862728 i 862787 862847 862906 862966 60 730 863323 863382 863442 863501 863561 59 731 863917 863977 864036 864096 864155 59 732 8645 1 1 864570 864630 864689 864748 59 733 865104 865163 865222 865282 865341 59 734 865696 : 865755 865814 865874 865933 59 735 866287 866346 866405 866465 866524 59 736 866878 866937 866996 867055 8671 14 59 867467 867526 867585 867644 867703 59 868056 8681 15 868174 868233 868292 59 739 868644 1 868703 868762 868821 868879 59 740 869232 869290 869349 869408 869466 59 741 869818 869877 869935 869994 870053, 59 ' 742 870404 870462 870521 870579 870638 5! 743 870989 i 871047 871 106 871 164 871223 58 744 871573 : 871631 871690 871748 871806 58 745 872156 872215 872273 872331 872389 58 746 872739 872797 872855 872913 87297c 5? 747 873321 : 873379 873437 873495 873553 58 748 873902 i 873960 874018 874076 874134 58 749 874487 874540 874598 874656 874714 58 For explanation see pp. 207-215 (254) OF NUMBERS Log. 875. No. 749. No. 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 716 717 718 719 720 721 722 723 724 725 720 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 746 747 748 749 845408 846028 846646 847264 847881 848497 8491 12 849726 850340 850952 851564 852175 852785 853394 854002 854610 855216 855822 856427 857031 857634 858236 858838 859439 860038 860637 861236 861833 862430 863025 863620 864214 864808 865400 865992 866583 867173 867762 868350 868938 869525 8701 1 1 870696 871281 871865 872448 873030 87361 1 874192 874772 6 845470 846090 846708 847326 847943 848559 849174 849788 850401 851014 851625 852236 852846 853455 854063 854670 855277 855882 856487 857091 857694 858297 858898 859499 860098 860697 861295 861893 862489 863085 863680 864274 864867 865459 866051 866642 867232 867821 868409 868997 869584 870170 870755 871339 871923 872506 873088 873669 874250 874830 845532 846151 846770 847388 848004 848620 849235 849849 850462 851075 851686 852297 852907 853516 854124 854731 855337 855943 856548 857152 857755 858357 858958 859559 860158 860757 861355 861952 862549 863144 863739 864333 864926 865519 8661 10 866701 867291 867880 868468 869056 869642 870228 870813 871398 871981 872564 873146 873727 874308 874888 8 9 845594 846213 846832 847449 848066 848682 849297 84991 I 850524 851136 851747 852358 852968 853577 854185 854792 855398 856003 856608 857212 857815 858417 859018 859619 860218 860817 861415 862012 862608 863204 863799 864392 864985 865578 866169 866760 867350 867939 868527 869114 869701 870287 870872 871456 872040 872622 873204 873785 874366 874945 845656 846275 846894 84751 1 848128 848743 849358 849972 850585 851 197 851809 852419 853029 853637 854245 854852 855459 856064 856668 857272 857875 858477 859078 859679 860278 860877 861475 862072 862668 863263 863858 864452 865045 865637 866228 866819 867409 867998 868586 869173 869760 870345 870930 871515 872098 872681 873262 873844 874424 875003 DiflE. 62 62 62 62 62 62 61 61 61 61 61 61 61 61 61 61 61 61 60 ' 60 60 60 60 60 60 60 60 60 60 60 59 59 59 59 59 59 59 59 59 59 59 59 58 58 58 58 58 58 58 58 ^11 (255) LOGARITHMS OF NUMBERS Log. 875. No. 750. Log. 903. No. 799. No. 1 2 3 4 Dili. 750 875061 875119 875177 875235 875293 58 751 875640 875698 . 875756 875813 875871 58 752 876218 876276 876333 876391 1 876449 58 753 876795 876853 876910 876968 1 877026 58 754 877371 877429 877487 877544 877602 58 755 877947 878004 878062 8781 19 878177 57 756 878522 878579 878637 878694 878752 57 757 879096 879153 87921 1 879268 879325 ; 57 758 879669 879726 879784 : 879841 879898 57 759 880242 880299 880356 880413 880471 57 760 880814 880871 880928 880985 881042 57 761 881385 881442 881499 881556 881613 57 76^ 881955 882012 882069 882126 882183 57 763 882525 882581 882638 882695 882752 57 764 883093 883150 883207 883264 88^321 57 765 883661 883718 883775 883832 883888 57 766 884229 884285 884342 884399 884455 57 767 884795 884852 884909 884965 885022 57 768 885361 885418 885474 885531 885587 57 769 885926 885983 886039 886096 886152 56 770 ' 886491 886547 886604 886660 886716 56 771 887054 8871 1 1 887167 887223 887280 56 772 887617 887674 887730 887786 887842 56 773 888179 888236 888292 888348 888404 56 774 888741 888797 888853 j 888909 888965 56 775 889302 889358 889414 889470 ' 889526 56 776 889862 889918 889974 890030 890086 56 777 890421 890477 890533 890589 890645 56 778 890980 891035 891091 891 147 891203 56 779 891537 891593 891649 891705 891760 56 780 892095 892150 892206 892262 892317 56 781 89265 1 892707 892762 892818 892873 56 782 893207 893262 893318 893373 893429 56 783 893762 893817 893873 893928 893984 55 784 894316 894371 894427 894482 894538 55 785 894870 894925 894980 895036 895091 55 786 895423 895478 895533 895588 895644 55 787 895975 896030 896085 896140 896195 55 788 896526 896581 896636 896692 896747 55 789 897077 897132 897187 897242 897297 55 790 897627 897682 897737 897792 897847 55 791 898176 898231 898286 898341 898396 55 792 898725 898780 i 898835 898890 898944 55 793 899273 899328 899383 899437 899492 55 794 899821 899875 899930 899985 900039 55 795 900367 900422 900476 900531 900586 55 796 900913 900968 901022 901077 901 131 55 797 901458 901513 901567 901622 901676 54 798 902003 902057 9021 12 902166 902221 54 799 902547 902601 902655 902710 902764 54 For explanation see pp. 207-215 (256) No. 750 751 752 753 754 759 760 761 762 763 764 769 770 771 772 773 774 SS 770 777 778 779 780 781 782 784 785 786 787 788 789 790 791 792 793- 794 795 796 797 798 799 875351 875929 876507 877083 877659 878234 878809 879383 879956 880528 881099 881670 882240 882809 883377 883945 884512 885078 885644 886209 886773 887336 887898 888460 889021 889582 890141 890700 891259 891816 892373 892929 893484 894039 894593 895146 895699 896251 896802 897352 897902 898451 898999 899547 900094 900640 901 186 901731 902275 902818 6 875409 875987 876564 877141 877717 878292 878866 879440 880013 880585 881 156 881727 882297 882866 883434 884002 884569 885135 885700 886265 886829 887392 887955 888516 889077 889638 890197 890756 891314 891872 892429 892985 893540 894094 894648 895201 895754 896306 896857 897407 897957 898506 899054 899602 900149 900695 901240 901785 902329 902873 8 875466 876045 876622 877199 877774 878349 878924 879497 880070 880642 881213 881784 882354 882923 883491 884059 884625 885192 885757 886321 886885 887449 88801 I 888573 889134 889694 890253 890812 891370 891928 892484 893040 893595 894150 894704 895257 895809 896361 896912 897462 898012 898561 899109 899656 900203 900749 901295 901840 902384 902927 875524 876102 876680 877256 877832 878407 878981 879555 880127 880699 881 27 1 881841 88241 1 882980 883548 8841 15 884682 885248 885813 886378 886942 887505 888067 888629 889190 889750 890309 890868 891426 891983 892540 893096 893651 894205 894759 895312 895864 896416 896967 897517 898067 898615 899164 8997 I I 900258 900804 901349 901894 902438 902981 9 875582 876160 876737 877314 877889 878464 879039 879612 880185 880756 881328 881898 882468 883037 883605 884172 884739 885305 885870 886434 886998 887561 888123 888685 889246 889806 890365 890924 891482 892039 892595 89315 1 893706 894261 894814 895367 895920 896471 897022 897572 898122 898670 899218 899766 900312 900859 901404 901948 902492 903036 Diff. 58 5| 58 58 58 57 57 57 57 57 57 57 57 57 57 57 57 57 57 56 56 56 56 56 56 56 56 56 56 56 56 55 55 55 55 55 55 55 55 55 55 55 55 55 55 54 54 54 • t (257) I I Ml ill Log. 903. No. 800, LOGARITHMS No. 800 801 803 803 804 805 806 807 808 809 810 811 812 814 815 816 ^n 818 819 820 821 822 823 824 8^ 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 ■ 846 847 848 849 903090 903633 904174 904716 905256 905796 906335 906874 9074 1 1 907949 908485 909021 909556 9I009I 910624 9III58 91 1690 912222 912753 913284 9I38I4 914343 914872 915400 915927 916454 916980 917506 918030 918555 919078 9 I 9601 920123 920645 921 166 921686 922206 922725 923244 923762 924279 924796 925312 925828 926342 926857 927370 927883 928396 928908 1 903144 903687 904229 904770 905310 905850 906389 906927 907465 908002 908539 909074 909610 910144 910678 911211 91 1743 912275 912806 913337 913867 914396 914925 915453 915980 916507 ■917033 917558 918083 918607 919130 919653 920176 920697 921218 921738 922258 922777 923296 923814 924331 I 924848 j 925364 i 925879 926394 926908 927422 927935 928447 928959 For explaiiaiion see pp. 207-215 903199 903741 904283 904824 905364 905904 906443 906981 907519 908056 908592 909128 909663 910197 910731 91 1264 911797 912328 912859 913390 913920 914449 914977 915505 916033 916559 917085 917611 918135 918659 919183 919706 920228 920749 921270 921790 922310 922829 923348 923865 924383 924899 925415 925931 926445 926959 927473 927986 928498 929010 903253 903795 904337 904878 905418 905958 906497 907035 907573 908110 908649 909181 909716 91025 1 910784 911317 91 1850 912381 912913 913443 913973 914502 915030 915558 916085 916612 917138 917663 918188 918712 919235 919758 920280 920801 921322 921842 922362 922881 923399 923917 924434 924951 925467 925982 926497 92701 1 927524 928037 928549 929061 903307 903849 904391 904932 905472 906012 906551 907089 907626 908163 908699 909235 909770 910304 910838 911371 91 1903 912435 912966 913496 914026 914555 915083 915611 916138 916664 917190 917716 918240 918764 919287 f 919810 920332 920853 921374 921894 922414 922933 923451 923969 924486 925003 925518 926034 926548 927062 927576 928088 928601 9291 12 Diff. 54 54 54 54 54 54 54 54 54 54 54 54 53 53 53 53 53 53 53 53 53 53 53 53 53 53 53 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 51 51 51 51 51 51 51 m (258; OP NUMBERS , Log. 929. . No. 849. No. 5 6 7 8 9 Diff. 800 903361 903416 903470 903524 903578 54 801 903904 903958 904012 904066 904120 54 802 904445 904499 904553 904607 904661 54 803 904986 905040 905094 905148 905202 54 804 905526 905580 905634 905688 905742 54 ^ 906066 9061 19 906173 906227 906281 54 906604 906658 906712 906766 906820 54 807 907143 907196 907250 907304 907358 54 808 907680 1 907734 907787 907841 907895 54 809 908217 908270 908324 908378 908431 54 810 908753 908807 908860 908914 908967 54 811 1 909289 909342 909396 909449 909503 54 812 909823 909877 909930 909984 910037 53 813 910358 910411 910464 1 910518 910571 53 814 ! 9I089I 910944 910998 911051 91 I 104 53 815 91 1424 91 1477 911530 91 1584 911637 53 816 91 1956 912009 912063 912116 912169 53 817 912488 912541 912594 912647 912700 53 818 9I30I9 913072 913125 913178 913231 53 819 913549 913602 913655 913708 913761 53 820 914079 914132 914184 914237 914290 53 821 914608 914660 914713 914766 914819 53 1 822 9I5I36 915189 915241 915294 915347 53 i 823 915664 915716 915769 915822 915875 53 1 824 9I6I9I 916243 916296 916349 916401 53 ) • 1 825 9I67I7 916770 916822 916875 916927 53 826 917243 917295 917348 917400 917453 53 827 917768 917820 917873 917925 917978 1 j-% 52 828 918293 918345 1 918397 918450 : 918502 52 829 9I88I6 918869 i 91 892 I 918973 919026 1 52 830 919340 919392 919444 919496 919549 52 831 919862 919914 919967 920019 1 920071 52 832 920384 920436 920489 920541 920593 52 833 920906 920958 921010 921062 921114 52 834 921426 921478 921530 921582 , 921634 52 83s 921946 921998 922050 922102 ' 922154 52 836 922466 922518 922570 922622 922674 11 i 837 922985 923037 923089 923140 1 923192 52 ; 83§ 923503 923555 923607 923658 923710 52 1 839 924021 924072 924124 924176 924228 52 840 924538 924589 924641 924693 924744 52 841 925054 925106 925157 925209 925261 52 842 925570 925621 925673 925725 925776 52 843 926085 926137 926188 926240 926291 51 844 926600 926651 926702 926754 926805 1 51 iti 927 1 14 927165 927216 927268 927319 51 927627 927678 927730 927781 927832 51 1$ 928140 928191 928242 928293 928345 51 928652 928703 928754 928805 928857 51 849 929163 929215 929266 929317 929368 1 51 I C259) -i il I '-I' il ^ LOGARITHMS Log ;. 929. No. 850 • No. 1 2 3 4 DiflL 850 r 929419 929470 929521 929572 929623 51 ?5' 929930 929981 930032 930083 930134 51 |52 930440 930491 930542 930592 930643 51 853 930949 931000 931051 931 102 931 153 SI 854 931458 931509 931560 931610 931661 51 f55 931966 932017 932068 9321 18 932169 51 855 932474 932524 932575 932626 932677 51 857 932981 933031 933082 933133 933183 51 858 933487 933538 933589 933639 933690 51 859 933993 934044 934094 934145 934195 51 860 934498 934549 934599 934650 934700 50 861 935003 935054 935104 935154 935205 50 862 935507 935558 935608 935658 935709 50 863 93601 I 936061 9361 1 1 936162 936212 50 864 936514 936564 936614 936665 936715 50 !55 937016 937066 937117 937167 937217 50 866 937518 937568 937618 937668 937718 50 867 868 938019 938069 938119 938169 938219 50 938520 938570 938620 938670 938720 50 869 939020 939070 939120 939170 939220 50 870 939519 939569 939619 939669 939719 50 571 940018 940068 9401 18 940168 940218 50 872 940516 940566 940616 940666 940716 50 87? 941014 941064 941 1 14 941 163 941213 SO 941511 941561 941611 941660 941710 50 ?75 942008 942058 942107 942157 942207 SO 876 942504 942554 942603 942653 942702 50 1^ 943000 943049 943099 943148 943198 49 943495 943544 943593 943643 943692 49 879 943989 944038 944088 944137 944186 49 880 944483 944532 944581 944631 944680 49 881 944976 945025 945074 945124 945173 49 882 945469 945518 945567 945616 945665 49 883 945961 946010 946059 946108 946157 49 884 946452 946501 946551 946600 946649 49 885 946943 946992 947041 947090 947140 49 886 947434 947483 947532 947581 947630 49 887 888 947924 947973 948022 948070 9481 19 49 948413 948462 94851 1 948560 948609 49 889 948902 948951 948999 949048 949097 49 890 949390 949439 949488 949536 949585 49 891 949878 949926 949975 950024 950073 49 892 950365 950414 950462 9505 1 1 950560 49 893 950851 950900 950949 950997 951046 49 894 951338 951386 951435 951483 951532 49 89s 951823 951872 951920 951969 952017 48 896 952308 952356 952405 952453 952502 48 8^ 952792 952841 952889 952938 952986 48 953276 953325 953373 953421 953470 48 899 953760 953808 953856 953905 953953 48 Eor explanation see pp. 207-215 (260) OF NUMBERS Log. 954. No. 899 No. 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 929674 930185 930694 931204 931712 932220 932727 933234 933740 934246 934751 935255 935759 936262 936765 937267 937769 938269 938770 939270 939769 940267 940765 941263 941760 942256 942752 943247 943742 944236 944729 945222 945715 946207 946698 947189 947679 948168 948657 949146 949634 950121 950608 951095 951580 952066 952550 953034 953518 954001 929725 930236 930745 931254 931763 932271 932778 933285 933791 934296 934801 935306 935809 936313 936815 937317 937819 938320 938820 939320 939819 940317 940815 941313' 941809 942306 942801 943297 943791 944285 944779 945272 945764 946256 946747 947238 947728 948217 948706 949195 949683 950170 950657 951143 951629 9521 14 952599 953083 953566 954049 8 929776 930287 930796 931305 931814 932322 932829 933335 933841 934347 934852 935356 935860 936363 936865 937367 937869 938370 938870 939369 939869 940367 940865 941362 941859 942355 942851 943346 943841 944335 944828 945321 945813 946305 946796 947287 947777 948266 948755 949244 949731 950219 950706 951 192 951677 952163 952647 953131 953615 954098 9 929827 930338 930847 931356 931865 932372 932879 933386 933892 934397 934902 935406 935910 936413 936916 937418 937919 938420 938920 939419 939918 940417 940915 941412 941909 942405 942901 943396 943890 944384 944877 945370 945862 946354 946845 947336 947826 948315 948804 949292 949780 950267 950754 951240 951726 9522 I I 952696 953180 953663 954146 929879 930389 930898 931407 931915 932423 932930 933437 933943 934448 934953 935457 935960 936463 936966 937468 937969 938470 938970 939469 939968 940467 940964 94 I 462 941958 942455 942950 943445 943939 944433 944927 945419 9459 I 2 946403 946894 947385 947875 948364 948853 949341 949829 950316 950803 951289 951775 952260 952744 953228 9537 1 1 954194 Difl. SI 51 51 51 51 51 51 51 51 51 50 50 50 50 50 SO 50 50 50 50 50 50 50 50 50 50 50 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 48 48 .48 48 48 ' '1 (261) LOGARITHMS s; Log. 954. No. 900. No. 1 2 3 4 Diif. 48 900 954243 954291 954339 954387 954435 901 954725 954773 954821 954869 954918 48 902 955207 955255 955303 955351 955399 48 903 955688 955736 955784 955832 955880 48 904 956168 956216 956265 956313 956361 48 905 956649 956697 956745 956793 956840 48 906 957128 957176 957224 957272 957320 48 907 957607 957655 957703 957751 957799 48 908 958086 958134 958181 958229 958277 48 909 958564 958612 958659 958707 958755 48 910 959041 959089 959137 959185 959232 48 911 959518 959566 959614 959661 959709 48 912 959995 960042 960090 960138 960185 48 913 960471 960518 960566 960613 960661 48 914 960946 960994 961041 961089 961 136 47 915 96142 I 961469 961516 961563 961611 47 916 961895 961943 961990 962038 962085 47 917 962369 962417 962464 96251 1 962559 47 918 962843 962890 962937 962985 963032 47 919 963316 963363 963410 963457 963504 47 920 963788 963835 963882 963929 963977 47 921 964260 964307 964354 964401 964448 47 922 964731 964778 964825 964872 964919 47 923 965202 965249 965296 965343 965390 47 924 965672 965719 965766 965813 965860 47 925 966142 966189 966236 966283 966329 47 926 96661 I 966658 966705 966752 966799 47 927 967080 967127 967173 967220 967267 47 928 967548 967595 967642 967688 967735 47 929 968016 968062 968109 968156 968203 47 930 968483 968530 968576 968623 968670 47 931 968950 968996 969043 969090 969136 47 932 969416 969463 969509 969556 969602 47 933 969882 969928 969975 970021 970068 47 934 970347 970393 970440 970486 970533 46 935 970812 970858 970904 970951 970997 46 936 971276 971322 971369 971415 971461 46 971740 971786 971832 971879 971925 46 938 972203 972249 972295 972342 972388 46 939 972666 972712 972758 972804 972851 46 940 973128 973174 973220 973266 973313 46 941 973590 973636 973682 973728 973774 46 942 974051 974097 974143 974189 974235 46 943 974512 974558 974604 974650 974696 46 944 974972 975018 975064 975110 975156 46 945 975432 975478 975524 975570 1 975616 46 946 975891 975937 975983 976029 1 976075 46 i 947 976350 976396 1 976442 976488 976533 46 ' 948- 976808 976854 976900 976946 976992 46 J 949 1 9772t)0 1 977312 1 97735S 977403 977449 46 For explanation see pp. 207-215 (262) OF NUMBERS Log. 977. No. 949, No. 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 6 954484 954966 955447 955928 956409 956888 957368 957847 958325 958803 959280 959757 960233 960709 961 184 961658 962132 962606 963079 963552 964024 964495 964966 965437 965907 966376 966845 967314 967782 968249 968716 969183 969649 9701 14 970579 971044 971508 97 197 I 972434 972897 973359 973820 974281 974742 975202 975662 976121 976579 977037 977495 954532 955014 955495 955976 956457 j 956936 i 957416 957894 958373 958850 959328 959804 960280 960756 961231 961706 962180 962653 963126 963599 964071 964542 965013 965484 965954 966423 966892 967361 967829 968296 968763 969229 969695 970161 970626 971090 971554 972018 972481 972943 973405 973866 974327 974788 975248 975707 976167 976625 977083 977541 8 9 954580 955062 955543 956024 956505 956984 957464 I 957942 958421 958898 •959375 959852 960328 960804 961279 961753 962227 962701 963174 963646 9641 18 964590 965061 965531 966001 966470 966939 967408 967875 968343 968810 969276 969742 970207 970672 971137 971601 972064 972527 972989 973451 973913 974374 974834 975294 975753 976212 976671 977129 977586 954628 ! 955110 ; 955592 956072 956553 ! 957032 957512 957990 958468 958946 959423 959900 960376 960851 961326 961801 962275 962748 963221 963693 964165 964637 965108 965578 966048 966517 966986 967454 967922 968390 968856 969323 969789 970254 970719 971 183 971647 9721 10 972573 973035 973497 973959 974420 974880 975340 975799 976258 976717 977175 977632 DiflE. 954677 955158 955640 956120 956601 957080 957559 958038 958516 958994 959471 959947 960423 960899 961374 961848 962322 962795 963268 963741 964212 964684 965155 965625 966095 966564 967033 967501 967969 968436 968903 969369 969835 970300 970765 97 I 229 971693 972157 972619 973082 973543 974005 974466 974926 975386 975845 976304 976763 977220 977678 48 48 48 48 48 48 48 48 48 48 48 48 48 48 47 47 47 47 47 47 47 47 47 47 47 47 47 47 47 47 47 47 47 47 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 i i II (263) LOGARITHMS OF NUMBERS Log. 977. No. 950. Log. 999. No. 999. ill No. 1 2 3 4 Diff. 950 977724 977769 977815 977861 977906 46 ( 951 978I8I 978226 978272 978317 978363 46 952 978637 978683 978728 978774 978819 46 953 979093 979138 979184 979230 979275 46 954 979548 979594 979639 979685 979730 46 955 980003 980049 980094 980140 980185 45 956 980458 980503 980549 980594 980640 45 957 980912 980957 981003 ■ 981048 981093 45 958 981366 981411 981456 981 501 981547 45 959 98I8I9 981864 981909 981954 982000 45 960 982271 982316 982362 982407 982452 45 961 982723 982769 982814 982859 982904 45 962 983175 983220 983265 983310 983356 45 963 983626 983671 983716 983762 983807 45 964 984077 984122 984167 984212 984257 45 966 984527 984572 984617 984662 984707 45 984977 985022 985067 985112 985157 45 ^ 985426 985471 985516 985561 985606 45 968 985875 985920 985965 986010 986055 45 969 986324 986369 986413 986458 986503 45 970 986772 986817 986861 986906 986951 45 971 987219 987264 987309 987353 987398 45 972 987666 98771 I 987756 987800 987845 45 973 9881 13 988157 988202 988247 988291 45 974 988559 988604 988648 988693 988737 45 975 989005 989049 989094 989138 989183 45 976 989450 989494 989539 98958^ 989628 44 977 978 989895 989939 989983 990028 990072 44 990339 990383 990428 990472 990516 44 979 990783 990827 990871 990916 990960 44 980 991226 991270 991315 991359 991403 44 ^' 991669 991713 991758 991802 991846 44 ^^ 9921 I I 992156 992200 992244 992288 44 983 992554 992598 992642 992686 992730 44 984 992995 993039 993083 993127 993172 44 985 993436 993480 993524 993568 993613 44 986 993877 993921 993965 994009 994053 44 987 994317 994361 994405 994449 994493 44 988 994757 994801 994845 994889 994933 44 989 995196 995240 995284 995328 995372 44 990 995635 995679 995723 995767 99581 1 44 991 996074 9961 17 996161 996205 996249 44 992 996512 996555 996599 996643 996687 44 993 996949 996993 997037 997080 997124 44 994 997386 997430 997474 997517 997561 44 995 997823 997867 997910 997954 997998 44 996 998259 998303 998347 998390 998434 44 997 998695 998739 998782 998826 998869 44 998 999131 999174 999218 999261 999305 44 999 999565 999609 999652 999696 1 999739 43 No. 950 951 952 953 954 950 957 958 959 960 961 962 963 964 967 968 969 970 971 972 973 974 977 978 979 980 981 982 983 984 985 986 987 988 For explanation see pp. 207-215 .(264) 977952 978409 978865 979321 979776 980231 980685 981 139 981592 982045 982497 982949 983401 983852 984302 984752 985202 985651 986100 986548 986996 987443 987890 988336 988782 989227 989672 9901 17 990561 991004 991448 991890 992333 992774 993216 993657 994097 994537 994977 990 995854 991 996293 992 996731 993 997168 994 997605 995 998041 998477 997 998913 998 999348 999 999783 6 977998 978454 978911 979366 979821 I 980276 980730 981184 981637 982090 982543 982994 983446 983897 984347 984797 985247 985696 986144 986593 987040 987488 987934 988381 988826 989272 989717 990161 990605 991049 991492 991935 992377 992819 993260 993701 994141 994581 995021 995460 995898 996337 996774 997212 997648 998085 998521 998956 999392 999826 978043 978500 978956 979412 979867 980322 980776 981229 981683 982135 982588 983040 983491 983942 984392 984842 985292 985741 986189 986637 987085 987532 987979 988425 988871 989316 989761 990206 990650 991093 991536 991979 992421 992863 993304 993745 994185 994625 995065 995504 995942 996380 996818 997255 997692 998129 998564 999000 999435 999870 ( 8 9 Diflt. 978089 978135 46 978546 978591 46 979002 979047 46 979457 979503 46 979912 979958 46 980367 980412 45 980821 980867 > 45 98127s 981320 45 981728 981773 45 982181 . 982226 45 982633 982678 45 983085 983130 45 983536 983581 45 983987 984032 45 984437 984482 45 984887 984932 45 985337 ; 985382 45 985786 985830 45 986234 986279 45 986682 986727 45 987130 987175 45 987577 987622 45 988024 988068 45 988470 988514 45 988916 988960 45 989361 989405 45 989806 989850 44 990250 990294 44 990694 990738 44 991137 991 182 44 991580 991625 44 992023 992067 44 992465 992509 44 992907 992951 44 993348 993392 44 993789 993833 44 994229 994273 44 994669 994713 44 995108 995152 44 995547 995591 44 995986 996030 44 996424 996468 . 44 996862 996906 44 997299 997343 44 997736 997779 . 44 998172 998216 44 998608 998652 44 999043 999087 44 999479 999522 44 999913 999957 43 (265) LOQARITHMS OF NUMBERS \\w No. I 2 3 4 5 6 I 9 10 II 12 13 14 15 i6 19 20 21 22 23 24 25 26 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 SO Log. 000000 301030 477121 602060 698970 778151 845098 903090 954243 000000 041393 079181 I I 3943 146128 1 7609 1 204120 230449 255273 278754 301030 322219 342423 361728 3802 1 1 397940 414973 431364 447158 462398 477121 491362 505150 518514 531479 544068 556303 568202 579784 591065 602060 612784 623249 633468 643453 653213 662758 672098 681241 690196 698970 No. 51 52 53 54 55 56 57 58 59 60 • 61 62 63 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 U 89 90 91 92 93 94 95 96 97 98 99 ICO Log. 707570 716003 724276 732394 740363 748188 755875 763428 770852 778151 785330 792392 799341 806180 812913 819544 826075 832509 838849 845098 851258 857333 863323 869232 875061 880814 886491 892095 897627 903090 908485 913814 919078 924279 929419 934498 939519 944483 949390 954243 959041 963788 968483 973128 977724 982271 986772 991226 995635 000000 No. lOI 102 103 104 105 106 108 109 110 III 112 "3 114 "5 116 117 118 119 120 121 122 123 124 "5 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 Log. For explanation see pp. 207-215 004321 008600 012837 017033 021 189 025306 029384 033424 037426 041393 045323 049218 053078 056905 060698 064458 068186 071882 075547 079181 082785 086360 089905 093422 096910 00371 03804 07210 10590 13943 17271 20574 23852 27105 30334 33539 36721 39879 43015 46128 49219 52288 55336 58362 61368 64353 67317 70262 73186 76091 No. 151 152 153 154 155 156 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 r64 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 Log. 178977 181844 I 8469 I 187521 190332 193125 195900 198657 201397 204120 206826 209515 212188 214844 217484 220108 222716 225309 227887 230449 232996 235528 238046 240549 243038 245513 247973 250420 252853 255273 257679 260071 26245 ^ 264818 267172 269513 271842 274158 276462 278754 281033 283301 285557 287802 290035 292256 294466 296665 298853 301030 LOGARITHMIC TABLES OF COMPOUND INTEREST AND ANNUITIES BY FEDOR THOMAN (266) /. TABLE I. SHOWING (A) The Logarithms of the Amount of ^i at the end of any number of years from i to 100 years. Log /^. (B) The Logarithms of the Annuity ^5*7o 0,03682*30 0,05898-91 0,04115-52 0.04332*12 0,04548*73 0,04765-34 0,04981*94 0,05198-55 0,05415-15 0,05631-76 0,05848-37 0,06064-97 0,06281-58 0,06498-19 0,06714*79 0,06931*40 0,0714800 0,07364-61 0,07581-22 0,07797-82 0,08014*43 0,08231*03 0,08447*64 0,08664*25 0,08880-85 0,09097*46 0,09314*07 0,0953067 0,09747*28 0,09963*88 0,10180-49 0,10397-10 0,10613*70 0,10830*31 Log. a" 0,00216*61 9,70221*77 9,52720-73 9' 40334 •04 9.30751*74 9,22941*43 9,16354*47 9,10662*90 9,05655 18 9,01186-88 8.97«M-97 8.934^3-38 8,901 r4-35 8,8700297 8,84113-64 8,81417-67 8.78891-61 8.76s»S-97 8, 742 7450 8,72i53-4' 8,70140*94 8,68226-97 8,66402-73 8,64660*57 8,62993*79 8,61396-47 8,59863-34 8,58389-75 8,56971-49 8,55604*81 8.54286*33 8,53012-96 8,51781-95 8-50590-74 8.4943703 8,48318*69 8,4723378 8,46180*52 8,45157-26 8,44162*47 8,43194-75 8,42252*77 8,41335-33 8,40441*31 8,39569-62 8,38719-30 8,37889*42 8,37079-" 8,3628757 8,35514-03 Log. a" 8,34757*77 8,34018*12 8,33294-45 8,32«;86*i6 8,31892-67 8,31213*45 8,30547-99 8,29895-81 8,29256*45 8,28629*48 8,28014*49 8,27411*08 8,26818-87 8,26237*52 8,25666*70 8.2510605 8,24555-30 8.24014*12 8,23482-25 8,22959-42 8,22445-35 8,21939-82 8,21442-58 8*20953*39 8,20472*05 8,1999833 8,1953205 8,19073*01 8,18621-02 8,1817589 8,17737-46 8,17305-56 8,1688004 8,16460*73 8,16047*48 8, 15640- 1 6 8,15238*61 8,14842*72 8>i44Si-35 8,14067*37 8,13687-67 8,13313*12 8,12943*61 8,12579-04 8,12219-29 8,11864-27 8»ii5i3*86 8,11167*99 8,10826-55 8,1048945 7,69897*00 For explanation see pp. 216-228 Log. r". 0,11046*91 0,11263*52 0.1148013 0,11696*73 0,11913-34 0,12129-95 0,12346-55 0,12563*16 0,12779-76 0,12996-37 0,13212*98 0,13429-58 0,13646- 19 0,13862-80 0,14079-40 0,14296-01 0,14512-61 0,14729*22 0,14945-83 0,15162*43 0,15379*04 0,1559564 0,13812-25 0,1602886 0,16245-46 0,16462*07 0,16678-68 0,16895-28 0,17111-89 0,17328-49 0,17545-10 0,17761*71 0,1 7978*31 0,18194-92 0,18411-52 0,18628*13 0,18844-74 0,19061*34 0,19277*95 0,19494*56 0,19711*16 0,19927*77 0,20144*37 0,20360-98 0,20577-59 0,20794-19 0,21010*80 0,21227-41 0,21444-01 0^21660*62 Years 51 52 53 54 56 5 I 61 62 63 64 65 66 67 68 69 70 7« 72 73 74 7' 77 78 81 82 83 84 1^ 87 88 89 90 9U 92 93 94 95 96 97 98 99 100 Perpi (269) 02 w T \ 1 1 '. ll 1 i ' i : 1 I V LOGARITHMIC TABLES OF Per Cent. Years Log. r-. Log. a". Log. o". Log. f. Yean I 0,00432 14 0,00432-14 8,4001^-73 8,30368-10 8,38738-20 0,22039-01 5' a 0,00864-27 9,70544-67 0,22471-14 52 3 0,01296-41 9.53150-71 0,22903-28 53 4 0,01728-55 0,02160-69 9,40871-66 8,38123-39 0,23335-42 54 i 9.31395-" 8,37523-13 8,3693688 0,23767-56 55 0,0259282 9,23691-09 0,2419969 56 I 0,0302496 9,1721014 8,36364-13 8,35804-40 0,24631-83 H 0.03457*10 0,03889-24 9,11624-34 0,25063-97 0,2549611 58 9 9,0672210 8,35257-23 ^ lO 0,04321-37 9,02359-02 8,34722-17 0,25928-24 II 0,0475351 8,98432-06 8,34108-82 8,33686-80 0,26360-38 61 12 0,05185-65 8,94865-15 0,26792-52 0.27224-65 62 »3 0,05617-79 0,06049-92 8,91600-53 8,88593-30 8,85807-85 8,33385-73 P M 8,32695-27 0,2765679 0,28088-93 64 IS 0,0648206 8,32215-04 U i6 0,06914-20 8,83215-49 8,31744-74 8,3128406 0,28521-07 '2 0,07346-34 8,80792-76 0,28953-20 ^ i8 0,07778-47 0,08210-61 8,78520-21 8,3083270 0,29^85-34 0,29817-48 19 8,76381-54 8,30390-41 69 20 0,08642-75 8,7436298 8,29956-87 0,3024962 70 21 0,0907488 8,7245277 8,29531-85 0,30681-75 0,31113-89 71 22 0,09507-02 8,70640-81 8,29115-10 72 23 0,09939-16 8,68918-31 8,28706-38 0,3154603 73 24 0,10371-30 8,67277-62 8,28305-45 0,31978-17 74 ^^ 0,10803-43 8,6571204 8,2791212 0,32410-30 7| 0,11235-57 8,6421565 8,27526-16 0,32842-44 76 IJ 0,11667-71 0,12099-85 0,12531-98 8,62783-20 8,27147-36 0,33274-58 11 8,61410-00 8,26775-54 0,33706-72 0,3413885 29 8,60091-87 8,26410-51 g 30 0,12964-12 8,5882506 8,26052*10 0,3457099 .»» 0,13396-26 8,5760617 8,25700-14 0,35003-13 81 3- 0,13828-40 8,56432-14 8,25354-42 0,35435-27 82 33 0,14260-53 8,5530010 8,54207-78 8,25014-80 0,35867-40 S^ 34 0,14692-67 8,24681-18 0,3629954 0,36731-68 84 '^ 0,15124-81 8,53152-59 8,2435336 u 0,15556-95 0,1598908 8,52132-52 8,24031 -21 0,37163-81 % 8,51145-62 8,23714-56 0,37595-95 u 0,16421-22 8,5019010 8,23403-34 0,38028-09 39 0,16853-36 l■J^■r^ 8,2309739 0,38460-23 89 40 0,17285-50 8,22796-52 0,3889236 90 41 0,17717-63 0,18149-77 8,47495-92 8,22500-72 8,22209-81 0,39324-50 0,39756-64 91 42 8,46650-62 92 43 0,18581-91 8,4582959 8,21923-68 0,40188-78 93 44 0,1901404 0,19446-10 8,45031 70 8,21642-22 8,21365-35 0,40620-91 94 i? 8,44255-89 0,41053-05 '4 0,19878-32 > 8,43501-17 8,21092-03 0,41485- 19 % 0,20310-46 8,4276663 8,20824-89 0,41917-3.3 H 0,20742-59 8,42051-42 8,20561-13 0,42349-^6 0,42781-60 98 49 o,2ii74-73 0,21606*87 8,41354-69 8.40675-69 |,203oi-53 99 50 8 20046-04 0,43213*74 100 8,00000-00 Pcrp. For explanation see pp. 216-228 (270) COMPOUND INTEREST AND ANNUITIES X ^^ ^*°^ Years I 2 3 4 I 9 10 II 12 «3 »4 \l \l 19 20 i 21 22 23 24 2 2 2 2 29 30 31 32 33 34 39 40 41 42 43 44 % 49 SO Log. r". 0,00646-60 0,01293-21 0,01939-81 0,02586-42 0,0323302 0,03879-63 0,0452623 0,05172-83 0,05819-44 0,06460-04 0,07112-65 0,0775925 0,08405-85 0,09052-46 0,09699-06 0,10345-67 0,10992-27 0,1163888 0,12285-48 0,12932-08 0,1357869 0,14225-29 0,14871-90 0,15518-50 0,16165-11 0,16811-71 0,17458-31 0,18104-92 0,18751-52 0,19398-13 0,20044-73 0,2069 1-34 0,2133794 0,21984-54 0,22631-15 0,23277*7.5 0,23924-36 0,24570-96 0,2521 7 56 0,2586417 0,26510-77 0,27157-38 0,27803-98 0,28450-59 0,29097-19 0,29743 79 0,3039040 0,31037-00 0,31683-61 0,3233021 Log. a". 0,00646*60 9,70865-71 9> 53577 -87 9,41404-49 9.32033-19 9,24433-95 9,18057-36 9,12575*45 9,07776-69 9,03516-62 8,99692-23 8,96227-45 8,93064*52 8,90158-54 8,87473-89 8,84981*90 8,826«;9-o8 8,80486*00 8,78446-37 8,76526-42 8,74714*37 8,73000-10 8,7137488 8,69831-03 8,68361 84 8,66961-41 8,65624-46 8,64346-33 8,63122-84 8,61950-22 8,60825-10 8,59744*40 8,58705-33 8,57705*37 8,56742-20 8,55813*71 8,54917*95 8,54053-14 8,53217-62 8,52409-87 8,51628-40 8,50872-18 8,50139-68 8,4942990 8,48741-78 8,48074-32 8,47426-61 8,46797-79 8,46187-03 8,45593*57 Log. a" 8,45016*73 8,44455*80 8,43910*15 8,43379*19 8,42862-34 8,4235909 8,41868*90 8,41391*32 8,4092587 8,40472-13 8,40029-69 8,3959815 8,.?9i 77*13 8,38766*27 8,38365*27 8,37973*78 8,3759^-50 8,37218-13 8,.36853-40 8,36497*01 8,36148-74 8,35808-32 8,35475*53 8,35150*12 8,34831-89 8,34520-62 8,34216-13 8,33918-21 8,33626-68 8,33341-34 8,33062-05 8,32788-65 8,32520-05 8,32258-81 8,32002-07 8,31750-61 8,31504-28 8,31262-96 8,31026-49 8,30794-79 8,30567 -7 » 8,.30345-i4 8,30126-97 8,29913-08 8.29703*39 8,29497-78 8,29296-14 8,29098-41 8,28904*46 8,28714-24 8,17609-13 Log. r*. 0,32976*82 0,33623-42 0^34270*02 0,34916-63 0,35563*23 0,36209*84 0,36856-44 0,3750304 0,3814965 0,38796*25 0,39442-86 0,40089*46 0,4073607 0,41382*67 0,42029-27 0,42675-88 0,4332248 0,43969-09 0,44615-69 0,45262-30 0,45908-90 0,46555*50 0,47202-11 0,47848*71 0,48495-32 0,49141-92 0,49788*52 0,50435*13 0,51081-73 0,51728-34 0,52374*94 0,5.^021-55 0,53668- 15 0,5431475 0,54961-36 0,5560796 0,56254*57 0,56901*17 0,57547*78 0,58194*38 0,58840-98 0,59487-59 0,601 34- 19 0,60780-80 0,61427-40 0,62074-01 0,62720-61 0,63367-21 0,64013-82 0,64660-41 Vears 51 52 S3 54 5^ 5 60 61 62 63 64 6s 66 67 68 69 70 71 72 73 74 M / 7' II 79 80 81 82 93 84 u 89 90 9» 92 93 94 95 96 97 98 99 100 Perp. II (271) LOGARITHMIC TABLES OF COMPOUND INTEREST AND ANNUITIES li 1 % 1 8 PerCtBt. Years I Log. f. Log. 1 6135 -24 0,16942-01 0,17748-77 o,«8S5S-S3 0,19362-29 0,20169-05 0,20975-82 0,21782-58 0,2258934 0,23396- 10 0,24202 87 0,25009-63 0,25816-39 0,26623-15 0,27429-91 0,28236-68 0,29043-44 0,29850-20 o,3<''656-96 0,31463-72 0,32270-49 o,33077'as 0,33884-01 0,3469077 0^35497-54 0,36304-30 0,37 1 II 06 0,37917-82 0,38724-58 0,39531-35 0.40338- 1 1 1 ^ 1 A 8 Per Cent. hog. 0,00806*76 9,7iio<-27 9..'^3896-40 9,41801*54 9,32508-31 9,2498669 9,18687-27 9,13282-10 9.08559-62 9,04375-38 9,00626-40 8,97236-58 8,94148-14 8,91316*21 8,88705-19 8,86286-36 8,84036-28 8.81935-49 8,79967-69 8,78119-14 8,7637805 8> 74734-31 8.73179*16 8,71704*94 8,70304-95 8,68973-27 8,6770465 8,66494-41 8,65338-36 8,64232*76 8,63174*21 8,62159-65 8,61 186-28 8,60251*60 8,58^*19 8,57657-41 8,56856-14 8,56083*74 8,55338-71 5.54619-59 8,53925-09 8,53254-01 8,52605-23 8,51977-69 8*51370-37 8,50782-39 8,50212-85 8,49660-98 8,4912601 i Log. a". 8,48607*21- 8,48103-92 8,47615-50 8.47»4i-35 8,46680*90 8,46233-64 8,45799-04 8,45376-62 8,44965-94 8,44566*57 8,4417808 8,43800*08 8,43432-22 8,43074-13 8,42725-47 8,42385-95 8,42055*23 8.41733-03 8,41419*08 8,41113-08 8,40814-80 8,40524-00 8,40240-42 8,39963-85 8,3969407 8,39430-88 8,.^9i74-o8 8,38923-47 8,38678*87 8,38440-11 8,38207*02 8,37979-41 8.37757-16 8,37540-09 8,37328-06 8,37120*95 8,36918*60 8,3672089 8,36527-70 8,36338-88 8.35130-6^ 8,34072-08 8,34818-80 8,.;j4667*98 8,27300*13 Log. f-. 0,41 144-87 0*4195 » 63 0,42758*40 0,43565-16 0,44371-92 0,45178-68 0.45985-44 0,46792*21 0,47598-97 0,4840573 0,49212*49 0,50019*25 0,50826-02 0,51632-78 0,52439-54 0,53246-30 0,54053-07 0,5485983 0,55666*59 0.56473-35 0,57280-11 0,58086-88 0.58893*64 0.59700-40 0,60507*16 0,61313-92 0,62120*69 0,62927*45 0,63734*21 0,64540*97 0.6534774 0,66154*50 0,66901-26 0,67768-02 0.68574-78 0,69381-55 0,70188*31 0,70995-07 0,71801*83 0,7260860 0,73415-36 0,74222*12 0,75028-88 0.75835-64 0,76642-41 0,77449-' 7 0,7825593 0,79062-69 0,79869*45 0,80676-22 For explanation see pp. 216-228 (274) Yean 52 53 54 li II 59 61 62 63 64 69 70 7« 72 73 74 81 82 2^ 89 90 9» 92 93 94 99 100 iPerp. m COMPOUND INTEREST AND ANNUITIES Per Cent. Yean 1 2 3 4 i I 9 10 II 12 »3 M \l % 19 20 31 22 23 24 Log. f*. 29 30 31 32 33 34 3 3 39 40 41 42 43 44 4 49 50 o,oo86o*o« 0,01720*03 0,0258005 0,03440*07 0,0430009 0,05160*10 0,06020-12 o,o688o'i4 0,07740-15 0,08600-17 0,09460*19 0,10320-21 0,11180-22 0,12040*2^ 0,12900*20 0,13760*27 0,14620*29 0,15480*31 0,16340*33 0,17200-34 0,18060-36 0,18920-38 0,19780-40 0,20640*41 0,2^1500*43 0,22360*45 0,23220-46 0,24080*48 0,24940-50 0,25800*52 0,26660*53 0.27520*55 0,28380*57 0,29240-58 0,30100*60 0,30960*62 0,31820*64 0,33680*65 0,33540*67 0,34400-69 0,35260*70 0,36120-72 0,36980*74 0,37840-76 0,38700-77 0,39560*79 0,40420-81 0,41280-82 0,42140-84 0,43000-86 Log. a\ 0,00860-02 9,71184-90 9,5400223 9.41933-40 9,3266602 9,2(5170-10 9,18896-21 9,13516*38 9,08819*08 9,04659*87 9,00935*71 8.97570-56 8,94506*63 8,01699*05 8,89112-17 8,86717-35 8,84491 '09 8,82413-95 8,80469-66 8,78644-42 8,76926-48 8,75305-73 8,73773-40 8,72321*83 8,70944-33 8,6963497 8,68388-50 8,67200-24 8,66066-02 8,64982-07 8,63945*01 Log. a" 8,62951*77 >'58 8,61685*89 8,61999- 8,60208-40 8,59364-99 8,58553-72 8,57772*80 8,57020-59 8.56295-56 8.55596-32 8,54921-53 8,5427002 8,53640-61 8,53032-30 8,5244406 8,51874-97 8,51324-20 8,50790-93 8,50274-40 8,49773*88 8,49288*73 8.48818-28 8,48361-96 8,47919-18 8,4748944 8,47072-20 8,46607-00 8,46273-38 8,45890-93 8,45519-19 8,45157-82 8,44806-42 8,44464-66 8,44132*18 8,43808*68 8,43493-85 8,431-87-38 8,42889-01 8,4259847 8,42315-50 8,4203986 8,41771-31 8,4150963 8,41254*59 8,41006*01 8,40763*67 8,40527-39 8,40296-99 8,40072*29 8.39853*" 8,3963929 8,3943069 8,39227*14 8,39028*51 8,38834-65 8,:t8645*44 8,3846072 8,38280*38 8,38104-31 8,37932-39 8,37764-48 8.37600-50 8.37440-34 8,37283-88 8,37131-04 8,36981*72 8.368.S5-82 8,36693*25 8,36553-93 8,30103-00 Log. r". 0,4386088 0,44720-89 0,45580*91 0,46440-93 0,47300-94 0,48160-96 0,49020-98 0,49881-00 0,50741-01 0,5160103 0,52461*05 0,53321-07 0,54181*08 0,55041-10 0,55901*12 0,50761-13 0,57621*15 0,58481*17 0.59341-19 0,60201 *20 0,61061 *22 0,61921*24 0,62781-25 0,63641*27 0,64501*29 0,65361*31 0,96221*32 0,67081*34 0,67041*36 0,68801*37 0,69661 -39 0^70521-41 0.71.^81*43 0,72241*44 0,73101-46 0,73961-48 0,74821*49 0,75681 51 0,76541-53 0.77401 55 0,78261*56 0,79121*58 0,79981*60 0,80841-61 0,81701-63 0,82561 65 0,83421*67 0,84281-68 0,85141-70 0,86001*72 Yean S» 5« 53 54 1^ 60 61 62 69 70 71 72 73 u 81 83 IS 89 90 9> 92 93 94 99 100 Perpi li il (275) rT I '' ! '■ ' 1 III Years Log. r". 1 2 3 4 i I 9 lO 11 12 »3 »9 20 21 22 23 24 2 2 29 30 31 32 33 34 3 I 39 40 41 42 43 44 49 SO o,oo9i3-2i 0,01826*41 0,02739-62 0,0365283 0,04566-03 o>05479-24 0,06392-45 o>o7305'66 0,0821886 0,0913207 0,10045-28 0,10958-48 0,11871-69 0,12784-90 0,13698-10 0,14611-31 o>>S524S2 0,1^3773 O' '7350-93 !64'i4 o,i82( '>.»9i77-3S 0,20090-55 0,21003-76 0,21916-97 0,22830-17 0,23743-38 0,2465659 0,25569-79 0,2648300 0,27396-21 0,28309-42 0,29222*62 0,3013583 0,31049*04 0,31062-24 o,32»75-45 0,33788*66 0,34701*86 0,3561507 0,36528-28 0,3 744 » -48 0,38354-69 0,39267-90 0,40181-11 0,4 '094*31 0,42007*52 0,42920-73 0,4383393 o,44747*»4 0,45660-35 LOGARITHMIC TABLES OF 24 1 8 Per Cent. Log. a". 0,00913-21 9,71264*41 9,54107*89 9,42065-01 9.32823*42 9.25353-10 9,19104*63 9,>3750-04 9,09077 79 9^04943 46 9,01244*01 8.97903-37 8.04863-78 8.02080-35 8,89517-46 8.87146*43 8,«4943-79 8,82890-09 8,80969*06 8,79166*90 8,77471 -88 8,75873-85 8,74364-08 8,7293489 8,71579-57 8,70292*24 8,69067-61 8,67901-02 8,66788*30 8,65725*67 8,64709-75 8,63737-48 8,62806-09 8,6191302 8,6105600 8,60232 -86 8,59441-70 8,58680-73 8,5794828 8,57242-85 8,565^3-03 8,55907-50 8,-5527508 8,54664-60 8,54075-03 8,53505-.^8 8,52954-74 8,52422-22 8.S«907-os 8.51408-44 Log. a*. 8,50925-70 8,50458-14 8,50005*14 8,49566-10 8,49140-45 8.48727-66 8,48327-23 8,47938-67 8,47561-55 8,47195-41 8,46839-85 8,46494*50 8,46158-98 8,4583292 8,4551600 8,45207-90 8,44908-33 8,44616-96 8,4433355 8,44057*81 8,43789-50 8,43528-36 8,43274-17 8,43026*70 8.42785-75 8,42551-09 8,42322-54 8,42099*91 8,4188300 8,41671 -66 8,41465-70 8,41264-97 8,410^)9-32 8,40878-59 8,4069263 8,40511-31 8,40334-50 8,40162*05 8,39903-86 8,39829-79 8,39669-74 8,39513-59 8,39361-23 8,39212*54 8.30067-46 8.^8925-85 8.38787-63 8,38652*73 8,38521-04 8,.38302-4^ 8,32735-89 For explanation see pp. 216-228 (276) Log. r". 0,46573 0,47486 0,48399 o,493'3 0,50226 0,51139 0,52052 0,52066 0,53879 0,54792 0,55705 0,56618 0,57532 0,5844s 0,59358 0,60271 0,61184 0,62098 0,63011 0,63924 0,64837 0,65750 0,66664 0,67577 0,68490' 0,69403 0,70316 0,71230 0,72143 0,73056- 0,73 o,748«2 0,75796 0,76709 0,77622 0,78535 0,79449 0,80362 0,81275 0,82188 0,83101 0,84015 o,8.<0-!8 0,85841 0,86754 0,87667 0,88581 0,89494 0,90407 0,91320 •55 •76 :?^ •38 .';9 •80 00 21 -42 *62 •83 -04 •24 :^ ■87 •07 •28 •49 69 90 '11 •31 ■52 73 94 «4. •35 •56 •76 -38 •59 -80 •00 •21 •42 -63 ■83 •04 •25 '45 66 87 o •2 49 70 I Year. 51 52 53 54 5 5 % 61 62 63 64 65 66 69 70 71 72 73 74 75 76 77 78 81 82 86 87 88 89 90 9' 92 93 94 96 97 98 99 100 II COMPOUND INTEREST AND ANNUITIES Yean I 2 3 4 i I 9 10 11 12 13 M '.i \l »9 20 21 22 23 24 2j 21 2 2l 29 30 Log. r*. 31 32 33 34 3 % 39 40 4« 42 43 44 45 46 % 49 50 o,oo966'33 0,01932*66 0,02899-00 0,03865-33 0,04831-66 0,05797-99 0,06764-32 0,07730-65 0,08696-99 0,09663-32 0,10629*6^ 0,11595-98 0,12562-31 0,13528-64 0,14494-98 0,15461*31 0,16427*64 0,17393-97 0,18360*30 0,19326-63 0,20292*97 0,21259-30 0,22225*63 0,23191*96 0,2415829 0,25124-62 0,26090*96 0,27057*29 0,28023*62 0,2898995 0,29956*28 0,30922-61 0,31888-95 0,32855-28 0,33821-61 0,34787-94 o,.3S754*27 0,36720-60 0,3768694 0,38653-27 0,39619*60 0,40585*93 0,41552 26 0,42518-59 0,43484-93 0,44451*26 0,45417-59 0,46383-92 0,47350-2 0,483 « 6*5 2ip. Cent. Log. a'» 0,00966*33 9,7134381 9.54213*37 9,42196*39 9,32980*50 9.25535-68 9.«93«2*53 9,13983*07 9.09335-76 9,05226*17 9.oi55»-27 8,98235*00 8,95219-58 8,92460*13 8,89921*03 8,87573-61 8,85394-38 8.83363*92 8,81465*92 8,79686-61 8,78014-23 8,764.38*69 8,7495«'«9 8,73.';44-«o 8,72210*71 870945*09 8,69742*01 8,68596*79 8,6750522 8,6646357 8.65468*47 8,64516-82 8,6360586 8,6273305 8,6189608 8,61092-85 8,60321-40 8,59579-96 8,58866-87 8,58180*61 8,575«9-79 8,5688309 8,56269*20 8.55677-28 8,55106-01 8.54554-47 8,54021*77 8.53507-03 8,5.^000*4 8,52528*2 Log. «r. 8,52062-79 8,51612*32 8,51176-23 8,50753-94 8,50344-87 8.49948-50 8,49564-32 8,49191*85 8,4883064 8,48480-26 8,48140-31 8,47810-38 8,47490-13 8,4717918 8,4687 7 -22 8,46583*92 8,46298*99 8,46022*11 8,45753-oa 8,45491*46 8.45237-16 8,44989-9» 8,4474944 8,445'S-54 8,44288*00 8,4406662 8,43851*20 8,4364' '53 8,4.M37-47 8,43238-82 8.4.^045-41 8,4285708 8,42673*69 8,4249508 8,42321*10 8,42151-63 8,41086*53 8,41825-66 8,4166890 8,41516*13 8,41367-26 8,41222*14 8,41080-69 8,40042*79 8,40808-36 8,40677-28 8,40549-46 8,40424-83 8,40303-28 8,40184-73 8.352 Log. I*. Yean B4-73 18*25 (277) 0,49282-92 0,50249*25 0,5121558 0,52181*91 0,53148*24 o,54»M*S7 0,55080*91 0,56047*24 0,57013-57 0.57979-90 0,58946*23 o, 599' 256 0,6087890 0,61845-23 0,62811-56 0.63777*89 0,64744*22 0,65710-55 0,66676*89 0,67643*22 0,68609-55 0,6957588 0,70542-21 o,7»5o8'54 0,72474-88 0,73441*21 o.74407-.«;4 0.75373-87 0,76340*20 0.7730653 0,78272*87 0,79239-20 0,80205*53 0,81171-86 0,82138-19 0,83104*52 0,84070-86 0,85037*19 0,86003*52 0,86969-^5 0.87936*18 0,88902-51 0,89868-^5 0,90835*18 0,91801-51 0,92767*84 0.93734- » 7 0,94700-50 0,95666-84 0,96633*17 5> 52 53 54 56 5 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 li 81 82 83 84 85 86 87 88 89 90 9» 92 93 94 V> 99 100 ; * I Team I 2 3 4 i I 9 lO II 12 M 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 ^2 39 40 41 42 43 44 49 50 Log. f-. 0401010*30 o,0203878 0,0305817 0,04077-57 0,05096*96 0,061 1 6*35 o>o8iSS'i3 0,09174*52 0,10193*91 0,11213*31 0,12232*70 0,13252*00 0,14271*48 0,15290-87 0,16310*26 0,1732966 0,1834005 0,19368*44 0,2038783 0,21407*22 0,22426*61 0,2344600 0,24465*40 0,25484-70 0,26504*18 0.27523-57 0,28542-96 0,29562*35 0,3058174 0,31601-14 0,32620-53 0,33639*92 0,34659-3 * o,3.';67»70 0,36698-09 o>377i7*4« 0,38736-88 0,39756-27 0,40775-66 0,4179505 o,428i4'44 0,4383383 0,4485323 0,45872-62 0,46892-01 0,47911-40 0,48930-79 0,49950-18 0,50969-57 LOGARITHMIC TABLES OF Ip-c...: Log. a". §: 0,01019-39 9,71423-09 9.54318-69 9.42327-52 9.33137-25 9,25717-86 9,19519-91 9,14215-48 9.09592-97 9,0550801 '.01857-51 '.98565-46 8.9557404 8,92838-40 8,90322-91 8,87098-90 8,8584288 8,83835-42 8,81960-24 8,8020355 8,78553*60 8,77000-26 8,75534-79 8,74149-52 8,72837-75 8.71593-57 8,70411-73 8,69287 -M 8,68216-82 8,67195-84 8,66221*19 8,65280-81 8,64398-93 8,63546-00 8,62728 74 8,61945-00 8,61192-87 8,6047055 8,59776-41 8,59108-91 8,58466-66 8,57848-34 8,57252-74 8,56678-76 8,56125-31 8,5559»-44 8,55076-19 8.54578-74 8,54098-27 8,53634-03 Log. a". 8,53185-29 8,52751-40 8,52331-72 8,51925*65 8,51532-64 8,51152-15 8,50783*67 8,50426-73 8,50080-89 8,49745-71 8,49420-78 8,49105-72 8,48800-16 8.48503-75 8,48216-16 8,47937-06 8,47666-16 8,47403-17 8,47147-80 8,46899-81 8,46658-92 8,46424-91 8.46197-53 8.45976-59 8,45761-83 8,45553-08 8,45350-14 8,45152-83 8,44960-94 8,44774- 3 8,44592-81 8,44416-24 8,44244-45 8,44077-30 8,43914-65 8,43756-35 8,43602*29 8,43452-32 8,43306*33 8,43164-21 8,43025-82 8,42891-07 8,42759-85 8,42632-05 8,42507-58 8,42386-35 8,42268-24 8,42153-20 8,42041-11 8,41931-90 8,37566-^6 For explanation see'pp. 216-228 Log. r*. 0,51988-97 0,53008-36 0,54027-75 0,55047-14 0,56066-53 0,57085-92 0,58105*31 0,59124*71 0,60144*10 0,61163*49 0,62182-88 0,63202-27 0,64221*66 0,65241*05 0,66260*45 0,67279-84 0,68299-23 0,69318-62 0,7033801 0,71357-40 0,72376-80 0,73396-19 0,74415-58 0,75434-97 0,76454-36 0,77473-75 0,78493-14 0,79512- 0.^531-93 0,81551-32 0,82570-71 o,83|90-io 0,84609*49 0,8562888 0,86648 28 0,87667*67 0,88687-06 0,89706*45 0,90725*84 0,91745-23 0,92764-62 0,9378402 0,94803-41 0,95822-80 0,90842-1 0,97861-5 0,98880-97 0,9990037 1,00919-76 1,01939*15 Ywn. 51 52 53 54 5 5 59 61 62 63 67 68 69 70 71 72 73 74 7« 81 82 1^ 1^ 1^ 89 90 91 92 93 94 U 99 100 Pop. (278) COMPOUND INTEREST AND ANNUITIES 2i PW CMtt. 1 2 3 4 I I 9 lb 11 12 »3 »4 •5 t6 ;i 19 20 21 22 23 24 2 2 Log. r". 29 30 31 32 33 34 39 40 41 42 43 44 % 49 50 0,01072*39 0,02144-77 0,03217*16 0,04289*55 o,o|36i-93 0,06434-32 0,07506-71 0,08579-09 0,09651*48 0,10723*87 0,11796-25 0,12868-64 0,1394103 0,15013-41 o,i6o8c-8o 0,17158-18 0,18230*57 0,19302-96 0,20375*34 0,21447-73 0,22520-12 o, 23592 •i.o 0,24064-89 0,25737-28 0,26809-66 0,27882-05 0,2895^-44 0,30026-82 0,31099-21 0,32171-60 0,33243-98 0,343 •6-37 0,3538876 0,36461*14 0,37533-53 0,3860^-92 o,3967»-30 0,40750-69 0,4182308 0,4289546 0,43967-85 0,45040-23 0,46112-62 0,47185-01 0,48257-39 0,49329-78 0,50402*17 0,51474-55 0,52546-94 0,53619-33 Log. fl". 0,01072-39 9,71502*27 9,54423-83 9,42458-42 9,3329.r68 9,2589962 9,19726-80 9,14447-26 9,09840-45 9,05788-95 0,02162-73 8,98894-73 8,95927>7 8,93215*16 8,90723-11 8,88422-30 8,86289-29 8,84304-63 8,8245204 8,80717-72 8,79089-94 8,77558-57 8,76114-85 8,74751-14 8,73460-72 8,7223768 8,71076-77 8.69973-31 8,68923-13 8,6792247 8,66967-94 8,66056-49 8,65185-33 8,6435 '"93 8,63553-99 8,62789-39 8,62056-18 8,61352-59 8,60676-08 8,60027-83 8,59403-72 8,5880336 8,58225-53 8,57669- 11 8,5713306 8,56616-35 8,561 18' 12 8,55637-48 8,55» 73-64 8,54725 84 Log. a". 8,5429336 8,53875-55 8,5347»-76 8,53081-40 8,52703-92 8.523.28-78 8,51985-48 8,5*643-54 8,51312-52 8,50991-99 8,50681-53 8.50380-78 8,50089-34 8,49806*90 8,49533-10 8,49267-63 8,40010-20 8,48760-50 8,48518-27 8,48283*24 8,48055*17 8,47833-80 8,47618-91 8,47410*29 8,47207*72 8,47010-99 8,46819-91 8,46634-31 8,46453-99 8,46278-79 8,4610853 8,45943-08 8,45782-26 8,45625*94 8,45473*97 8,45326-23 8,45i82-c6 8,45042-85 8,44906-09 8,44774-84 8,44646-31 8,44521-27 8,4439964 8,44281-29 8,44166-15 8.44054-10 8,43945-07 8,43838-9S 8,43735-68 8,43635-16 8,3979400 Log. r". 0,54691-71 0,55764-10 0,56836-49 0,57908-87 0,58981-26 0,60053-65 0,61126-03 0,62198-42 0,63270-81 0,64343- 19 0,65415-58 0,66487-97 0,67560-35 0,68632 74 0,69705- 13 0,70777-5' 0,71849-90 0,72922-28 0,7399467 0,75067-06 0,76139-44 0,77211-83 0,7828^*22 0,79356-60 0,80428-99 0,81501*38 0,8257376 0,8364615 0,84718-54 0,85790-92 0,86863-31 0,8793570 0,89008-08 0,90080-47 0,91152-86 0,92225-24 0,93297-63 0,9437002 0,95442-40 0,96514-79 0,97587-18 0,98659-56 0,9973 » -95 1,00804-33 1,01876-72 1,02949-11 1,04021-4 1,05093 1,06166-27 1,07238-65 Tean 5» 52 53 54 5 I 61 62 63 64 ^6^ % 69 70 71 72 73 74 81 82 83 84 87 88 89 90 9» 92 93 94 9' 99 100 (279) •I iii. i '-': LOGARITHMIC TABLES OF Years I 1 3 4 i I 9 lo II 12 «4 \i % ao ai 22 23 24 39 30 3« 3» 33 34 3 37 38 39 40 4« 42 43 44 :^ 47 4» 49 Log. r*. 0,01125-32 0,02250-63 o>03375*95 0,04501-27 0,0562659 0,06751-90 o,o7877'22 0,09002-64 0,10127-85 o."»S3i7 o.i«378*49 0,13503-80 0,14629-13 0,15754-44 0,16879-76 0,18005-07 o. 19130-39 0.20255-71 0,21381-03 0,33506-34 0,23631-66 0,24756-97 0,25882-29 0,27007-61 0,28132-93 0,292582^ °'-^°3«3-S6 0,31508-88 0,32634- 19 0.33759-51 0,3^483 0,36010-14 0,37135-46 o,382f)0-78 0,39386-10 0,40511-41 0,41636-73 0,4276205 0,43887-36 0,45013-68 0,46138-00 0,47263-31 0,48388-63 0,49513-95 0.50639-27 0,51764-58 0,52889-90 0,54015-33 0,55*40-53 J365-85 0,563 5 8 Lor. a". 0,01125-32 9. 7 > 581 -33 9.54528-79 9,42589-07 9.3,^449-80 9,26080-97 9.19933-16 9,14678*41 9,10105-19 9,06069-03 9,02466-94 0,99222-85 8,96278-97 8.93590*43 8,91 131 -61 8,88843-83 8,86733-61 8.84771-55 8,82941-31 8,81229-15 8,79623-30 8,78113-65 8,76691-42 8,75348-99 8,74079-64 8.7287745 8,71737-17 8,70654-14 8,69624-17 8,68643-53 8,67708-78 8,66816-90 8,65965-11 8,65150-88 8,64371-89 8,63626-03 8,62911-38 8,62226-13 8,61568-65 8,6093742 8,60331-05 8.59748-33 8,59187-73 8,58648-43 8,58129-29 8.57629-35 8.57147-65 8.56683-36 5,56235-68 «»S58o3-84 Per Cent Log. a". 8,55387-14 8,54984-90 8,54596-5 » 8,54221-36 8.53858-90 8,53508-61 8.53169-96 8,52842-49 8.52525-77 8,52219-35 8,51922-83 8.51635-83 8.51357-98 8,51088-94 8,i;o828-38 8.50575-97 8,5033' -43 8,50094-45 8,49864-78 8,49642- 15 8,49426-29 8,49217-00 8,49014-01 8,48817-13 8,48626-14 8,48440-84 8,48261 -04 8,48086-55 8,47917-20 8,47752-80 8.47593-21 8,47438-26 8,4728781 8,47141-70 8, 46999 -So 8,46861-98 8,46728-10 8,46598-05 8,46471-69 8,4634891 8,46229-63 8,4611368 8,46001 -01 8,45801-50 8,45785-06 8,45681 59 8,45581-00 8,45483-23 8,45388-13 8,45295-69 Log. f*. 0,57391 -'7 0,58516-48 0,59641-80 0,60767-13 0,61892-44 0,63017-75 0,6414,3-07 0,65268-39 0,66393-70 0,67519-02 0,68644-34 0,69769-65 0,7089497 0,72020-29 o,73»45-6i 0,74270-92 0,75396*24 0,76521-56 0,77646-87 0,78772-19 0,79897-51 0,81022-82 0,82148-14 o,832'73 46 0,8439878 0,8^514-09 0,86649-41 0,87774-73 0,88900-04 0,90025-36 0,91150-68 0,92275-99 0,93401-31 0,94526-63 0,95651-95 0,96777-26 0,97902-58 0,99027-90 1,00153-21 1,01278-53 1,02403-85 i,03M9-i6 1,04654-48 1,05779-80 1,06905-12 1,08030-43 i.o9»55-75 1, 10281 07 1,11406-38 1, 1 2531-70 Ymuk SI S» 53 54 5 li 61 62 69 70 71 72 73 74 75 76 \i 80 81 82 83 84 II 87 88 89 90 91 92 93 94 95 96 99 100 For explanation see pp. 216-228 (280) Yean I 2 3 4 ? I 9 10 II 12 >3 14 '5 16 \l 19 30 31 22 »3 24 25 26 27 28 29 30 3« 32 .33 34 35 36 ^ 39 40 41 42 43 44 % 49 SO COMPOUND INTEREST AND ANNUITIES Log. r". 0,01178-18 0,02356-37 0,03534-55 0,04712-73 0,05890*92 0,07069-10 0,08247-28 0,09^35-^6 0,10603-65 0,11781-83 0,12960-01 0,14138-20 0,15316-38 0,16494-56 0,17672-75 0,18850-93 0,20029-11 0,21207-29 0,22385-48 0,23563-66 0,24741 84 0,2592003 0,2709821 0,28276-39 0,2945458 0,30632-76 0,31810-94 0,32989-13 o..34»67-3i 0,35345-49 0,36523-67 0,37701 86 0,3888004 0,4005822 0,41236-41 0,42414-59 0,43592-77 0.44770-96 0,4594914 0,47127-32 0,48305-51 0,49483-69 0,50661-87 0,5184005 0,53018-24 0,54196-42 0,5537460 0,56552-79 0,5773097 0,58909-15 Si 4 Per Cent Log. fl". 0,01178-18 9,71660-28 9.546.33-59 9,42719-49 9.3.3605-59 9,26261-92 9,20139-02 9,14908-96 9,10360-17 9,06348-24 9,02770-14 8,99549' 79 8,9662944 8,9.3964- « 9 8,91518-44 8,89263-51 8,87175-80 8.85236-18 8,83428-09 8.81737-85 8,80153-69 8,78665-49 8,77264-51 8,7594309 8,74694-52 8,73512-89 8,72392-96 8,7133005 8,70319-98 8.69359-00 8,68443-72 8,67571-08 8,66738-32 8,65942-80 8,65182-48 8,644^5-00 8,^758-51 8,63091-21 8,62451-47 8,6183777 8,61248-72 8,60682-99 8,60139-40 8,5961681 8,5011417 8,5863o-5i 8,5816^-91 8,5771651 8i686^i8 Log. o". 8,5646678 8,56079-64 8,55706-15 8,55.345-71 8, 54997 78 8,54661-81 8.54337-31 8,5402381 8,5372085 8,5342802 8,53M4-9i 8.5287114 8,52606-34 8,52.35017 8,52102-30 8,51862-41 8,51630-21 8,51405-41 8,51187-74 8,5097693 8,50772-75 8.5057495 8.50.383-30 8.5019759 8,50017-61 8,49843-16 8,49674-05 8,4951010 8,49351-12 8,49196-96 8,49047-45 8,48902-44 8,48761-76 8,48625-38 8,48492-87 8,48364-40 8,48239-72 8,48118-72 8,48001-29 8,47887:30 8,47776-64 8,47669-23 8,47564-94 8,4746368 8,47.36535 8,47269-87 8,47177-15 8,47087-10 8.46999-64 8,4691469 8.43933*7 Log. 0,6008734 0,61365-53 0,62443-70 0,63621-88 0,648000^ 0,65978-35 0,67156-^3 0,68334-63 0,69512-80 0,70690-98 0,71869-17 0.73047-35 0.74225-53 0,75403-72 0,76581-90 0,7776008 0,78938-26 0,80116*45 0,81294-63 0,82473-81 0,83651-00 0,84829*18 0,86007-36 0,87185*55 0,88363-73 0,89541-91 0,9072009 0,91898-28 0,9307646 0,9425464 0,9543283 0,9661 1 -01 0,9778910 0,98967-38 1,00145-56 1,01323-74 1,02501-93 1,03680-11 1,04858-29 1,06036*47 1,07314*66 1,08392*84 1,09571 03 1,10749*21 1,11927-39 1,13105-57 1,1428376 i,im6i-94 1,16640*13 1,17818*31 "^i Yean 51 5» 53 54 % 59 60 61 63 'd 69 70 71 72 73 74 II 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 99 100 Petyi (281) i 1 i i I LOGARITHMIC TABLES OF 2 S Per Cent. X Yean I Log. f-. Log. a\ Log. of*. Log. f*. T«ui 5> 0,01230-98 0,01230-98 8,57532-4» 0,6278023 3 0,02^61*97 0,03692-95 9,71739-' 2 8,57»59-90 8,56800-85 0,64011-31 52 3 9,54738-21 0.65243*20 0,66473-18 53 4 0,0^92394 0,06154-92 9,428^9-66 8,56454-64 54 1 9 9,3376107 8,56120-75 0,67704-17 11 11 0,07385-01 0,08616-80 9,26442-45 9,20344-58 9,15138-89 9,10614-43 8,55798-62 8,55487-76 0.68935-15 0,70166-13 0,09847-88 0,11078-86 8,55187*72 8,5489803 0,7139712 0,72628-10 lO 0,12309-85 9,06626-59 8,54618-27 0,7385909 II 0,13540-83 9.03072*35 8,99875-58 8,54348-06 0,75090-07 0,76321-06 61 12 0,14771-82 8,54086-99 62 13 '4 0,16002-80 0,1723379 0,18464-77 8,9697860 8,94336-46 8,53834-72 8,53590-80 0,7755204 0,7878303 64 15 8,31913-59 8,89681*29 8,53355-18 0,8001401 U ID 0,19695-76 8,53127-28 0,81 245 00 '^ 0,20926-74 8,87616-09 8,52906-89 0,82475-98 0,83706-97 ^ 18 0,22U7-73 0,23388-71 0,24619-70 8,85698-5^ 8,83912-38 8,82243-82 8,5260372 8,52487-51 8,52288-00 »9 20 *''2^937-95 0,86168-94 69 70 21 22 0,258^0-68 0,27081-67 8,80681 12 8,79214*13 8,52094-94 8,51908-09 0,87399-92 0,88630-91 0,89861-89 71 72 23 0,28312-65 8.77834-13 8,51727-23 73 24 0,29543-64 8.76533-45 8,51552-14 8,51382-63 0,91092-88 74 ^1 0,30774-62 8,75305-39 0,9232386 li 0,32005 -61 0,3323659 8,7414405 8,73044-16 8,51218*47 0,93554-85 0,94785-83 0,96016-82 ^1 8,51059-50 11 . 0,34467-57 0,35698-56 0,36929-54 8,72001-06 8,50905-53 8,50756-38 8,50611-90 29 30 8,71010-58 8,70068-95 0,97247-80 0,98478*79 S 31 0,38160-53 8,60172-80 8,6831907 8,67504-98 8,50471-90 0,9970977 81 32 0,39391 ^^ 8,50336-25 1,00940*76 82 33 0,40622*50 8,50204-80 1,02171-74 S^ 34 o,4i8«-48 0,4308447 8,6672800 8,5007741 1,03402-72 1,046.33-7' 84 ^? 8,65985-83 8,65276-36 8,4995392 il 0,44315-45 0,45546-44 0,46777-42 0,48008-41 8,49834-22 1,05864-69 1,07095-68 1,08326-66 37 8,64597-66 8,49718-19 ii 38 8,63947-92 8,4960569 88 39 8,6332^-52 8,62728-96 8,49496-62 1,09557-65 1,10788-63 89 40 0,49239-39 8,4939086 90 41 0,50470*38 8,62156-81 8,49288-30 8,49»88-83 8,40092-36 8,48998-80 1,12019-62 9' 4* 0,5 » 701 36 8,61607-79 1,1325060 1,14481*59 92 43 0,52932-35 8,6108069 93 44 0,54163-33 8,60574-36 8,60087-70 8,59619-98 «,iS7'2-57 94 t 0,55394-32 o,5662«*30 0,57856*29 0,59087*27 0,60318*26 8,48908-04 8,4882000 1,16943-56 1,18174-54 u i^ 8,5017002 8,5873706 8,4873459 8,48651-73 1,19405-53 1,20636-51 u 49 8,58320-31 8,4857i;34 1,21867-50 1,2309848 99 50 0,61549*24 R. 57918-99 8;458?3-7^ 100 Perp For explanation see pp. 216-228 (282) Years I 3 3 COMPOUND INTEREST AND- ANNUITIES Par Cmt. Log. r* I 9 to u 13 '3 14 \i \l «9 20 21 22 23 24 25 26 27 28 29 30 31 32 S3 34 li 37 38 39 40 4' 42 43 44 % 49 50 0,0128372 0,02567*44 0,03851*17 0,05134-89 0,06418*61 0,07702-33 0,08986-06 0,10269*78 0,11553-50 0,12837*22 0,14120*95 0,15404*67 0,16688-39 0,17972-11 0,19255-84 0.20539*56 0,21823-28 0,23107-00 0,2439073 0,25674-45 0,26958-17 0,28241-89 0,2952562 0,30809-34 0,3209306 0,3337678 0,34660-51 0,35944-23 0,37227-95 0,38511-67 0,39795-40 0,4107912 0,42362-84 0,43646-56 0,44930-29 0,46214*01 0,47497-73 0,48781*45 0,50065*18 0,5 '34890 0,52632-62 o,539'6-34 0,5520007 0,56483-79 0,57767-51 0,59051-23 0,60334-96 0,61618-68 0,62902-40 0.64186- 1 2 Log. «". 0,0128372 9,71817-84 9,5484267 9,42979-59 9,33916-23 9,26622-58 9,20549-22 9,15368-19 9,10867-95 9,06904*07 9.03373-51 9,00200-22 8,97326-43 8,94707*25 8,92307*08 8,90097-23 8,880^4-22 8,8615864 8,84394-18 8,82747-08 8,81205-58 8,79759-57 8,78400-29 8,77120-09 8,75912-27 8,74770-92 8,73690-79 8,72667*20 8,71696-00 8,70773-4' 8,69896*07 8,69060-91 8,68265-15 8,67506-27 8,66781-98 8,66090-15 8,6542885 8.64796-30 8,64190-86 8,63611-04 8,63055-4' 8,62522-68 8,62011-63 8,61521*17 8,61050-23 8,60597-85 8,60163-10 8,59745-14 8,59343' »6 8.58956-42 Log. «• 8,58584-21 8,58225-86 8,57880-78 8,57548-32 8,57227-98 8,56919*22 8,56621-52 8,563.34-42 8,56057-53 8,55790-35 8,55532-53 8,55283-67 8,55043-4' 8,54811-42 8,54587-36 8,54370-93 8,54161*83 8,53959-78 8,53764-5] 8,53575*76 8.53393-29 8,53216-86 8,53046-27 8,52881*27 8,52721-68 8,5256730 8,52417*94 8,52273-41 8,52133-56 8,519^-21 8,51867-20 8,51740-38 8,51617-61 8,51498-76 8,5'383-67 8,51272-22 8,51164-30 8,51059-77 8,50958-53 8,50860-46 8,50765*46 8,50673-42 8,50584*25 8,50497-85 8,5041414 8,50333-02 8,50254*40 8,50178-22 8,50104-37 8,5003280 8,477i2*M (283) Log. r-. 0,6546985 0,66753-57 0,6803729 0,69321-01 0,70604-74 0,71888-46 0,7317218 0,74455-90 0,7573963 0,7702335 0,78307*07 0,7959079 0,8087452 0,82158-24 0,83441-96 0,8472568 0,86009-41 0,87293- 13 0,8857685 0,89860*57 0,91144-30 0,9242802 0,937 'I -74 0,94995-46 0,96279-19 0,97562-91 0,9884663 1,00130-35 1,0141408 1,02697-80 1,03981*52 1,05265-24 1,0654897 1,07832-69 1,09116-41 1,10400-13 1,116838 1,129675 1,14251-30 1,1553502 1,16818-74 1,18102-47 1,1938619 1,2066991 1,21953-63 I,23237-.S6 1,2452108 1,25804-80 1,27088*53 1,28372*35 Yean 5' 52 53 54 5^ I 59 60 61 62 63 64 65 66 67 68 69 70 7* 71 73 74 81 82 83 84 87 88 89 90 91 92 93 94 99 100 P«rp R I M 1^^ i ; i ' Years I t i 4 I I 9 lO II 12 M ;i i8 '9 20 21 22 23 24 2 27 28 29 30 31 32 33 34 ^^ 3 39 40 41 42 43 44 45 46 J^ 49 50 Log, r". 0,01336-40 0,0267279 0,04009' 19 0.05345 "58 0,06681-98 0,08018-38 0,09354-77 o, 10^)91-17 0,12027-57 o.>3363'96 0,14700-36 0,1603675 0,17373*15 0,18709-55 0,20045-94 0,21382-34 0,22718-73 0,24055-13 o. 2539 » 53 0,26727-92 0,28064-32 0,29400-72 0,30737" 0,32073-51 0,3340990 0,3474630 0,36082-70 0,3741909 0,38755*49 0,40091-88 0,41428-28 0,42764-68 0,44101-07 o,45437'47 0,4677387 0,48110-26 0,49446 66 0,5078305 0,52119-45 0,53455-85 0.54792-24 0,56128-64 0,5746503 0,58801-43 0,60137-83 0,61474-22 0,62810-62 0,64147-02 0,65483-4' 0.66819-81 LOGAHITUMIC TABLES OK 3i S Per Cent. Lo g. a\ 0,01336-40 9- 7 '896-45 9.54946-96 9,43109-29 9,3407 1 08 9,26802*30 9.20753-57 9' 1 5596-89 9,11120-74 9,07180-68 9.0367369 9.00523-70 8,97672-96 8,95076-56 8,92698-91 8,00511-32 8,88490-32 8,86616-47 8,84873-51 8,83247-65 8,81727-12 8,80301-83 8,78963-02 8,77703-03 8,76515-18 8,75393*54 8.74332-87 8,73328-51 8,72376-27 8,71472-42 8,70613-55 8,69796-63 8,69018-87 8,68277-75 8,6757097 8,66896-42 8,6625216 8,6563644 8,65047-58 8,64484*10 8,6394458 8,6342775 8,62932-37 8,62457-34 8,62001-62 8,61564-23 8,61144-26 8,60740-86 8,60353*23 8,59980-62 Log. a". 8,5962233 8,59277-69 8,58946-09 8,58626-95 8,58319-69 8,58023-81 8,57738-81 8,57464-21 8,57'99-59 8,56944-52 8,5601. _ 8,55799jS 8,5559369 8,55395-39 8,55203-95 8,55019-12 8,54840-62 8,54668-24 8,54501-74 8,54340-89 8,54185-47 8,5403530 8,53890-17 8.53749-9» 8,53614-32 8,53483-25 8,53356-52 8,53233-99 8,53115-50 8,53000-90 8,5289007 8,5278286 8,52670- 16 8,52578-84 8,52481-77 8,52387-86 8,5229698 8,52209-04 8,52123-93 8,52041 56 8,51961 84 8,51884-67 8.51809-97 8.5173766 8,51667-65 8,5»599-87 8.51534*25 8.49485-00 Log. r". 0,68156-20 0,69492 -to 0,7082900 0,72165-39 0,73501-79 0,7^^3818 0,76174-58 0,77510-98 0,78847-37 0,80183-77 0,81520-17 0,82856-56 0,84192-96 0.85529-35 0,86^5-75 0,88202-15 o,89«8-S4 0,90874-94 0,92211*34 0.93547*73 0,94884*13 0,96220-52 0,97556-92 0,9889332 ,00229-71 ,01566*11 ,02902*50 .04238-90 .05575*30 ,06911-69 ,08248-09 ,09584-49 ,10920-88 ,12257-28 .I3.';93'67 ,14930-07 ,16266*47 ,i7to2-80 ,18939-26 ,20275-65 ,2161205 ,22948-45 ,24284-84 ,25621-24 ,26957-64 ,28294*03 ,2963043 ,3096682 ,32303-22 .33639-62 Years 5' 52 S3 54 55 56 5 61 62 63 64 69 70 71 72 73 74 II II 80 81 82 83 84 1^ 87 88 89 90 91 92 93 94 97 98 99 100 Perp For explanation see pp. 216-22S (284) COMPOUND INTEREST AND ANNUITIES 3^ 4 Per Cent Yewij I 2 3 4 I I 9 10 II 12 »3 14 \i '.I «9 20 21 22 «3 »4 II 27 28 29 30 31 3» 33 34 3 31 11 39 40 41 42 43 44 t 49 SO Log. I*. 0,01380-01 0,02778*01 0,04167-02 0,05556-02 0,06945-03 0,08334-04 0,09723-04 0,1111205 0,12501-05 0,13890-06 0,15270-07 0,16668*07 0,18057-08 0,19446*08 0,20835-09 0,22224-10 0,23613-10 0,25002-11 0,26301 11 0,27780-12 0,29160-13 0,30558-13 0,31947-14 0,33336-14 0,34725*15 0,36114*16 0,37503*16 0,38802-17 0,40281-17 0,41670-18 0,43059-19 0,44448- 19 0,45837*20 0,47226-21 0,49615*21 0,50004*22 o,5»393-22 0,52782*23 0,541 7 I '24 0.55560-24 0,56940-25 0,58338*25 0,59727*26 0,011 16'27 0,62505*27 0,63894-28 o,6§283*28 0,66672*29 0,68061*30 0,69450-30 Log. a". 0,01389*01 9,71974-96 9,55051-08 9.43238*76 9,3^225-60 9,26981-63 9,20057-41 9,15824-08 9,11372-80 9,0745643 9,03072-87 0,00846*04 8,98018-18 8,95444*30 8,9308908 8,90923*57 8,88924-38 8,87072*07 8,85350-37 8.8374S*S> 8,82245*73 8,80840-92 8,79522-32 8,78282-30 8,77114-14 8, 76011 94 8,74970*45 8,73985*00 8,73051-44 8,72165-99 8,71325*20 8,70526*28 8,69766*18 8,69042*48 ;<,68352-86 8,67695-24 8,6706767 8,66468-37 8,65895*73 8,65348-21 8,64824*42 8,6432307 8,63842-97 8,63382-97 8,62942-06 8,62519-25 8,62113*63 8,61724*36 8,6x350-65 8,60991-73 Log. a*. 8,60646-92 8,60315-55 8,59997*00 8,5969069 8,59396*07 8,59112-62 8,58839-84 8,58577*28 8,58324*47 8,58081*02 8,57846-52 8,57620-62 8,57402-93 8,57193*13 8,56990-90 8,56795*93 8,56to7-92 8,56426-61 8,56251 72 8,56083-01 8,55920-33 8.55763-15 8,55611-56 8,55465-23 8,55323*98 8,55187-62 8,55055-96 8,54028-82 8,54806-03 8,54687-46 8,54572-89 8,54462-24 8,5435534 8,54252-05 8,54152-24 8,54055-79 8,53962-59 8,53»72-5i 8,53785-45 8,53701-28 8,53619-93 8,53541-28 8,53465-23 8,5339171 8,53320-63 8,53251-89 8,53185-41 (285) Log. r*. 0,70830-31 0,72228*31 0,73617*32 0,75006-33 0,76395*33 0,77784*34 0,79173*34 0,80;,' 0,819s I 31 562-35 1*36 0,83340*36 0,8^720*37 0,86118-37 0,87507*38 0,88806-39 0,90285*39 0,91674-40 0,9306340 0,94452*41 0,95841*42 0,97230*42 0,98610*43 1,00008-43 1,01307*44 1,02786-45 1,04175-45 1,05564*46 1.06953-46 1,08342*47 1.09731*4 1,11120*48 1,12500*49 1,13808-49 '''5?87*5<> 1,16676-51 1,18065*51 1,19454-52 i,2o84VS^ 1,22232-53 1,23621-54 £,25010-54 i,a63oo*55 i,27788*SS 1,29177-56 1,30566-57 1,31955-57 1,33344-58 1.34733-58 1,36122-59 1,37511-60 1,38900-60 Ytan 5« 52 53 54 5 5 5' i9 61 62 63 64 'd 69 70 71 72 73 74 '^ li 81 82 83 'd 89 90 9« 92 93 94 '^ '^ 99 100 P««V R2 LOGARITHMIC TABLES OF 31 P«r Cent. Ytars Log. r*. Log. a". Log. a". Log:, r". Ye*rs 1 0,01^1-55 0,02883-10 0,01441-55 8,61658-14 o,73Si9-»7 5» 2 9> 72053-35 8,61339-61 0,74960-72 52 3 0,04324-66 9>5Si5502 9,43367-98 8,61033-67 0,76402-27 53 4 0,0576621 8,6073976 0,77843-82 ^4 i 0,07207-76 0,08649-31 9.34379-82 9,27160-56 8,60457-33 8,60185-85 0,79285-37 0,80726-93 11 I 0,10090-87 9,21160-74 8,59924-85 0,82168-48 % 0,11532-42 9,16052-46 8,59673-85 0,83610-0? 9 0,12973-97 9,11624-14 8,59432-41 0,85051-58 0,86493-14 59 lO 0,14415-52 9.07731-34 8,5920013 II 12 0.1585707 0,1729863 0,18740-18 9,0427106 9,01167-24 8,58976-61 8,58761-47 • 0,87934-69 0,89376-24 0,90817-79 61 62 «3 8,98362-11 8,95810-76 8,58554-37 ^J •4 0,20181-73 8,58354-97 8,58162-94 0,9225934 54 IS 0,21623-28 8,93477-62 0,93700-90 i6 17 0,23064-84 0,24506-39 8,91333-99 8,89356-40 8,57977-98 8,57799-81 8,57628-15 0,95142-45 0,9658400 i8 0.25947-94 8,87^5 -43 0,98025-55 68 »9 0,27389-49 8,8582480 8,5746275 0,99467-11 1,00908-66 69 20 0,2883 I 05 8,84240-71 8,57303-32 70 21 0,30272-60 8,82761-44 8,5714967 1,02350-21 71 22 o,3»7»4-iS 8,81376-87 8,57001-56 >,0379i-76 72 23 0,3315570 8,8007824 8,5685874 i!o667^-87 1,08116-42 73 24 0,34597-25 0,36038-81 8,78857-90 8,56721-04 74 25 8,77709-16 8,76626-12 8,56588-25 11 26 0,37480-36 0,38921-91 8,56460-18 1,09557-97 27 8,75603-53 8,5633665 1,1099952 ^l 28 0,40363-46 8,74636-72 8,56217-50 1,12441 08 78 29 0,41805-02 8,7372151 8,7285417 8,56102-52 8,55991-60 1,13882-63 29 30 0,4324657 1,15324-18 80 3» 0,44688-12 8,72031 •« 8,71249-89 8,55884-57 1,16765-73 81 32 0,46129-67 8,55781-29 1,18207-29 82 33 0,47571-22 8,70507-13 8,69800-50 8,55681-61 1,19648-84 83 34 0,49012-78 8,55585-40 1,21090-39 84 1^ 0,50454*33 0,51895-88 8,60127-71 8,68486-66 8,55492-53 8,55402-88 1,22531-94 1,23973-49 85 86 37 0,53337-43 0,54778-99 8,67875-41 8,55316-34 »,254i5-o5 1,26856-60 ll 8,67292-19 8,55232-79 88 39 0,5622054 8,66735-37 8,5515212 1,28298- IS 89 40 0,57662-09 8,66203-45 8,55074-23 1,29739-70 90 41 42 0,59103-64 0,60545-19 8,6569<-oi 8,65208-77 8,54999-00 8,54926-35 1,31181-26 1,32622-81 9' 92 43 0,61986-75 8.64743-53 8,642^-18 8,54856-21 8,54788-44 1,34064-36 93 44 0,63428-30 1.35505*91 94 ti 0,6^869-85 0,66311-40 8,63871-66 8,63463-02 8,54723-01 8,54659-79 1,36947-46 1,38389-02 <»3983o-57 v> 47 0,67752-96 8,63071-35 8,54598-73 8,54539-70 % 48 0,6919^-51 0,7063606 8,62695-79 1,41272-12 49 8,623«-56 8,61^-91 8,5448277 1,42713-67 99 SO 0,72077-61 8,54427-70 1.44155-23 100 . . 8.52827-38 J rurp. For explanation see pp. 216-228 (286) COMPOUND INTEREST AND ANNUITIES ^Vw C«Bl Tean I Log. r*. Log. a"* Log. or. Log. »-. Tean 0,01404-03 0,01494-03 8,62656-17 0,76105-78 0,77689-82 51 2 0,02988-07 9,72131-63 8,62350-0- 8,62056-28 52 3 0,04482-10 9.55258-81 0,79183-85 S3 4 0,05976-14 9,43496-97 8,61774-35 0,80677-89 54 i 0,07470-17 9,34533-72 8,6150366 0,82171*92 11 0,08964-21 9.27339-07 8,61243-7* 8,60994-06 0,83665-96 I 0,10458-24 9.21363-59 0,85159-99 5? 0,11952-28 9,16279-32 8,6075419 0,8665403 58 9 0,13446-31 9,11874-74 8,60523-67 0,88148-06 g 10 0,14940-35 9,08005-39 8,60302*11 0,89642*10 11 0,16434-38 9,04568-27 8,60089-11 0,91136-13 61 12 0,17928-42 9,01487-30 8,59884-30 0,92630*17 62 »3 0,19422-45 8,98704-74 8,59687-33 0,94124-20 63 M 0,20916-49 8,96175-67 8,59497-87 0,95618-24 64 \i 0,22410-52 0,23904-56 8,93864-51 8,91742*58 8,59315-60 8,59140-20 0,97112-27 0,98606-31 'd ' 'I 0,25398-59 8,89786-42 8,58971-42 1,00100-34 U 18 0,26802-63 8,87976-57 8,58808-95 1*01594-38 «9 0,28386-66 8,8629678 8,58652-57 1,03088-41 69 ao 0,29880-70 8,84733-25 8,58502*01 1,04582-45 70 21 0,31374-73 0,32868-77 0,34362-80 8,8327426 8,58357-02 1,06076-48 71 • sa 8,81909-67 8,58217-40 i,o757o-52 72 *3 8,80630-76 8,5808292 1,09064-55 73 24 0,35856-84 8,79429-86 8;57828-6o »* 10558-59 74 1 li 0,3735087 8,78300-29 1,12052-62 li 0,38844-91 8,77236-13 8,57708-38 1,13546-66 ! ^ 0,40338-94 0,41832-98 & 76232- IS 8,75283-67 8,57592-53 8,57480-89 1,15040-69 i>»6534-73 11 29 o,4-J327-oi 8,74386-54 8,57373-31 1,18028-76 g 30 0,44821-05 8,73536-99 8,57269-01 1,19522-80 31 0,46315-08 8,72731-67 8,571696s 1,21016-83 81 32 0,47809-ia 8,7196752 8,57073*29 8.56980-39 1,22510-87 82 33 0,49303*15 8,71241-75 1,24004-90 1,25498-94 1,2690297 1,28487-01 83 34 0,50797- 19 8,70551-87 8,69895-57 8,5689083 8,5680446 84 % 0,52291*22 85 0,53785-26 8,69270-7^ 8,68675-46 8,68107-96 8,56721-18 86 u 0,55279-29 0,56773-33 8,566^087 8,56563-41 8,564M-7i 1,29981-04 1,3147508 87 88 39 0,58267-36 8,67566-61 1,32969-11 89 40 0,59761-40 8,6704989 8.56416-65 1,34463-15 90 4» 42 0,61255-43 0,62749-47 8,66556-43 8,6608492 8.56347-'4 8,56280-09 1,35957 18 1,37451-22 9' 92 43 0,64243-50 8,65634-16 8,56215-41 1,38945-25 93 44 0,65737-54 8,65203-04 8,56153-00 1,40439-29 94 45 0,67231-57 0,68725-61 8,64790-53 8,64395-66 8,56092-79 1,41933-32 95 46 8,56034-69 1,43427*36 96 J ^l 0,70219-6^ o,7i7i3»68 8,64017-52 8,5597864 1,4492.-39 97 ' 48 8,63655-27 8,63308-11 8,55924*54 8,55872-35 1,46415-43 98 49 0,73207-71 1,47909-46 99 50 0,74701-75 8.62975-31 8,55821-06 8,5440680 1,4940350 100 Petp (287) i r I' :l!::.l LOGARITHMIC TABLES OF I s 3 4 « I 9 lO II 12 '9 20 31 23 23 24 29 30 31 3* 33 34 f? 3 39 40 41 42 43 44 45 46 ^1 48 49 50 31 P» Cmi. Log- »*• 0,01546-45 0,03092-91 0,0^59-36 0,06185*83 0,07732*27 0,09:7873 0,10825' 18 0,12371-63 0,13918-09 o> 15464-54 0,17011-00 °»i8557-45 0,20103-91 o,2i65o-.q6 •36 -83 0,23196 0.24743-27 0,2628972 0,27836-18 0,2938263 0,3092909 0,32475-54 0,34022 00 o>35568-4S o,37"4-90 0,38661 •a6 0,40207-81 0,41754-27 0,43300-72 0,44847-18 0,46393-63 0,4794009 0,49486-54 0,5*032 '99 0.52579-45 0,54135-90 0.55672*36 0,57218-81 0.58765-27 0,6031173 0,61858-17 0,63404-63 0,6^51-08 o»66497-54 0,68043-99 0,69590-45 0,71136-90 0,72683-35 0,74229 81 o> 75776-26 0,77333-73 Log. a". 0,01546-45 9,72209-80 9.55362-44 9.4362572 9,34687-31 9.27517-19 9.»i565-94 9,16505-60 9,12124-62 9,08278-59 9,04864-47 9,oi8o6'33 8,9904607 5.96539-" 8.94249-77 8,92149-36 8,00214-43 8,88435-49 8,86766-33 8,85333-13 8.8378418 8.82439-36 8,81170-91 8,70008-20 8,7^7-52 8,77841-97 8,76856-33 8,75925-90 8, 75046-55 8,74214-50 8,73426-39 8,72679-19 8,71970' 10 8,71396-63 8,7065648 8,700^7-54 8,69467 -89 8,67i 8,67408-76 8.66951-59 8,66514*94 8,66097-69 8.65698-79 5.65317-23 8,6495228 8,64602-93 8.64268-44 8.63948-08 Log. a*. 8,63641-15 8,633^7-00 8,63065-02 8,62794-62 8,62535-28 8,62286-^5 8,62047-69 8,61818*53 8,61598-50 8,61387-32 8,61184-31 8,60089-39 8,60802*13 8,60633-17 8,60449-31 8,60282*94 8,60123-11 8,59969'4i 8,59821-61 8,59679*46 8,59542-71 8,59411*16 8,59284-57 8,59162-77 5.59045-57 5,58932-74 5.55834-15 8,58710-61 8,58618-97 8,5853307 8,58428-77 8,58338-9« 8,58252-38 8,5816904 5-55088-76 8,58011-44 5'57796o3 8,5772941 5.5766533 5.57603-37 5>57543-75 5'57486*3o 5'S7430-94 f»57377-57 8,57326-15 5'57276-57 8,57328*78 8,57»82-7i $,5593080 For explanation see pp. 216-228 Log. 0,78869-17 0,80415-63 0,81962-08 0,83508-54 0,55054-99 0,86601 '44 0,88147-90 0,8969435 0,91240-81 o,93787*26 0.94333-72 0,95880-17 0,97426*62 0,98973*08 *'005i9*53 i,03o6s*99 1,03613-44 1,05158-90 1,06705-35 1,08251*81 1,09798-26 ».i»344-7* 1,13891-17 «,i4437'63 1,15^-08 <»« 753053 1,19076-99 1,30633-44 1,22169-89 «> 237 16-35 1,25262-80 1,26809-26 «»28355-7i 1,39903*17 1,3144863 1,32995-07 1.34541-53 1,36087-98 >.37634-44 i,39»8o-89 1,40727-35 1,42273-80 1,43820-26 i>4S366*7i 1,46913-16 1,48450-63 1,50006-07 i,5i552 53 1,5309898 '»54645-M Tomb 51 52 53 54 5 5 9 61 62 63 64 69 70 71 72 73 74 '^ 81 82 1^ 1^ 1^ 89 90 9» 92 93 94 9! 99 100 Peip. (288) COMPOUND INTEREST AND ANNUITIES Yean I 2 3 4 5 6 I 9 10 II 12 13 14 \l 17 18 19 20 21 22 23 24 'J ^9 30 31 32 33 34 39 40 41 42 43 44 % % 49 50 Log. r". 0,01598-81 0,03197-62 0,04796-43 0,06395-24 0,0799405 0,09592 -86 0,11191-67 6,12790-48 0,14389-29 0,1598811 0,17586-92 0,19185-73 0,20784*54 0,22383-35 0,23982-16 0,25580-97 0,27179-78 0,28778-59 0,3037740 0,31976-21 0.3357S-02 0,35173-83 0,36772-64 0,38371*45 0,39970-26 0,41569-07 0,43167-88 0,4476670 0,46365-5' 0,47964-32 0,49563- 13 0,51161-94 0,52760-75 0,5435956 0,55958-37 o,57SS7-»8 o,59»5S-99 0,60754-80 0,62353-61 0,63952-42 0,65551-23 0,67150-04 0,6874885 0,7034766 0,71946-47 0,73545-28 0,7514410 0,76742-91 0,78341-72 0,7994053 4 Per Cent. Log. a" 0,01598-81 9,72287-86 9,5546588 9.4375425 9,34840-59 9,2769492 9,21767-79 9,16731-26 9 1237379 9,08550-94 9.05159-71 9,02124-02 8,99386-12 8,96901-11 8,94633-40 8,92554-32 8,90640-40 8,88872-20 8,87233-45 8,85710-38 8,84291-25 8,82965-95 8,8172572 8.8056203 8,70470-89 8,7844369 8,77476-09 8,7656343 !'7S7oi-55 8,74886-70 8,74115-52 8,7338495 8,72692-23 8,7203485 8,71410-50 8,70817-10 8,70252-72 8,69715-60 8,69204-10 8,68716-73 8,68252*09 8,6780890 8,6738597 8,66982- 19 8,66596-52 ■ 8, 662 28 01 8.65875-75 8,65538-91 8,6521669 8,6490837 Log. c^. Log. 8,64613-25 8,6433069 8,6406006 8,6380081 8,6355238 8,63314-26 8,63085-99 8,62867-09 8,6265714 8,6245574 8,62262-50 8,62077-05 8,61899-00 8,61 728- 18 8,61564-11 8,61406-56 8,61255-26 8,61109-89 8,60970-26 8,60836-09 8,60707-iS 8,60583-25 8,60464-16 8,6034967 8,60239-62 8,60133-80 8,6003205 8,59934-21 8,59840-11 8.5974960 8,5966254 8,5957879 8,59498-22 8,5942071 8,59346-13 8,59274-37 8, 59205 -31 8,59138-85 8,5907489 8,59013-33 8,5805408 8,58897-05 8,58842-14 8,^8789-29 8,58738-41 8,1^8689-42 8,58642-26 8.58596-86 8.58553- 13 8,58511*03 8.57493*13 0,81539-34 0,83138-15 0,84736-96 0,86335-77 0,87934-58 0,89533-39 0,91132*20 0,9273101 0,94329-82 0,95928-63 0,97527-44 0,99126-25 1,00725*06 1,0232387 1,03922-69 1,05521-50 1,07120-31 1,08719-12 1,10317-93 1,11916-74 1,13515-55 1,15114-36 1. 16713-17 1,18311-98 1. 19910-79 1,21500-60 1,23108-41 1,24707-22 1,26306-03 1,27904-84 1,29503-65 1,31102-46 1,32701-27 i,343«509 1,35898-90 1.374977 » 1,39096-52 1,40695-33 1,42294-14 1.43892-95 1. 45491-76 1,47090-57 1,48689-38 1,50288- 19 1,51887-00 1,53485-81 1,55084-62 1,56683-43 1,58282-24 1,59881-05 Yean 51 52 53 54 5 II 61 62 67 68 69 70 71 73 73 74 81 82 83 84 u 87 88 89 90 91 92 93 94 95 96 97 98 99 100 Perp. I I (289) LOGARITHMIC TABLES OF :: ! W Years i 7 8 9 lO u 12 •9 20 21 22 23 24 25 26 1^ 29 30 31 32 33 34 3 37 38 39 40 41 42 43 44 46 47 48 49 50 Log. r*. 1 0^01651*10 2 0,03302-21 ? 0.04953 3 « 4 0,06604-41 0.08255-52 0,09906-02 0,1155773 0,1320883 0,1485993 0,1651 1 04 0,18162*14 0,19813-24 0,21464*35 0,23115-45 0,2^766-56 0,26417-66 0,28068 76 0,29719-87 0*3*370-97 0,33023-07 <>>34673i8 0,36324-28 0,37975-38 0,3962649 o,4» 277-59 0,42928-70 0,44579-80 0,46230-90 o,478»2-oi o,49S33<« 0,51184-21 0,52835-32 0,5^86-42 o,5o'37-53 o>577^-63 0,5943973 0,61090-84 0,62741-94 o> 64303 04 0,66044-15 0,67695-25 0,69346-35 0,70997-46 0,7264856 0,74299-67 0,7595077 0,77601-87 0,79252-98 0,80904 08 0,82555-18 3S P«r CMit. Log. a-. o,oi66-35 Loj?. For explanation see pp. 216-228 8,65572-6^ 8,65301-26 8,65041-60 8,6479308 8,64555-17 8,64327-3 327-35 109-16 8,64 8,63900- 14 8,6369986 8,6350792 8,63323-9^ 8,63147-56 8,62078-43 8,62816-23 8,6266065 8,62511-40 8, 62368 20 8,62230-79 8,62098-91 8,61972-33 8,61850-82 8,61734-17 8,61622-15 8,61514-59 8,61411-30 8,61312-08 8,6i3i6'79 8,61125-24 8,61037-30 8,60952-79 8,60871-60 8,60730-58 8,60718-60 8,60646-54 8,60577-28 8,605 1072 8,60446 73 8,60385 -22 8,6032608 8, 60269 23 8,60214-55 8,6016200 8.60111-46 8,6006286 8,60016-13 8,5997»-»8 ■ 8,59927-96 8,5988640 8,59846*42 8,50807-96 8,588a2-i7 Log. r*. 0,84206 -29 0,85857-39 0,87508-50 0,891 59-60 0,90810*70 0,92461-81 0,94112-91 0,9576401 0.9741C12 0,99060*22 1,00717-32 1,02368-43 1,04019-53 1,05670-64 1.07321-74 1,08972-84 1,10623-95 1,12275-05 1,1392615 i.»5577-26 1,17228-36 1,18879-46 1,20530-57 1,22181-67 i,2.?832-78 1,25483-88 1,27134-98 1,2878609 1.30437-19 1,32088-29 ».33739-40 '.35390-50 1,37041-61 1,38692-71 1,40343-81 1,4199^-92 1,4364602 1.45297-12 1,46948-23 ».48S99-33 1,50250-43 1.51901-54 1.53S52-64 1.55203-75 .1.56854-85 '.58505-95 1,6015706 1,61808 16 1.63459-26 1.65110-37 Tean 51 S» 53 54 5 I 59 60 61 62 63 66 67 68 69 70 71 72 73 74 li II L' 81 82 84 85 86 87 88 89 90 9' 92 93 94 99 100 Perp. COMPOUND INTEREST AND ANNUITIES (290) Veara 1 2 3 4 I 9 10 II 12 13 14 1^ M '9 20 21 22 23 24 % 29 30 3' 32 33 34 % % 39 40 41 42 43 44 45 46 % 49 50 Log. r". 0,01703-33 0,03406-67 0,0511000 0.06813-34 0,0851667 O, I0220'00 0,11923-34 0,13626-67 0,15330-01 0,17033-34 0,18736*67 0,20440*01 0,22143-34 0,23846-68 0,25550-01 0,27253-34 0,28956-68 0,30660-01 0,32363-34 0,34066 68 0,35770-01 0,37473- 0,39176 0,40880-01 0,42583 -.^5 0,44286-68 0,45990*02 0,47693-35 0,4939668 0,51100-02 0,52803-35 0,54506-69 0,56210*02 0,5791.3-35 0,59616-69 0,61 ^20-0''. 0,63023*3(5 0,6472669 0,66430*02 0,68133*36 0,69836-69 0,71540*03 0,73243-36 0,7^946-69 0,76650*03 o,78353-.36 0,8005669 0,8176003 0,8346336 0,85166-70 P«r Cent. Log. a*. 0,01 703* « 9.72443-65 9,55672-28 9.44010*59 9.35146-22 9,28049*16 9,22170-01 9,17180*78 9, 1 2869-97 9,09093-12 9.05747-23 9,02756*23 9,00062*38 8,97620*77 8,95395-82 8,93358-85 8,91486*40 8,85759-04 8,88160-50 8,86677*02 8,85296-84 §,84009*86 8,82807*3$ 8,81681-66 8,80626- 12 8,79634-80 8,78702-48 8,7782^-52 8,76996-73 8,76215*40 8,7547714 8,7477892 8,74117-97 8,73491-80 8,72898*10 8,72334-80 8,71799-95 8,71291-83 8,70808-79 8.70349-33 8,69912*00 8,69495*78 8,69099-20 8,68721-27 8,6836094 8,68017-27 8,67689*37 8,67376-39 8,67077*56 8.66792-16 Log. a" 8,66510*48 8,6625800 8,66009-81 8,65771*64 8,65543*85 8,65325*96 8,65117*45 8,64917*91 8,64726*91 8,6454404 8,64368*93 8,64201*22 8,64040*56 8.63886-65 8,63739*16 8,63597-82 8,63462*35 8,63332-48 8,63207-97 8,6308859 8,62974*11 8,62864*32 8,62759*01 8,62657-99 8,62561-08 8,62468*09 8,6237889 8,62293*26 8,62211-11 8,62132*25 8,6205656 8,61983-91 8,61914-16 8,61847*21 8,61782-92 8,61721-20 8,61661-94 8,61605-03 8,61550-38 8,61497-89 8,61447-48 8,61399-08 8,61352-58 8,61307-91 8.61265-01 8,61223-80 8,61184-21 8,61146*18 8,61 109-64 8,61075*53 8,60200*00 Log. r". 0,86870*03 »,88573-36 0,90276*70 0,9198003 0,9368337 0,95386-70 0,97090-03 0,98793-37 1,00496*70 1,02200*04 1,03903-37 1,05606-70 1,0731004 1.09013-37 1,10716*71 1,12420*04 1.14123-37 1,15826-71 1,1753004 1.19233-38 1,30936*71 1,22640-04 1.2434338 1,26046-71 1,37750-04 1,29453-38 1.31156-71 1,32860-05 1.34563-38 1,36266-71 1,370700s 1.39673-38 1.41376-72 1,43080-05 1,44783-38 1,46486-73 1,4819005 1.49893-39 i.5'S96-72 1.53300*05 1.5500,3-39 1,56706-72 1,5841006 1,60113-39 1,61816*72 1,63520*06 1,65223*39 1,66936*73 1,68630-06 1.70333-39 Ye»n S» s» 53 54 5^ 57 58 60 61 63 63 64 % 67 68 69 70 71 73 73 74 ]i \l IS, 81 83 83 84 85 86 1^ 89 90 9» 93 93 94 ^? 9t 98 99 100 Perp. (291) \ f m ! J Hi LOGARITHMIC TABLES OF Years I 3 3 4 I I 9 lo II 12 «3 M 20 21 «3 24 2 2 2 29 30 31 3a 33 34 ^4 39 40 41 4a 43 44 :^ 49 |0 Log. »*. 0,035 II 00 0,0526650 0,0702201 0,08777-51 o»">S3.roi 0,12288-51 0,1 4044 01 o> 1579951 o.»755Soi o.»93»o*52 0,2106602 0,22821-52 0,24577-02 0,26332-52 0,2808802 o. 29843-52 o>3i599 03 0.33354-53 o.3S»>oo3 0.36865-53 0,38621-03 0,40376-53 0,42132-03 0,43887-54 0,45643-04 0.47398-54 0,49154-04 0,5090954 0,5266504 0,54420-54 0,56176-05 0.57931-55 0,59687-05 0,61442-55 0,6319805 0.64953-55 0,66709-05 0,68464-56 0,70220-06 0,7197556 0,73731-06 0,75486-56 0,77242-06 0,78997*56 0.80753-07 0,82508-57 0,84264-07 0,86019-57 0,8777507 § Per Cent. Log. a". 0.01755-50 9,72521-38 9.55775-22 9.44138-41 9.3529856 9,28225-70 9,22370-38 9,1740465 9,13116-98 9,09362-95 9.06039-52 9,0307066 9,00398-60 8,97978-44 8,95774-61 8,93758-43 8,91906-43 8,90199 19 8,88620-44 8,8715642 8,85795-38 8.84527-23 8,83343-21 8,82235-70 8,81198-01 8,80224-25 s! 78448-13 8.77636-97 8,76871-95 8,761^9-70 8,75467-20 8,74821-68 8,74210-64 8,73631-76 8,7308304 8,72562-48 8,7206834 8,7*599-02 8,7i»53oo 8.70728-94 8,70325*53 8,69941-61 8,69576-03 8,69227-85 8,6889605 8,68570-77 8,68278-17 8,67990-48 8,67715-96 Lopr. a". 8,67453-95 8.67203-7S 8,66964-88 8,66736-68 8,66518-65 8.66310-27 8,66111-09 8,65920-66 8'65 73854 8.65564-36 8.65.W-73 8,65238-31 8.65085-75 8,64939-74 8,6479998 8,64666-16 8,6453804 8,64415-35 8,64297-84 8,64185-29 8,64077-48 8,63074-18 8,63875-20 8.63780-36 8,63689-47 8,63602-38 8,63518-88 8,6343884 8,63362-11 8,63288-56 8,6331803 8,63150-40 8.63085-55 8,63023-37 8,62963-73 8,62006-52 8,62851-67 8,62799-04 8,62748-56 8,62700-13 8,62653-67 8,62609-10 8,6256634 8,6252532 8,6248595 8,62448-18 8,62411-93 8.62377-15 8.62343-77 8.62311-74 8,61542:40 For explanation see pp. 216 228 (292) Log, r*. 0,89530-57 0,9128607 0,9304 « 58 o,9jf797-o8 0,9655258 0,98308-08 1,00063-58 1,01819-08 »,03574-58 ",05330-09 1,07085-59 1,08841 -09 >> 10596-59 «, 1 2352-09 '>i4'07-59 1,15863-/0 1,1761860 1,19374-10 1,21129-60 1, 22885- 10 1,2^640*60 1,26396-10 1,28151-61 1,29907-11 1,31662-61 1,33418 II »,3Si 73 61 1,36929-11 1,38684-61 1,40440- 1 2 1,42195-62 i,4395»-»2 1,45706-62 1,47462-12 1,49217-62 1,50973-12 1,5272863 1,54484-13 1,56239-63 «,57995-»3 «,S9750-63 1,61506-13 1,63261-63 1,6501 7- 14 1,66772-64 1,6852814 1,70283-64 ',7203914 ». 7379464 i. 7555014 Years 5» 52 53 54 i 61 62 69 70 71 72 73 74 li 81 82 ?^ u 89 90 91 92 93 94 9 9 '^ 99 100 Ptrv COMPOUND INTEREST AND ANNUITIES Years I 2 3 4 i I 9 10 II 12 13 •4 •5 16 >7 18 »9 20 21 22 23 24 21 2 29 30 31 32 33 34 35 36 39 40 41 42 43 44 47 48 49 50 Log. r". 0,01807-61 0,03615-21 0,05422-82 0,07230-43 0,09038-03 0,10845-64 0,12653-24 0,14400-85 0,16268-46 0,18076-06 0,19883-67 0,21691-28 0,2349888 0,2530649 0,27114-10 0,28921-70 o,.^o729-3i o,32536-9» o,.M344-52 0,3615213 0.37959*73 0,39767-34 0,41574-95 0,43382-55 0,45190*16 0.46997-77 0,48805-37 0,50612-98 0,52420-58 0,54228-19 0,56035-80 0,57843*40 0,59651-01 0,61458-62 0,63266-22 0,65073-83 0,66881-44 0,68689-04 0,7049665 0,72304-25 0,74111-86 o. 759 » 947 0,77727-07 0,79534-68 o.§i342-29 0,83149-89 0,84957-50 0,86765-11 0,88572-71 0,90380-31 Log. a 0,01807-61 9,7259901 9,5587801 9,44266-01 9.3545062 9,28401-84 9,22570-26 9,17627-92 9. '3363-29 9,0963 1 94 9,0633085 9.0.3383-97 9,00733-55 8,9833469 8,961; I 80 8,9415622 8,92324-48 8,9063717 8,8907801 8,87633-24 8,86291*12 8,85041- 8,8387s 8,82786-22 8,81766-13 8,80809-65 8. 799" 55 8,70067-16 8,78272-3^ 8,77523*30 8,76816-83 8,7614975 8,75519*36 8.74923-13 8,74358-80 8,73824-30 8,73317*68 8,72837-21 8,72381-26 8,71948-36 8,71537*12 8,71146-29 8,7077466 8,70421-13 8,70084-71 8,69764-42 8,69459-41 8,69168-82 8,68891-89 8.68627-91 4 Per Cent. Log. a". 8,68376-10 8,68136-08 8,67907-02 8,67688-42 8,67479*75 8,67280-54 8,67090-29 8,66908-58 8,66735-01 8,66569-14 8,66410*64 8,6625914 8,66114*32 8,65975*84 8,6584343 8,65716-79 8.65595-66 8,6547078 8,65368-02 8,65262-84 8,65161-3^ 8,6506418 8,64971-21 8,64882-20 8,64796-99 8,64715-40 8,64637-30 8,64562-« 8,64490-89 8,64422-30 8,64356-61 8,6429368 8,64233-41 8,6417569 8,64120-37 8,64067-38 8,64016-61 8,6396797 8,63021-36 8,63876-70 8,63833-01 8,63792-80 8,63753-58 8,63715-92 8,63679-81 8,63645-21 8,6^612-04 8,63580-26 8,63549-78 8.6v';20-58 8J»'28i8-89 (293) Log. »*. 0,92187-92 0,93995-53 0,95803-14 0,97610-74 0,99418-35 1,01225-96 1,0.3033-56 1,04841-17 1,06648-78 1,0845638 1,10263-99 1,12071 59 1,1387920 1,15686-81 1,17494-41 1,19302-02 1,21109-63 1,22917-23 1,24724-84 1,26532-45 1,283400s 1,30147-66 i,3'9.S5'26 1,3376287 1,3557048 1,3737808 1,39185-69 1,40993 -.30 1,42800-90 1,44608-51 1,46416-12 1,48223-72 1,50031-33 i,5»838-93 1,53646-54 1,55454' 15 1,57261-75 1,59069-36 1,60876-97 1,62684-57 1,64492- 18 1,66299-79 1,68107-39 1,69915-00 1,71722-60 1,73530-21 1,75337-82 1,77145*42 1,7895303 1,80760-64 Years 51 52 53 54 % 61 62 63 64 ^6^ 69 70 71 72 73 74 ?? & 81 82 1^4 89 90 91 92 93 94 9' 99 100 Perp. ii f^ t T. Hi i f fi LOGARITHMIC TABLES OF 8 41 42 43 44 4 47 48 49 50 Tews 1 2 3 4 I 9 10 II 12 «3 M 1^ \l 19 20 21 22 »3 24 ^9 30 31 32 33 34 3 3 39 40 Log. »*. 0,01859-65 o.037i9'3o o»oS57«*9S 0,07438-60 0,0929824 0,11157-89 0,1301754 0,14877-19 0,16736-84 0,1859649 0,20456-14 o,"3iS79 o^24«7S-44 0,26035-08 0,27894-73 0.29754-38 0,3161403 0,3347368 0,3533333 0,37192-98 0,39052-63 0,40912-27 0,42771-92 0,44631-57 0,46491*22 0,48350-87 0,50210-52 0,52070-17 0,53929-82 0,55789-47 0,57649-11 0,59508-76 0,61368-41 0,6322806 0,65087-71 0,66947-36 0,68807-01 0,7066666 0,72526-31 0,74385-95 0,76245-60 0,78105-25 0,7996490 0,81824-55 0,83684-20 0,8554385 0,87403-50 0,89263-14 0,91122*79 0,92982-44 Log. 0,01859-65 9,72676-52 9,55980-63 9,44393-37 9,35602-36 9.28577*58 9,22769-65 9,17850-60 9, 13608-89 9,09900-10 9,06621-22 9,03696-18 9,01007-23 8,98689-51 8,96527-40 8,9455 2 24 8,9274058 8,9107300 8,80533-21 8,88107-48 8.86784-06 8,8555285 8,84405-12 8.82330-50 8,81391-05 8,801509-64 8,79^1-64 8,78902-88 8,78169-64 8.77478-56 8,76826-60 8,76211-02 575629-31 8,75079-21 8,74558-62 8,7406564 8,73598-50 8,73»5S-S2 8,72735-50 8,7*336-76 8,7195814 8,7*598-45 8,71256-62 8, 7093 '-63 8,70622*51 8,70328-41 8,70048-49 8,69781-98 8.69528-17 Per Cent. Log. a"' 8,69286*38 8;6883i38 8,68627-02 8,68427*38 8,68236-96 8,68055-30 8,67881-98 8,67716-57 8,6755867 8,67407-93 8,67263*99 8,67126-54 8,66995-25 8,66869-85 8,6675003 8.6663J-55 8,66526- 14 8,66421*58 8,66321-63 8,66226-11 8,66134-77 8,66047-44 5.65963-94 8,65884-09 8,65807-72 5.65734-67 8,6566481 5'65597'98 8,65534*05 8,65472-89 8,65414-36 8,65358-36 5,65304-78 5,65253-53 8,65204*46 5'65i57-5o 8,65112-55 f.65060-54 8,65028*37 5,64988-95 8,64951-24 5,64915-13 8.64880*56 8,64847-46 8,64815-78 5,6478544 8,6475640 8,64728-59 8,64701 06 &64P07-BI For explanation see pp. 216-228 (294) Log. »-. 0,94842*09 0,96701*74 0,98561*39 1,00421-04 1,02280-69 1,04140-34 ',05099-98 1,07859-63 1,09719-28 >,»»578 93 «,«3438-58 1,15298-23 »,i7i57-88 '''9017-53 1,20877-18 1,22736-82 1,24596-47 1,26456*12 «,283iS-78 ".30175-42 '.32035-07 «.33894-72 ».35754-37 1,37614-01 1,39473-66 1.4I333-3I 1,43192-96 1,45052-61 1,46912*26 1,48771-91 ",50631 -56 1,52491-21 ".54350-85 1,56210*50 1,58070-15 1,5992980 1,61789-45 1,63649-10 ',65508-75 ".67368-40 1,69228-05 1,71087-69 ',72947-34 1,74806-99 1,76666-64 1,78526-29 1,5038594 1,82245-59 1,84105-24 1,8596488 Teara 5' 5» 53 54 5 I 6i 62 69 70 71 7a 73 74 81 82 89 90 91 92 93 94 99 100 COMPOUND INTEREST AND ANNUITIES 1 2 Per Cent Y—nl Log. r" I 2 3 4 i i 9 10 II 12 13 14 \i 17 18 '9 20 21 22 23 24 2 2 2 i 29 30 31 32 33 34 li % 39 40 41 42 43 44 % 49 50 0,01911-63 0,03823-26 0,05734-89 0,07646-52 0,09558- 1 5 0,11469-77 0,13381-40 0,15293-03 o, 1 7204-66 0,19116*29 0,21027-92 0,22939-55 0,24851-18 0,26762-81 0,28674-44 0,3058606 0,3249769 0,34409-32 0,363209 0,382325 0,40144-21 0,4205584 0,43967-47 0,45879-10 0,47790-73 0,49702-36 0,51613-98 0,53525-61 0,55437-24 0,57348-87 0,59260-50 0,61172-13 0,63083 76 0,64995-39 0,66007-02 0,68818-65 0,70730-27 0,72641-90 0,7455353 0,76465- 16 0,7837679 0,8028842 0,82200-05 0,84111-68 0,86023-31 0,87934-94 0,89846-57 0,91758-19 0,93669-82 0,95581-45 Log. a\ 0,01911-63 9,72753-93 9,56083-09 9,44520-50 9,35753-78 9.28752-94 9,22968-56 9,18072-68 9, '3853-79 9,10167-43 9,06910-61 9,04007-27 9,01399-67 8,9904291 8,96901-41 8,9494650 8,93154-73 8,91506-67 8,8998607 8,88579-16 8,87274-21 8,86061-13 8,84931-18 8,83876-74 8,82891-13 8,81968-46 8,81103-49 8,80291-60 8,7952863 8,78810-85 8,78134-92 8,77497-81 8,7689674 8,76329-26 8,7579306 8,7528608 8,74806-41 8,74352-30 8,73922-14 8,735"4-4H 8,73127-9' 8,7276118 8,72413-12 8,72082-64 8,71768-73 8,71470-45 8,71186-91 8,70917-3' 8,70660-87 8,70416-90 Log. a" 8,7018469 8,69963-65 8,69753-17 8,69552*71 8,69361-74 8,69179*78 8,69006-37 8,68841-06 8,68683-47 8,68533-19 8,68389-87 8,68253-16 8,6812274 8,67998-31 8,67879-57 8,67766-24 8,6765807 8,6755480 8,67456-22 8,67362-09 8,67272-20 8,67186-36 8,67104-37 8,67026-06 8,66051-2 8,66879-7 8,66811-51 8,66746-27 8,66683-9 8,66624-3 8,66567-43 8,6651302 8,66461 02 8,66411-32 8.66363-81 8,66318-40 8,66274-98 8,66233-48 8,66193-80 8,66155-86 8,6611959 8,66084-91 8,6605 1*74 8,66020-04 8,65989*71 8,65960-71 8,65932-98 8,65906*46 8,65881*10 8,65856-85 8,65321*25 Log, r". Yean 0,97493-08 0,99404-71 1,01316-34 1,0322797 1,05139-60 1,07051-23 1,08962-86 1,10874-48 1,12786*11 1,14697-74 1,16609-37 1,18521-00 1,20432-63 1,22344-26 1.2425589 1,2616752 1,28079-15 1,29990-78 1,31902-40 1,33814-03 1,35725-66 1,37637-29 1,39548-92 1,41460-55 ',43372-18 1,45283-81 ',47'95-44 1,49107-07 1,51018-69 ',52930-32 1,54841-95 ',50753-58 1,58665-21 1,60576-84 1,62488-47 1,64400-10 1,66311-73 1,68223-36 1,70134-98 1,72046-61 1,73958-24 1,7586987 1,77781-50 ',79693-13 1,81604-76 1,83516-39 1,85428-02 ',8733965 1,89251*28 1,91162-90 5* $3 54 61 62 63 64 65 66 67 68 69 70 7" 72 73 74 \l II 79 8c 81 82 83 84 85 86 87 88 89 90 9' 92 93 94 95 95 9/ 99 100 Perp (295) LOGARITHMIC TABLES OF ll I Years 1 2 3 4 Log. r*. 0,01963-55 0,03927-09 0,0589064 0,07854-19 0,09817-74 0,11781-28 0'»3744-83 o.»S7o8-38 0,17671-93 o> 1963547 0,2159902 o>«3S62S7 0,2552611 0,27489-66 o»294S3'2i o,3i4»6-75 0,33380-30 o>35343-85 0,37307*39 0,3927094 o>4"34'49 0,4319804 0,45*61 58 0-47I25I3 0,4908868 0,51052-22 0,53015-77 0.54979*32 0,5694287 0,58906-41 0,60869-96 0,62833-51 0,64797-05 0,66760-60 0,68724-15 0,7068770 0,72651*24 0,7461479 0,76578*.^ 0,78541*88 0,80505-43 0,82468-98 0,84432-53 0,86396-07 0,8835962 0,90323*17 0,92286-71 0,94250-26 0,96213-81 0,98177-36 41 8 P«r Cent Lop. a". o;oi963-55 9,72831-23 9,56185-38 9,44647*40 9,3590490 9,28927-90 9,2316698 9,18294-10 9,14097-98 9,10433-93 9,0719905 9.04317*27 9,01730-84 «»99394*89 8,97-^73-83 8,9533899 8,93566-93 8,91938-2 r 8.00436-58 8,8904829 8,87761-60 8,86566-43 8,85454-04 8,84416-79 8,8344805 8,825418^ 8,81693-11 8,8089707 8,80149-62 8,7944703 8,7878596 8,78163-38 8.7757656 8,77022-99 8,76500-40 8,76006-73 8,7554006 8,7509867 8,74680-94 8,7428539 8,73910-67 8.73555-52 8,732«8-74 8,72899-29 8,72596-13 8,7230835 8,7203504 8.71775-43 8,71528-73 8,71294-24 For explanation see pp. 216-228 Log-, ef. 8,71071-30 8,70859-26 8,70657-58 8,70465-67 8,70283-03 8,70109-20 8,69943-60 8,6978608 8.69635-97 8,69492-98 8.6935676 8,69226-94 8,69103-24 8,6898532 8,68872-92 8.68765-77 8,68663-58 8,68566-15 8,68473-23 8,6838459 8,68300-05 8,68219-39 8,68142-44 8,68069-0^ 8,67998-95 8,67932-11 8,67868-30 8,67807-40 8,6774928 8,67693-79 8,6764083 8,67590-27 8,67542-00 8.6749590 8,67451-90 8,67409-89 8.67369-77 8.67331-45 8,6729485 8,67259-91 8,6722654 8,67194-66 8,67164-22 g.6713514 8,67107-38 8,6708084 8,67055-51 8,67031-30 8,67008-17 8,66986-08 8,66511-17 (296) i Log. f-. T«Ar« 1,00140-90 1,0210^-45 i,odo68-oo 1,06031-54 '»o7995-o9 1,0995864 I>II922-l8 ',13885-73 I, 15849-28 1,1781283 '>»9776-37 1,21739-92 ''23703-47 1,2566701 '>2763o-56 '>«9594.'" '»3i557-66 1,33521-20 '.35484-75 '>3744»*3o ',394' I 84 '»4»375*39 »»4.U=j8-94 '»45302-49 1,47266-0^ 1,49229-58 ''S"93-»3 '.53156-67 ',55'2o-22 '.57083-77 '.59047 -32 1,61010-86 1,62974-41 ',6493796 1,66901-50 1,68861; -05 1,70828-60 1,7279214 '.74755-69 '.76719-24 1,78682-79 1,80646-33 1,82609*88 '.84573*43 '.86536-97 1,88500-52 1,90464-07 1,92427-62 '.9439' ''6 '.96354*7' 5' 52 S3 54 5 i 61 62 69 70 7« 72 73 74 li 80 81 82 84 85 86 87 88 89 90 9' 92 93 94 9i 99 100 Porp. COMPOUND INTEREST AND ANNUITIES 3 4 P«r Cent Yeus 1 2 3 4 i 9 10 11 12 »3 '4 '5 16 \l '9 20 21 22 23 24 Log. f. % 29 30 31 32 33 34 3 % 39 40 41 42 43 44 t 47 48 49 50 0,02015-40 0,04030-81 0,060^6-21 0,08061 -61 0,1 0077 02 0,12092-42 0,1^107*82 0,16123-23 0,18138-63 0,20154-03 0,22169-43 0,24184-84 0,26200-24 0,28215-64 0,30231-05 0,32246-45 0,34261-85 0,36277*26 0,38292-66 0,4030806 0,4232347 0,4433887 0,46354-27 0,4836968 0,50385-08 0,52400-^8 0,54415-89 0,5643' 29 0,584^6-69 0,60462-09 0,62477-50 0,64492-90 0,66508-30 0,68523-71 0,70539" 0,72554-5' 0,74569*92 0,76585-32 0,78600-72 0,80616-13 0,82631-53 0,84646-93 0,86662-34 0,88677-74 0,90693- 14 0,9270855 0,94723-95 0.96739-35 0,98754*76 1,00770-16 Log. 0,02015-40 9,72908-42 9,56287-51 9,44774-06 9.36055-72 9,29102*49 9.23364-92 9,«85'5-o9 9,14341-46 9,10699-61 9,07486-53 9,04626*17 9,02060*78 8,99745-47 8,97644-69 8,95729*73 8,9397719 8.92367-61 8,9(^4-76 8,8951488 8,88246-23 8,87068-74 8,85973*67 8,84953*41 8,84001-27 8,83111-39 8,82278-54 8,81498-08 8,80765-87 8,80078-20 8,7Q43'*72 8,78823-40 8,78250-53 8,77710-58 8,77201-31 8,76720-63 8,7626667 8,75837-68 8,7543206 8,75048-34 8,74685-14 8,74341-23 8,74015-43 8,7370668 8,734'3-95 8, 73 '36-33 8,7287294 8,72622-99 8,72385*7' 8,72160*37 Log. a" 8,7'946-35 8,7174301 8,7»549-78 8,71366-10 8,71191-48 8,71025-44 8,70867-50 8,70717-27 8,70574*32 8,70438-3? 8,70308-84 8,70185-62 8,7006^-30 8,699 156-60 8,698'5o*24 8,69748-94 8,69652-44 8,69560-54 8,6947297 8,69389-54 8,69310-05 8,69234-29 8,69162-io 8,69093-28 8,69027-69 8,68965-17 8,68905-56 8,6884^-74 8,68794-56 8,6874290 8.68693-64 8,68646-64 8,68601-87 8,68559-15 8,68518-40 8,68479-5.^ 8,6844247 8,68407-12 8,6837339 8,68341 -22 8,68310-52 8,68281-24 8,68253-31 8,68226-66 8,68201-23 8,68176-07 8,68153-83 8,68131-74 8,681 10 67 8,68090-56 8,67669-36 Log. r*. 1,02785-56 1,04800-96 i,o68i6'37 1,08831-77 1,10847-17 1,12862*58 1,14877*98 1,16893-38 1,18908-79 1,20924*19 '.2293959 1,24955-00 1,26970-40 1,28985-80 1,31001-21 1.33016*61 '.35032*01 ',37047 ^i 1,39062-82 1,41078-aa '.43093-62 1,45109-03 1,47124-43 i.49'3983 '.S"SS'24 1,53 '70-64 1,55186-04 1,57201-45 1,59216-85 1,61232-25 1,63247*66 1,65263-06 1,67278-46 1,69293-87 1,71309-27 1,73324-67 1.75340-07 ',77355*48 1,79370-88 1,81386-28 1,83401-69 1,85417-09 1,87432-49 1,89447-90 ',9'463-30 ',93478-70 1,95494" ',97509s' ',995249' 2,oi54»-3a Years ii 5' 52 53 54 61 62 ^^ % % 69 70 71 72 73 74 \i 81 82 1] % 89- 90 9' 92 93 94 99 100 Perp (297) LOGARITHMIC TABLES OF 4 7 8 P«r C«Bt. Yean T 1 a 3 4 i 9 lO II 12 «3 '4 '9 20 21 22 23 24 2 2 2 29 30 31 32 33 34 3 3 37 38 39 40 41 42 43 44 4 47 48 49 50 Log. I*. 0,02067 20 0.04 134 '39 0,06201 '59 0,0826879 0.10335 99 0,1 2403 18 0,14470-38 0,16537-58 0,1860478 0,20671-97 0,2223917 0,24806-37 o>26873-57 0,28940-76 0,3100796 0,33075* '6 0,35142-36 0,37209-55 0,392767s o,4i343-95 o,434"'iS 0,4547834 0,47545-54 0,49612-74 0,51679-93 0,53747-13 0,55814-33 0,57881-53 0,59948-72 0,62015-93 0,64083-ia 0,66150-33 0,68217-51 0,7028471 o, 7235 > '91 0,7441911 0,76486-30 0,78553-50 0,80620-70 0,82687 90 0,8475509 0,86822 29 0,88889-49 0,9095668 0,9302388 0,95091 -08 0,97158-28 0,99225-47 1,01292-67 '.03359-87 1 Log. a". 0,02067 20 9,7298550 9,56389-48 9.44900-52 9,36206-24 9,29276-63 9,2356238 9,18735-42 9,14584-26 9,10964-48 9,o7773'07 9,0493397 9,02389-47 0,00094*66 8,98013-97 8,96118-75 8,94385-53 8,92794-91 8,01330-63 8,89978-94 8,8872813 8,8756810 8,86490- 12 8,85486-59 8,84550-83 8,83676-96 8.82859-78 8,82094-66 8,81377-44 8,80704*41 8,80072-24 8,79477-91 8,78918-68 8,78392-07 8,7789582 8,7742786 8,76986-30 8, 76569-40 8,76175-59 8,75803-37 8,75451*40 8,75118-42 8,74803-29 8,74504-91 8,74222-31 8.73954-54 8,73700-75 8,7346012 8,73231*93 8,73015-45 Log. a" 8,7281003 8,72615-06 8,72429-97 8,722<4-20 8, 72082 27 8,71928-69 8,71778-03 8,71634-85 8,71498-77 8,71369-41 8,71246-42 8,71129-47 8,71018-25 8, 709 1 2 •46 8,70811-83 8,70716-10 8,70625-00 8,70538-33 8,70455-84 8.70377*33 8,70302-61 8,70231-47 8,70x63-75 8,70099-29 8,7003790 8,69979-44 8,69923-78 8,69870-77 8,69820-29 8,69772-21 8,69726-41 8,6968278 8,69641-23 8,69601-64 8,6956393 8,6952800 8,69493-77 8,69461-16 8,69430-07 8,69400*47 8,69372 •2S 8,69345-36 8.69319*74 8,69295-32 8,6927201; 8,69249-8^ 8,69228-74 8,69208-60 8,69189-40 8,69171-11 8,68797-46 I For explanation see pp. 216-228 (298) Log. >*. 1,05427-07 1,07494-26 1,09561-46 1,11628-66 1.1369586 1.1576305 1,17830-25 1,19897-45 1,21964-65 1,24031-84 1,26099-04 1,28166-24 1.30233-44 1,32300-63 1,34367-83 1.36435*03 1,38502-23 1,40569-43 1,42636-62 1,44703*82 1,46271-01 1,48838-21 1.50905*41 1.52972-61 i.SSO.^9-80 1.57107-00 1.59174-20 1,61241-40 1.63308-59 '.65375*79 1,67442-99 1,6951010 1.71577*38 1.73644-58 1,75711 78 1.7777897 1,79846-17 1,81913*37 1,83980-57 1,86047-76 1,88114-96 1,90182-16 1,92249-36 1.94316-55 1,96383-75 1,9845095 2,00518-15 2,02585-34 2,04652-54 2,06719-74 Yem SI 5* S3 54 5 k 61 62 63 64 u 69 70 71 72 73 74 77 78 ^ 81 82 ^•^ 84 85 86 87 88 89 90 91 92 93 94 95 96 97 99 100 COMPOUND INTEREST AND ANNUITIES I Tears I" I 2 3 4 i I 9 10 II 12 13 14 \i \l 19 20 31 22 23 24 29 30 31 S3 34 li % 39 40 41 42 43 44 % 49 SO Leg. 1*. o, o 0,021 18-«3 04237*86 0,0635679 0,08475-72 0,10594-6 0,12713-5 0,14832-51 0,16951-44 0,19070-37 0,21189*30 0,23308-23 0,25427-16 0,27546-09 0,29665-02 0,31783* 0,33902- 0,36021-81 0,38140-74 0,40259-67 0,42378-60 1,46016-46 0,48735*39 0,50854*32 0,52973*25 0,55092-18 0,57311-11 0,5933004 0,61448-97 0,63567-90 0,65686-83 0,67805 'lb 0,69924-69 0,72043-62 0,74162-55 0,76281-48 0,78400-41 0,805 iQ-34 0,82638-27 0,84757-20 0,86876-13 0,88995*00 0,91113*99 0,93232-93 0,95351*85 0,97470*78 0.99589*71 1,01708-64 1,03827-57 1,05946-50 Log. t^. 5 pm* 0,02118-9^ 9,73062-48 9, 56491 '<8 9,450 26-7* 9,30356*45 9,29450-47 9,2375936 9,18955 15 9,1482635 9,11328-51 9,0805865 9,05240-70 9,02716*92 9.00442-44 8,98381*70 8,96506-01 8,94791*94 8,9^220-08 8,91774-18 8,90440-49 8,89207-30 8,88064-50 8,87003-40 8,86016-37 8,85096-74 8,842^866 8,8343689 8,82686-83 8,81984-33 8,81325-70 8,8070756 8,8012694 8,79581-08 8,79067-52 8,78584-01 8,78128-46 8,77699-01 8,77293-92 8,76911-60 8,7655058 8,76209-53 8,75887*19 8,75582-41 8,75294-11 8,75021-31 8,74763*09 8,745'8-58 8,7428698 8.74067-57 8,73859*61 Gwt. Log. tT- 8 73662-40 8,7347S*5» 8,7329832 8,73130-16 8,72970-62 •8,72819-22 8,72675-52 8,72539*10 8,72409*57 8,72286-57 8,73160-75 8,72058-78 8,71953*37 8,7i8S3*5«> 8,yi75»«2 8,71667-58 8,71581 60 8,7149988 8,71422 21 8,7134834 8,71278-11 8,71211-34 8,71147*85 871087-46 8,7103003 8,70975*40 8,70923*43 8,7087400 8,70826-98 8,70782-24 8,70739-67 8,70699-17 8,70660-63 8,70623-97 8,70589-07 8,70555*86 8,70524-26 8, 70494- 18 8.70465*56 8,70438*32 8,70412*39 8,70387*70 8,70364-21 8,70341*85 8, 70320-56 8,70300-30 8,70281*04 8,70262-64 8,70245-16 8,70228*53 8^69897 -00 Log. r*. 1,08065-43 1,10184*36 1,12303-28 1,14422-21 1,16541-14 1,18660-07 1,2077900 1,22897-03 1,25016-86 1,27135*79 1,29254*72 1,31373-65 1,33492*58 1,35611*51 1,37730-44 1,39849-37 1,41968-30 1,44082-23 1,46206-16 i.4832S-«9 1,5044403 1^56800-81 i.$89ia*74 1,61038-67 1,6315760 1.65276-53 1.67395-46 1.69514*39 1,71633*32 1.73752*25 1,75871*18 1,27990*11 1,80109-04 1,82227*97 1,84346-90 1,86465-83 1,8858476 1,90703*69 1,92822-62 1,9494^*55 1,97060-48 1,99179*41 2,01298-34 2,03417-37 2,055.^6* 20 .2,o;()55-i3 a,o9274-o6 3,11892-99 Yean 51 52 bb 54 li 61 62 69 7» 71 73 73 74 81 82 89 90 91 92 93 94 '4 99 100 p ?i • (299) i i 11 LOGAKITILMIC TABLES OF COMPOUND INTEREST AND ANNUITIES Tran X 2 3 4 7 8 9 lO II 12 «4 \i 17 i8 «9 20 21 22 26 27 28 29 30 31 32 33 34 3 3 3 39 40 41 42 43 44 45 46 '47 48 49 50 Log. r". o,o2i7o"6o 0,04341-20 0,06511-80 0,08682-40 0,10853-00 0,1302361 0,151941: 0,17364-81 o>'9535'4« 0,2170601 0,2387661 0,26047-21 0,28217-81 0.30388-41 0,3255901 0,34729-61 0,36900-21 0,3907082 0,41241*42 0,43412-02 0,45582-62 o,477S3'22 0,49923-82 0,52091-42 0,54265 02 0.56435 62 o,;8oo6-22 0,60/76 82 0,6*9 47 '43 0,65118-03 0,6728863 0.69459-23 0,7162983 0,73800-43 o. 7597 « -03 0,78141 63 0,80312-23 0,8248283 0,84653-43 0,86824-04 0,88994-64 0,91165-24 0=9333584 0,95506-44 0,97677-04 0,9984764 1,02018-24 1,04188-84 ',0635944 1 ,0853004 O 4: Percent. 8 Log. a* 0,02170-60 9.7313934 9,56592-92 9,4Si52-7a 9,36506-37 9,29623-89 • 9.2395585 9.»9'74-3> 9.1506775 9,1 « 491 73 9,08343-27 9>o5546-32 9,03043-14 9,00788-84 8,98747-86 8,96891-55 8.95 '96-44 8,93643- «6 8,92215-44 8,90899-55 8,80683-75 8,88557-9^ 8,87513.^1 8,86542-75 8.8;639-o3 8,8 1796-48 8,84009-88 8,8.^274-64 8,82586-60 8,8194208 8,8i337-7» 8,8077053 880237-78 8 7973698 8,79265 92 8,78822-51 8.78404-37 8,78011-28 8,77640-17 8,7729008 8,76959-63 8, 76647 63 8,7635290 8,76074-38 8,75811-08 8,75562-10 8,75326-57 8, 75' 03-70 8,74892-76 8,7469304 Log. a\ 8.74503 '90 8.74324-76 8.74155-02 8.7.^994-18 8. 7384' -73 8,73697-20 8,73560-17 8,73430-22 8,73306-96 8,73190-03 8, 73079- 'o 87297384 8.7287394 8.72779 13 8,72689-12 8,72603-69 8,72522-58 8,72445-55 8,72372-41 8,7230295 8,72236-98 8,72174-32 8,72114-79 8,72058-25 8,7200453 8, 7 '953-49 8,71904-99 8,71858-91 8,71815-11 8,71773-50 8, 7' 733*9 8,71696-31 8,71660-65 8,7162669 8,71594-41 8,71563-73 8, 71534-56 8,71506-33 8,71480-48 8,71455-43 8,71431-60 8,71408-96 8,71.^87-43 8, 7 '.^66-95 8,71347-48 8,71328-97 8, 7 13" 37 8,71294-64 8,71278-73 8,71263-60 8,70969-39 Log. r». [Tears 1,10700-64 1,12871-25 I.X504I-85 1,17212-45 1,19383-05 »>2i553-65 1,2372425 i,2?894-85 1, 2806; -45 1,30236-05 1,32406-65 1,34577-25 1,36747-86 1,3891846 1,4108906 1,43259 i»6 1,45430-26 1,4760086 1,49771-46 1,5194206 1,5411266 1, 56283 26 1,58453 -86 1,60624-47 1,6270507 1,64965-67 1,67136-27 1,69306-87 i,7'477-47 1,73648-07 1,75818-67 1,7798927 1,80159-87 ',82330-47 i,84(;oio7 1,86671-68 1,88842-28 1,91012-88 ',93'83-48 ',9535408 1,97524-68 1,99695-28 2,0186588 2,0^036-48 2,06207-08 2,08377-68 2,10548-29 2,12718-89 2,14889-49 2, 1 706009 51 52 53 54 5 <7 58 61 62 63 64 65 66 67 68 69 70 7« 72 73 74 75 76 II 79 80 81 82 83 84 8 8 87 88 89 90 9' 92 93 94 99 100 Perp For explanation see pp. 216-228 (300) • 6 4 Per Cent. Years 1 Lopr. r". Loj?. a». Log. a*. Log. r-. Y.*re 51 0,02222-21 0,02222-21 8,75.^3445 ',1.3.332-73 2 0.04444-42 9,73216- 10 8,75162-77 '.15.554-94 52 3 o,oUt(t(>-6^ 9,5669440 8,75000-28 '.'7777-'5 53 4 0,0888884 9,45278-48 8,7484645 1.19999-36 54 i 0, 1 1 1 1 1 -05 o,i3.?.^3'26 9.^6655-99 8,7470080 1,22221-57 li 9,29796-92 8.74.562-87 1,24443-79 I 0,15555-47 9.24151-87 8,74432-23 i,26f>66-oo 57 0,17777-68 9,19392-89 8,74,^08-46 1,28888-21 58 9 0,19999-89 9.1530845 8,7419119 1,3' 110-42 1.. 33.332-63 59 10 0,22222-10 9,11754-15 8,74080-07 60 II 0.24444-31 9,08626-97 8,7.^974-74 1..35554-84 61 12 0,26666-5^ 9,05850-87 8,7.3874-92 1,377 7 7-05 62 «3 0,28888-74 9,03368-13 8,73780-28 '.3999926 63 14 0,31110-95 9,01 133-85 8.7.3f'90-55 1,42221-47 6.4 >5 o,.^.U=J3-i6 8,99112-48 8,7.3605-47 1,444 4.rf>8 65 • 16 0,35555-37 8,97275-36 8,7.3524-79 i,46C)6s-89 66 '7 0,37777-58 8.95599-05 8,7344827 1,48888- 10 67 18 0,39999-79 8,94064-15 8,7.337569 1,51110-31 68 '9 0,4222200 8,92654-41 8,7.3306-85 1,5.3.332-52 69 20 0,4444421 8,91356-11 8,7.3241-53 1.55.554*73 70 21 0,4^)666-42 8,90157-50 8,73179-58 ',57776-94 71 22 0,48888-63 8,8(^48-55 8,73120-78 '.59999'5 72 23 0,51110-84 8,88020-51 8,73065-00 1,62221-36 73 24 0,5.^333-05 0,55555-26 8,87065-78 8,73012-07 1.64443-57 74 '^ 886177-73 8, 72961 84 1,6666^78 li 26 0,57777-47 8,85350-45 8,72914-16 1,68887-99 - l^ 0,59999-68 8,84;78-8o 8,72868-91 1,71 iiO-20 1 / 0,62221-89 8,8?8:;8-ii 8,72825-97 ',7.3332-42 78 29 0,64444-10 8,83184-28 8,72785-20 1,75554-63 79 .?o 0,66666-31 8,82553-61 8,72746-50 1,77776-84 80 31 0,68888-52 8,81962-75 8,72709-77 i,7999«;o5 81 32 0,71110-73 8,81408-72 8,72674-90 1,82221-26 82 33 o,7.?.332-94 8,8088880 8,72641 79 1,84443-47 83 34 0,75555-16 8.80400-51 8,72610-36 i,8f)66s-68 84 U 0,77777-37 0,79999-58 8,79q4i-6i 8,7258051 1,88887 89 u 8,7951005 8,72552-17 1,91110-10 • % 0,82221-79 8,79103-94 8,72525-27 1,9.3332-3' 87 0,84444-00 8,78721-58 8,72499-72 1. 955.54-52 88 39 0,86666-21 8,78361-39 8,72475-46 ',97776-73 89 40 0,88888-42 8,78021-91 8,72452-42 1, 99^)98-94 90 41 0,91110-63 8,77701-81 8,7243055 2,02221*15 91 42 0,93.^32-84 8,7739984 8,72409-77 2,04443 -.36 92 43 0,95555-05 0,97777-26 8,77114-85 8,72390-04 2,0666s -t; 7 93 44 8,7684582 8,72371 31 2,08887-78 94 ^ 0.99999-47 8,7659' -74 8,72.353-51 2,11109-99 ^ 46 1,02221-68 8,76351-69 8,7233661 2,1333220 % 1,0444389 8,7612486 8,72320-55 2,15,554-41 % 1,06666-10 8,75910-41 8,72305-31 2,17776-62 49 1,08888-31 8,757076? 8,7229084 2,19998-83 99 50 1,1111052 8,75515-83 8,7227707 8,72015-93 2,22221-05 100 Perp (301) S 2 LOGARITHMIC TABLES OF It t t 51 Per Cent. Years! Log. r". X 2 3 4 5 6 7 8 9 lO II 12 13 14 15 i6 17 i8 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 0,02273*76 0.04547 '52 0,06821 28 0,0909504 0,1136879 0,13642-55 0,15916-31 0,18190-07 0,20463 83 0,22737-59 0,25011-35 0,27285 11 0,29558-86 0,31832-62 0,34106-38 0,36389-14 0,38653-90 0,40927 66 0,43201 -42 0.45475 tS 0.47748-93 0,50022-69 0,52296-45 0,54570*21 0,56843-97 0.5911773 0,61391 -49 0,63665-25 0,65939-00 0,68212-76 0,70486-52 0^72760 28 0.7503404 0,7730780 0.79581 56 0.81855-32 0,84129-07 0,86402 83 0,88676-59 0,9095035 0,93224 -II 0.95497 87 0.97771 63 1,0004539 1,0231914 1,0459290 1,06866-66 1,09140-42 1,11414-18 1,13687-94 Log. a". 0,02273-76 9,7329275 9,5679573 9,45404-02 9.36805-31 9. 29969 "57 9, 24347 41 9,19610-89 9,15548-48 9,12015-75 9,08909-72 9,06154-34 9,03691 89 9,01477*48 8,9947554 8.97657 "46 8,9599976 8,9448307 8,93091-12 8,9181020 8,90628-57 8,89536-21 8,88524-37 8,87585-47 8,86712-84 8, 85900 -62 8,85143-64 8,84437-27 8.83777 '40 8,83160-32 8,82582-71 8,82041 -58 8,81534-22 8,81058-15 8,80611 14 8,80191-15 8.79796-30 8,79424 89 8,79075*33 8,78746-19 8,78436-12 8,78143-91 8,77868-41 8,77608-56 8.77363*39 8,77132 01 8,76913*57 8,76707-27 8,765x2-41 8,76328-28 Log. a". 8,76154-27 8,75989-78 8,75834-25 8,75687-16 8.75548-05 8,75416-42 8,75291 90 8,7517404 8,75062-50 8.74956*91 8,74856-94 8,74762 28 8,74672-65 8,74587*75 8.74507*34 8,74431 17 8.7435901 8,74290-63 8,74225-86 8,74164-46 8,74106-27 8,74051-13 8.73998-87 8.73949*34 8.73902-38 8,73857*87 8,73815-66 8,7377564 8,73737*70 8.73701 '73 8,73667-62 8,73635*28 8,73604-60 8.73575*51 8.73547*92 8,73521*76 8.73496-95 8,73473*40 8,73451 08 8,73429*91 8,73409-83 8,73390-77 8,7337271 8,73355*57 8,73339*30 8,7332387 8,73309*24 8,73295*36 8, 73282 19 8,73269-69 8.73037*85 Log. r". Years 1,15961-70 1.18235-46 1,20509-21 1,22782-97 1,25056-73 1,27330-49 1,29604-25 1,31878 01 1.34151*77 1,36425-53 1,38699-28 1.40973*04 1,43246-80 1,45520-56 1.47794*32 1,50068 08 1,52341-84 1,54615-60 1.56889-35 I. 59163-11 1,61436-87 1,63710-63 1.65984-39 1,68258-15 1. 70531 "91 1,72805-67 1.75079-42 1.77353-18 1,79626-94 1,81900-70 1,84174-46 1,86448-22 1,88721-98 1.90995*74 1,93269-49 1.9554325 I. 97817 01 2,00090-77 2,02364 53 2,04638 29 2,06912 05 2,09185-81 2,11459-56 2,13733*32 2,16007-08 2,18280-84 2,20554-60 2,22828-36 2,2510212 2.27375 -88 f^ 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 Perp. For explanation see pp. 216-228 1(302) • COMPOUND INTEREST AND ANNUITIES ^1 Years I Log. r'*. 0,02325-25 Log. a«. Log. a". Log. r". Tears 51 0,02325-25 8,76963*55 1,18587-54 2 0,0465049 9,73369*31 8.76805-96 1,20912-79 52 3 0,0697574 9,56896-88 8.76657-12 1,23238 04 S3 4 0,09300-98 9.45529*33 8,76516-51 1,25563*28 54 5 0,11626*23 9.36954*32 8,76383-64 1,27888*53 55 6 0,13951-48 9,30141-85 8,76258*08 1,30213-77 56 7 0,16276-72 9,24542-48 ; 8,76139*40 1*32539 02 57 8 0,18601-97 9,19828-31 8,76027-21 1,34864-27 58 9 0,20927-21 9,15787-81 8,75921-14 1.37189-51 59 10 0,23252-46 9,12276*54 8,75820-82 1,39514*76 60 XI 0,2557771 9,09191-53 8.75725-94 1,41840*00 61 13 0,27902-95 9,06456-75 8.75636*22 1,44165 -25 63 • 13 0,30228-20 9,04014-42 8.75551*34 1,46490-50 63 14 0,3255344 9,01819-73 8,75471-04 1,48815*74 64 15 0.34878-69 8.99837*09 8,75395*06 1,51140-99 65 16 0,37203-94 8,98037-86 8.75323-16 1.53466-23 66 17 0,39529*18 8,96398-59 8.75255*12 1.55791*48 67 •18 0.4185443 8.94899*91 8,75190*72 1,58116*73 68 19 0,44179-67 8.93£25*55 8,75129*77 1,60441*97 69 20 0,46504-92 8,92261-82 8,75073*08 1,62767-22 70 21 0,48830-17 8,91096-99 8,75017*47 1,65092*46 71 22 0,51155-41 8,90021-00 8.74965*76 1,67417*71 72 23 0,53480-66 8,89025-13 8,74916*81 1,69742*96 73 24 0.55805-90 8,88101-82 8,74870-46 1,72068-20 74 25 0,58131-15 8,87244-38 8,74826-57 1.74393*45 75 36 0,60456-40 8,86446-99 8,7478502 1,76718*69 76 27 0,62781-64 8,85704-46 8,74745*66 1.79043*94 77 28 0,65106-89 8,85012-16 1 8,74708-39 1,81369*18 78 29 0,67432-13 8,84365-98 8,74673*09 1,83694*43 79 30 0,69757*38 8,83762-25 8.74639-67 1,86019-68 80 31 0,72082-62 8,83x97-63 8,74608 00 1,88344*92 81 32 0.74407*87 8.82669-X4 8,74578-00 1,90670*17 82 33 o,76733'i2 8,82174-07 8,74549*60 1.92995*41 83 34 0,79058-36 8,81709-96 8,74522 -68 1.95320*66 84 35 0,81383-61 8,81274-58 8,74497-18 1.97645*91 85 36 0,83708-85 8,80865-88 8,74473-04 1,99971*15 86 - 37 0,86034-10 8,80482-02 8,74450-16 2,02296*40 87 38 0.88359-35 8,80121*27 8,74428*49 2,04621-64 88 39 0,90684-59 8,79782*07 8,74407*95 2,06946 -89 89 40 0,93009-84 8,79462-99 8.74388-49 2,0927214 90 41 0,95335*08 8,7,9162-68 8.7437006 2,11597-38 91 42 0, 97660*33 8.78879-93 8.74352*59 2,13922-63 92 43 0,99985*58 8,78613-62 8.74336*05 2,1624787 93 44 1,02310-82 8,78362*69 8,74320-36 2,18573*12 94 45 1,04636-07 8,78126*17 8,74305*52 2, 20898 37 95 46 1, 06961 -31 8.77903*16 8,74291-44 3,23223-61 96 47 1,09286-56 8,77692*83 8,74278-10 2,25548 86 97 48 i,ii6ix-8i 8,77494*41 8,74265-45 2,27874-10 98 49 1,13937*05 8,77307*16 8,7425348 2,3019935 99 50 1,16262-30 8,77130*41 8,74242-13 .8,74036*27 2,32524-60 100 Perp. f (303) m LOGARITHMIC TABLES OF COMPOUND INTEREST AND ANNUITIES 6i r«r Cent Years I 2 3 4 7 8 9 lO 1 1 li «3 •4 '5 i6 »7 i8 '9 20 21 22 »3 24 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 4» 42 43 44 % 47 49 SO Log. r*. 0,02376-67 0.04753-34 0.0713002 0,09^0669 0,11^83-36 0,14260-03 0,16636-7*1 0,19013-38 0,2139005 0,2376672 0,26143-39 0,28:; 20-07 0,30^96- 74 0,3327341 0,3565008 0,38026-76 0,40403-43 0,42780-10 0,45 '56-77 0,4753344 0,49910-12 0,52286-79 0,5466^ 46 0,57040-13 0,5941680 0,6 « 79348 0,64170-15 0,66546-82 0,6892349 0,71300-17 0,73676-84 o, 760535 « 0,78450-18 0,8080685 0,83183-53 0,85^60-20 0,87936-87 0,903 •3-54 0,92690-22 o,95o(>6 89 0,9744356 0,99820-23 1,02196-90 «,04573S8 1,06950-25 1,0932692 1,11703-59 1,1^080-27 i,i64S6'94 i.i88.«-6i Log. a". 0,02376 9,73445 9.56997 945654 9.37103 9.30313 9.24737 9,20045 9,16026 9.12536 9,09472 9,06758 9.04335 ■ 9,02160 9,00197- 8,98416- 8,96795- 8 953 « 4' 8.93957- 8,92711- •67 -76 ■88 •42 ■04 '^ 08 16 •45 ■53 •42 06 76 62 10 55 54 68 74 00 8,9156274 8,90502-91 8.89522-82 8,88614-87 8,87772-41 8,8r;o89-6i 8,86261-26 8,85582-80 8, 84950 08 8,84359-43 8,83807-55 8,83291-44 8,8280840 8,8235600 8,81931-97 8,81534-31 8,8; 161-15 8,80810-80 8,80481-69 8,80172-38 8,79881-56 8, 79608 02 8,7935062 8, 79 '08-3^ 8,78880-18 8,78665-27 8,78462-79 8,78?7'-96 8,7809206 8.77922-42 M^. a 8.77762-42 8,77611-49 8,77469-07 8.773.M-67 8,77207-81 8,77088-05 8,7697498 8. 768(18-19 8,76767-32 8,76672-05 8,76582-04 8, 7649 7 00 8,76416-63 8,7634069 8,76268-91 8,76201-06 8,7613692 8,76076-29 8,76018 97 8, 75964- 76 8, 75913-5 • 8,75865-03 8.75819-18 8,75775-84 8,75734-84 8,75696-05- 8,7565936 8,75624-66 8.75591-83 8,75560-77 8,75531-38 8,75503-57 8.75477-27 8. 75452 -.18 8,7542884 8,75406-54 8,75385-46 8,75365-50 8,75346-62 8,75328-74 8,753»i-84 8,75295.-82 8,75280-68 8,75266-34 8,75252-77 8.75239-93 8,75227-77 8.75216-27 8,75205-38 8,75195-07 8,7soia-a5 Log. r*. Ye»Tt 1,21210-28 1,23586-95 1,25963-63 1,28.^0-30 1,3071697 1,33093-64 1*35470-32 1,37846-99 1,40223-66 1,42600-33 1,4497700 ». 47353 -68 1.49730-35 1,5210702 1,54483^ 1,56860-37 1,59237-04 1,61613-71 ».639<>0 38 1,6636705 1,68743-73 1,71120-40 i. 7.^497 07 1.75873-74 1,78250-41 1,8062709 1,83003-76 1,8538043 1,8775710 1,901.^3-78 1,92510-45 1,94887-12 1,97263-79 1,99640-46 2, 02017*14 2,04393-81 2,06770-48 2,09.47-15 2,11523-83 2,1390050 2,16277-17 2,18653-84 2,2103051 2,23407- 19 2, 2 5783 -86 2, 28 1 6053 2,30537-20 2,32913-88 2.35290-55 2,3*/667-22 S» 52 53 54 5^ 5 J9 61 -62 63 64 U ^7 68 69 70 7« 72 73 74 & 81 82 87 88 89 90 9> 92 93 94 9« 99 100 Terp. Years Loc:. »*. I 2 3 4 I 9 10 II 13 »3 •4 15 16 «7 18 19 20 21 22 23 24 26 27 28 29 30 3« 32 34 36 38 39 40 4» 42 43 44 45 46 4« 49 SO 0,02428 04 0,0485608 0,07284-11 0,09712-15 0,12140-19 0,14.^68-23 0,16996-26 0,19424-30 0,21852-34 0,2428038 0,26708-41 0,29136-45 0,31564-49 o,33992-.«;3 0,3642056 0,3884860 0,41276 64 0,43704-68 0,46132-71 0.48560-75 0.50988- 79 0,5.^416-83 0,5584486 0,58272-90 0,60700-94 0,63128-98 0,65557-02 CV67985-0S 0,70413-09 0,72841-13 0,7526917 0,77697-20 0,80125-24 0,82553-28 0,84981-32 0,87409-35 0,89837-39 0,92265*43 0,94693-47 0,97121-50 0,99549-54 1,01977-58 1,04405-62 1,06833-65 1,09261-69 1,11689-73 1,14117-77 I, 16545 81 1,18973-84 1,21401-88 Log. oT 0,0242804 9.7.352209 9.57098-71 9.45779-29 9,37251-46 9.304F523 9,24031-21 9,20261-44 9,16264-41 9.12795-72 9-09752-37 9,07058-33 9,0465588 9,02500-15 900555-60 8.98793-.56 8.97190-62 8.95727-42 8.94387-69 8.93157-74 8.92025-85 8«rx>8i-98 8,./JOi7-44 8.89121-64 8,88296-93 8,87.528*47 8 8f)8i4*io 8.86149-22 8.85529-71 8,84951 92 8,84412-52 8.83908-53 8.83437-28 8.82096-30 8,82583-38 8.82196-48 8,81833-77 8,81493-54 8.81174-25 8,80874-47 8.80592-87 8.80328-26 8,80079-50 8.79845-58 8.79625-54 8.794>8-47 8.79223-57 8.79040-07 8,78867-25 8,78704-46 3 4 Per C«i»t Log. a 8.78551-08 8.78406-54 8,7827030 8.78141 -80 8,7802075 8.77906-53 8,7779880 8,77697 18 8.77601-30 8,77510-82 8,774254s 8,77344-8*^ 8.77268-80 8,77196-99 8,77129-19 8,77065-18 8,77004-74 8,7694766 8,76893-75 8,76842-84 8,76794-75 8,76749-32 8,76706-41 8,7666586 8,76627-57 8.76591-37 8,76557-18 8,7652486 8.76494*34 8.76465-49 8.76438-23 8 76412-47 S 76388- 11 8. 76365 10 8.76.343-.35 8.76322-79 8.76303-3f> 8,7628498 8,76267-63 8,76251-21 8,76235-70 8,76221 04 8.76207-18 8,76104-08 8,76181-68 8,76169-97 8.7615889 8,76148-42 8,76138-53 8,76129*17 8,75966-78 Log. I*. Year* 1.23829-92 1.26257-96 1,28685-99 1,31114-03 1-3354 2 07 1. 3.^070- 11 1.38 ^98- 14 1.40K26-18 i,432.=;4-22 i,45(>82-26 1,48110-29 1,505.^8-33 1,52966-37 i,5.'!394-4' 1,57822-44 i,6o2£;o-48 1,62678-52 1,65106-56 ^67534-.^9 1,69962-63 1,7239067 5' 52 53 54 % % 60 6i 62 63 64 6; r)6 67 68 (V) 70 71 1.74818-71 I 72 1,77246-74 1.79674-78 1,82102-82 i,84.';.3o86 i,8(>9.58-90 1,80.^86-93 1,91814-97 1,94243-01 1,96671-05 1,9909908 2,01527-12 2,03955-16 2,06383-20 2,08811-23 2,11239-27 2.1.3667-31 2 16095-35 2 18523*38 1 20951-42 J 2.3379-46 i 25807-50 2 28235-53 ?.,3o663-57 2.33091-61 2.35519*65 2,37947-68 2,40375'7« 1,4260? -76 73 74 75 76 77 t8 • 79 80 81 82 §-^ 84 85 86 87 88 89 <>o 9' 92 93 94 95 96 97 98 99 .100 For explanation see pp. 216-228 (304) (305) LOGAKITHMIC TABLES OF COMPOUND INTEREST AND ANNUITIES Tsani I a 9 4 i 9 lO II 12 »3 '4 \i «9 20 21 22 23 24 »9 30 31 32 33 34 3 39 40 41 42 43 44 49 50 Log. f*. 0,0247934 0,0495868 0,0743803 0,099^7 37 0,1239671 0,1^7605 o> 1 7355-40 0.1983474 0,2231408 o> 247934a 0,2727377 0,29752- 1 1 0,32231 45 0,3471079 0,37190 '3 0,3966948 0,42148-82 0,44628-16 0,47107-60 0,49586-85 0,52066-19 o, 54545 "53 0,57024-87 0,5950422 0,61983-56 0,64462*90 0,66942*24 0,69421-59 0,71900-93 0,74380-27 0,76850-61 0,79338-95 0,81818-30 0,84297-64 0,8677698 0,89256-32 o,9> 73567 0,9^215-01 0,96694-35 o»99i73-69 ,0165304 ,04132-38 ,06611-72 ,09091-06 ,11570-40 ,14049-75 ,16529-09 ,19008-43 ,21487-77 .13967-12 51 Lo 4> 42 43 44 % 49 50 0,0253059 0,05061-17 0,07591 76 0,10122-35 0,12652-93 0,15183-52 0,17714-11 0,20244-69 0,22775-28 0,35305-87 0,37836-45 0,30367-04 0,32897-63 0,35428-21 0,37958-80 0,40489-38 0,4301997 0,45550-56 0,48081*14 0,50611*73 0,53142-32 0,55672-90 o,58203'49 0,60734*08 0,63264-66 0,65795*25 >,6833. " 5,68a3K-84 >,7<^56-42 o,7o85e 0,73387-01 0,75917-60 0,78448-18 0,80978-77 0,83509-36 0,8603994 0,8857053 0,91101*13 0,93631 '70 0,96163*39 0,9869287 1,01223-46 1,03754-05 1,06284-63 1,08815-22 1,11345-81 i,i.?876-39 1,16406-98 1,18937-57 1,31468-15 1,23998-74 1.36539*33 1 6 Per Gent Log. io309'5o 9,0765508 9,0529252 9.03175-13 9,01268-01 8,99542-52 8,97975-23 8,96546-77 8,95240-91 8,94043-96 8,92944-33 8,91931-64 8,90997-56 8,90134-39 8,89335-51 8,8859509 8,87907-97 8,87269*55 8,86675*75 8,86133*91 8,85607*7^ 8,85127-26 8,84678*81 8,84250-95 8,83868-45 8,83503-33 8,83159-74 8,82839-00 8,82538-58 8,82257-04 8,81993-11 8,81745-57 8,81513-34 8,81295-38 8»8io9o-77 8,80898-60 8,8071809 8,8054849 8.8038909 8,80339-35 8,80098-36 8,79965-87 8,79841 25 8,79723- 8,79613- 87950986 8,79412-15 8,79320-16 8,7923356 8,79153-02 8,79075-24 8,70002-03 8,78034-82 8,78870-67 8,78810-23 8,78753-29 8,78699-65 8,78649-09 8,78601*46 8,7855656 8,78514*36 878474-38 8,78436-80 8,78401*37 8,78.36797 8,7833649 8,78306-81 8,78278-83 8,78252-45 8,78227*58 8,78204-13 8,7818201 8,7816117 8,78141-51 8,78122-97 8,78105-48 8,78088-99 8,78073-45 8,78058-78 8,78044*95 8,78031-91 8,78019-62 8,7800801 8,7799708 8,77986-75 8,77977-02 8,7796784 8,7795918 8,77951-01 §,77943*31 «,77«5>3 Log. »*. 1,2905991 «,3iS90-5o 1,3412109 i,.3665i-67 1,39182-26 1,41712-85 1,44243-43 1,46774-02 1,49304-61 i,5i835-'9 1,54.^65-78 1,. '16896*36 i,.59426-95 1,61957-54 1,64488-12 1,67018-71 i,69549-.=?o 1,72079-88 1,74610-47 1,77141-06 1,79671*64 1,82202-23 1,84732-82 * 1,87263-40 1,89793-99 1,92324*58 1,9485516 1,97385-75 1,99916-34 2,02446-92 2,04977-51 2,07508-10 2,10038-68 2,12569-27 2,15099-86 2,17630-44 3,20161-03 2,22691-61 2,25222-30 2,27752*79 2,30283-37 2,32813*96 2,35344-55 2,37875-13 2,40405-72 2,42936-31 2,45466-80 2,4799748 2,5052807 2,53058-65 Teart 52 53 54 \i 61 62 67 68 69 70 7« 72 73 74 j^ \l IS 81 82 83 84 u u 8q 90 91 92 93 94 95 90 97 98 99 100 Paip. (307) LOGARITHMIC TABLES OF COMPOUND INTEREST AND ANNUITIES M iJ Years Lopf. r*. 0,02632 89 0,07898-68 0' '053' -58 o. '3 '6447 o^ '5797*36 0,18430*26 0,21063*15 o,2369"6-04 0,26328*94 0,28961-83 «'3 '59473 0,34227-62 0,36860*51 0-39493*4' 0,42126*30 0,44759-20 0.4739209 0,50024*98 0,5265788 0,55290-77 o,57923-^>7 0,60556*56 0,63189*45 0,65822*35 0,6845; -24 0,71088-13 0,7372 1 03 0,76353-92 0,78986*82 31 0,81619*71 32 0,84252*60 .^^ 0,86885*50 34 0,89518*39 35 0,92151-29 36 0,94784*18 37 0,97417*07 38 1,00049*97 39 1,02682*86 40 1,05315-75 1,07948*65 1,10581*54 1,13214*44 '.'5847-33 1,18480*22 1,21113*12 1,2374601 1,2637801 ny 1,29011*80 50 I 1,31644-69 1 I 2 3 4 I k 9 10 11 12 »3 •4 »5 16 '7 18 '9 20 21 22 23 24 25 26 27 28 29 30 4" 42 43 44 46 47 48 49 6 1 4 Per Cent. Log. m'. 0,02632-89 9.73826*39 9.57500*48 9,46276-53 9,37842-10 9.3 "67 -48 9-25703-02 9,21120*86 9,17209*49 9,13824*52 9,10862*97 9,08248*81 9.05924-36 9,03844*73 9.01974*43 9,00284*80 8,98752*47 8,97358-03 8,96085*31 8,94920*58 8,93852*19 8,92870- 1 1 8,91965*64 8,91131-26 8.90360*33 8«9647-o5 8,88986-25 8.88373*38 8,87804*36 8.87275*53 8,8678363 8.86325*70 8,8^899-07 8.85501*33 8,85130*29 8,84783-92 8,84460*46 8,84158-20 8,83875-63 8,8^.611-35 8,83364*09 8,83133-63 8,82915*93 8,82712*95 8,82522-77 8,82344-54 8,82177.4s 8,82020*77 8,8i873-'«4 8, 8 1 736 -co Log. Lopr. 8,81606*66 8.81485-28 8,8i37r35 8,81264-40 8,8n6v97 8,81069*66 8,8o()8i-io 8,80897*90 8.80819*75 8.80746*32 8,80677*32 8,80612-48 «-8o55i-55 8,80494*27 8 80440-4^ 8.80389-82 8,80342*25 8.80297*51 8-80255.45 0,80215-91 8.80178*72 8,80143-75 8,801 10*86 8,80079*93 8,80050*84 8,80023-47 8.79997*74 8.79973-53 8,7995076 8,79929*33 8,79909*18 8,79890-22 8,79872*38 8,79855-61 8,79839-82 8.79824-97 8,79810-99 8,7979784 8,79785-47 8,79773-83 8,79762.88 8,79752-57 8,79742-87 8,79733*75 8,79725*'6 8.79717-08 8,79709-48 8,79702-32 8,79695*59 8.79689-25 8.79588-00 For explanation see pp. 216-228 (308) ''3427759 1,36910-48 ».39543'38 1,42176-27 1,44809-16 1,47442 06 '.50Q7495 '.5270784 '.5534074 '.5797363 1,60606-53 '»63239-42 i>65872-3i 1,68505*21 1,71138-10 '. 73771 -oo 1,76403-80 1,79036-78 1,81669 68 1,84302-57 '.86936-46 '.89568-36 1,92201-25 '.94834-15 1,97467-04 2,0009993 2,02732-83 2.0536.'; -72 2,0799862 2,10631-51 .2,13264*40 2, '.5897*30 2, 18530* 19 2,21163*09 2,23795-98 2,26428*87 2,29061-77 2.3'694*66 2>34327-S5 2.36960-45 2.39593*34 2,42226*24 2,44859*13 2,47492*02 2,50124*92 2.52757-81 2.55390-7' 2,58023-60 2,606^649 2,63289*39 Yeara if ears Log. f. I 2 3 4 7 8 9 10 II 12 '3 14 »5 16 '7 18 '9 20 21 22 23 24 26 2: 29 30 3J 32 S3 34 35 36 .^8 39 40 0,027^4*96 0,05460*92 0,08204 88 0,10939-84 0,1367480 0,16409 76 0,19144-73 0,2187969 0,24614 65 0,2734961 0,30084 57 0.3281953 o,35554--19 0,38289*45 0,41024-41 0.43759*37 0,46494-33 0,49229-29 0,51964*25 0,54699-22 o,57434-'8 0,60169*14 0,62904- 10 0,6563906 0,68374-02 0,71108 98 0,7384394 0,7657890 0,793 '3 -86 0,82048 82 0,84783-78 0,87518*74 0,902.53-7' 0,92988-67 0,95723-63 0,98458-59 1,01193*55 1,03928-51 1,06663-47 1,09398 43 41 1,12133-39 42 1,14868-35 43 1,17603-31 ■ 44 1,20338-27 45 1.23073-24 46 1,25808-20 47 1.28543-16 48 1. 31278-12 49 1,3401308 50 1,36748-04 b 2 ^^' ^®*'*~ Log. a". Log. a 0,0273496 9.7397792 9.57700*41 9,46523-82 9.38135-80 9.3'5o6-37 9,26086-14 9,21547-18 9,17677-99 9,14334-18 9,11412 77 9.08837-77 9.06551-46 9,04509*01 9,02674*88 9,01020*48 8,9052241 8,98161*30 8.96920*96 8,95787-72 894749-9« 8.03797 50 892921-85 8,921 i5-4« 8,91.^71 58 8,<^684-56 8,90049*21 8.80^6009 8,88915-82 8,88410-09 8,87940-52 8,87504-19 8,87098-44 8,86720-87 8,86369-31 8,86041*78 8,85736-47 8,85451*74 8,85186-07 8,84938-09 8,84706-52 8,84490*21 8,8428808 8,84099-13 8,83922-46 8,83757*23 8,83f)02-65 8.83458-00 8.83522-62 8.83195*89 8.83077-22 8.8296609 8.8286200 8,82764-56 8.82673- '« 882587-53 8.8250731 8.82432- 1 1 8.82561-62 8,82295-53 8.82233*58 8,82175.48 8,82121-00 8,82069-90 8,82021-99 8,8197704 8,81934-88 8.81895-33 8,8i8s8-32 8,81823-41 8,81790-75 8.81760-10 8,81731-35 8,81704-36 8,81679-04 8,8165527 8,81632-98 8,81612-05 8,81592-41 8,81573-97 8,8155667 8,81540-43 8,8152519 8,81510-88 8,81497-44 8,81484-84 8,8147301 8,81461-89 8,8'4SJ 47 8,81441-67 8,81432-48 8,81423-86 8.81415-75 8,81408-16 8.81401*02 8,81394*32 8,81388*02 8,81582-12 8,81376-57 &,8'37'*36 8.81291-34 Log. I*. 1,39485-00 1,42217-96 1,44952-92 1,47687 88 1,50422-84 «. 53' 57*80 1,55892*76 1,58627-73 1,6136269 1,6409765 i,6(')832-6i 1.69567*57 1,72302-53 i,7S037*'*9 1,77772-45 1.80507-41 1,83242*37 • ,8.5977*33 1,88712-29 1,91447 25 1,94182-22 1,96917 18 1,99652-' 4 2,02387-10 . 2,05«22-06 2,07857-02 2,10591-98 2,13326-94 2,16061-90 2,1879686 2,21531-82 2,24266-78 2,27001*74 2,29736-71 2,32471 67 2,35206-63 2,37941*59 2,40676-55 2,434iy5» 2,4614647 1,48881-43 2,51616*39 2, 5435 » -35 2.57086*31 2,59821*27 2,6255623 2,65291 20 2,68026- 16 2,70761-12 2,73496-08 Years 5' 53 54 55 56 61 62 64 65 66 67 68 69 70 7» 72 73 74 11 81 82 83 84 \l 89 90 9' 92 93 94 96 97 98 99 100 rery (309) LOGARITHMIC TABLES OF 61 Par Cent. Years Log. r*. I 2 3 4 2 9 iO II 12 «3 M \i \i «9 ao ai 32 34 21 29 30 31 32 33 34 li U 39 40 41 42 43 44 45 46 47 48 49 SO 0,0283679 0,08510-37 o> "347*15 o^»4i«3'94 0,1702073 0.19857-52 0,22694*31 0,2«3I-io 0,28367 -88 0,31204-67 0*34041 -46 0,36878-25 0,3971504 0.4255^ 83 o,453»8-6i 0,48225-40 0,51062*19 0,53898-98 0^5673577 0*5957256 0,62409-34 0,65246-13 0,68082-92 0,70919*71 0,73756-50 0,7659329 0,79430-07 0,82366*86 0,85103*65 0,87940*44 0,90777 23 0,93614*02 0,96450-80 0,99287-59 1,02124-38 1,04961*17 1,07797*96 1,10634*75 '.13471-53 1,16308-32 1.19145'" 1,21981-90 1,24818 -69 1.27655-48 1,30492-27 1.33329-05 1,36165-84 1,39002-63 1,41839*42 Log. a". o,o2»36-79 I 9,74129-03 9.5789971 9,46770*33 9.38^ " 9, 9. 9,21971-27 9,18143*83 9, 14840*71 9,11958-96 9,09422-58 9,0717386 9.0516797 9>03369-43 9,01749*60 0,00285*12 8,98956-6< 8,97747-98 8,96645-47 8,9563747 8,94713-96 8,93866-31 8,93086-99 8,92369-42 8,91707-81 8,91097-05 8,90532-59 8,90010*40 8,89526-87 8,80078*74 8,88663-09 8,88277-31 8,87919-00 8,8758601 8,87276*38 8,86988*30 8,86720-17 8,86470-49 8,86237*90 8, 86021 -12 8,85819-04 8,85630-58 8.8545478 8,85290-74 8.85i37'63 8,84994*69 8.84861-21 8,84736-54 8,84620-09 Log. a". Log. r". 8,84511-27 8,8440958 8,84314-55 5,84225*70 8,84142*64 8,84064*98 8,83992-35 8,8392443 8,83^0-89 8,83'tei*46 8,83745-86 8,83693-84 8,83645-16 8,83599-62 8,8355700 8,83517*10 8.83479-77 8,^3444*82 8,83412*11 8,8335-49 8,83352-83 8,83325-99 8,833oS*g7 8,83377*36 8.83255-33 8,83234*70 8,83215*40 8,83107*32 8,83180*40 8,83164*55 8,83149*70 8,83135*60 8,83122*78 8,83110-58 8,83078*47 8,83069*09 8,83060-30 8,83052*08 8.83044-37 8,83037-15 8.83030*30 8,83024*06 8,83018-13 8,83012*57 8,83007*37 8,83002*50 8,82997*94 8,82993*8 8,83930*38 For explanation see pp. 216-228 (310) 1,44676*21 »,475'3-oo '.50349-78 '.53186-57 '.5602336 i,|886o-i5 1,61696*94 '.6453373 '.67370-51 1,70207-30 1,73044*00 1,75880-88 1,78717-67 '>«i554-46 '.8439' -24 1,8722803 1,90064-82 1,92901-61 '.95738-40 '>98S7SI9 2,01411*97 2 04248*76 2.07085*55 2.09922*34 2. '275913 2. '5595 92 2,18432*70 2,21269-40 3,24106*28 3,36943*07 2,39779*86 2,33616*65 2.3545343 3,38390*22 2,41127*01 2.43963-80 2,468oo*59 2.49637-38 2,52474'6 2.55310*95 2.58147-74 2.60084*53 2,63831-32 2,66658*11 2,69494*90 2. 7233 '-68 2.75168*47 2,78005*26 2,80842*05 3,83678-84 Yean 5» 52 53 54 5 k 61 62 J^ u u 69 70 71 7a 73 74 81 83 U 89 90 91 93 93 94 9« 99 100 COMPOUND INTEREST AND ANNUITIES Per Cent. Yeart I a 3 4 5 6 7 8 9 10 II 13 «3 14 Log. I*. Log. a*. »9 30 31 33 23 24 % 29 30 3« 3« 33 34 f4 39 40 41 42 43 44 45 46 % 49 0,02938-38 0,05876-76 0,08815-13 0,11753-5' 0,14691-89 0,17630-27 0,20568-64 0,23507-02 0,26445-40 0.29383-78 0,32322*16 o,.l526o-53 0,38198-91 0,41137-29 0,44075-67 0,47014-04 0,49952-42 0,52890*80 0,50829*18 0,58767*56 0,61705*93 0,64644-3' 0,67582*69 0,70521*07 0.73459-44 0,76397-83 0,79336*20 0,82274*58 0,85213*96 0,88151*33 0,91089-71 0,94020*09 0,96966*47 0,99004-84 1,02843-22 1,01^781-60 1,0^710-98 1,11658-36 •> 14596-73 «,I753S-" «, 20473-49 1,23411-87 1. 26350-24 1,29288-62 1,32327*00 '.35'6S-38 i. 38103-76 •1,4104213 ',43980-5' 1,4691889 Log. a" Log. r*. 0,02938*38 9,7427072 9.58098-38 9,47015-78 9.387 '952 9,3217969 9,26846-85 9,22393-12 9,18607-01 9.'S344'4 9,13501*56 9.10003*26 .^07791 -58 9.05821*70 9,04058-10 9,02472-23 9,01040-68 8,99744*14 8,98566*45 8,97493*95 8,96514-99 8,95619-62 8,94799* 18 8,94046*18 8,9335406 8,92717*03 8,9213000 8,91588-47 8,91088-30 8,90626-18 8,90198-61 8,89802-78 8,89436-08 8,89096-14 8,8878083 8,88488-21 8,88216-49 8,87964-09 8,87729-51 8,87511-42 8,87308-58 8,87119-87 8,86944-23 8,8678072 8,86628-48 8,86486-67 8,86354-55 8,86231*45 8,86116*71 8,86009-74 8,85910-02 8,8581 7-02 8,85730-29 8,85649-39 8,85573-91 8.85503-50 8.85437-79 8,85376-47 8,85319-24 8,85265-82 8,85215-96 8.85169-41 8.85125-95 8,85085-37 8,85047-48 8,85012-11 8,84979-07 8,84948-21 8,84919*39 8,84892*48 8,84867-34 8,84843-87 8,84821-93 8,84801*44 8,84782-30 8,84764-42 8,84747-73 8,84733*11 8,84717*54 8,84703-91 8,84691-19 8,84670*30 8,84668*19 8,84657-81 8,84648-11 8,84639-05 8,8463058 8,84622-67 8,84615-28 8,8460^-37 8,84601-93 8,84595-88 8,84590-25 8.84584-98 8.8458006 8,84575-46 8.8457'-'5 8,84567-14 8,84563*40 8.84^=i9-88 8,84509-80 1,49857-27 1,52795-64 1,55734-02 1,58672-40 1,61610-78 1,64549-16 1,67487-53 1,70425-91 1,73364-29 1,76302-67 •1,79241-04 1,82179-42 I 85117-80 1.88056-18 1,90994*56 1,93932-93 1,96871-31 1,9980069 2,02748-07 3,05686-44 3,0862483 3,11563-20 3,14501-58 2,17439-95 2,20378-33 2,2331671 2,26255-09 3,29193*47 3,32131-84 2,35070-33 2,38008-60 2,40946-98 3,43885*35 3,46823-73 3,49763-11 3,52700-49 2,55638*87 2,S»S77**4 2,61515 62 2,64454-00 2,67392-38 2,70330-75 2,73269- '3 2,76207-51 2,79145-89 3,82084-27 2,85022-64 2,87961-02 2,90899-40 2,93837-78 Yean 51 s» S3 54 60 61 62 69 70 7> 73 73 74 II Si 83 M 87 88 89 90 9' 92 93 94 91 91 98 99 100 Perp. (311) LOGARITHMIC^ TABLES OF 1 „ 2 Per Cent. Years Log. r". J 2 3 4 I 9 lO II 12 M i^ 1 6 i? i8 19 20 31 23 2.? 24 »S 26 27 28 29 30 0,03140-85 0,06281 69 0.09422-54 0'»2563-39 0,15704-23 0,18845-08 0,21985 92 0,2512677 0,28267-62 0,31408-46 31 32 33 34 ;ll 37 38 39 40 41 42 43 44 4I 49 50 o>34549-3' 0,376(^16 0,40831 00 0.4397^-85 0,47112-70 0.50253-54 0.53394-39 0.56535-24 0,5967608 0,6281 693 0,65957-77 0,6*^98 -63 0,72239-47 0,75380-31 0,78521-16 0,8 r 662 01 0,8480285 0,87943-70 0,91084-55 0,94225 39 0,9736624 1,0050709 1,0364793 1,06788 78 1,09929-62 1,1307047 1,16211-33 '. '9352 16 1,22493-01 •.2563386 «. 2877470 '.3i9»5 55 •.3505640 »,38i97-24 •,4133809 •44478-94 1,47019-78 1.50760-63 '.53901-47 «.57042'32 Log. o,03i4o-«5 9w"45r9''5^ 9.58493-88 9,47504-25 9,39298-64 932847-11 9.27600-27 9.23230-23 9. •95255' 9, '6341 76 9. •3576-05 9, '1 152-40 9,09013-17 9.07' 13-56 9,05418-10 9,03898-22 9,02530-60 9,01295-93 9,0017808 8.99 163 -44 8,98240-41 8.9739904 8,9663073 8,9592803 8.95284-41 8,94694-14 8.94I52-I5 8.9365399 8,93195-65 8.92773-59 8,9238462 8,92025-89 8.91694-84 8,91389-ij 8,91 106-65 8,90845-53 8, 90604 04 8,9038058 8,90173-74 8,89982-22 8.89804-82 8.89640-43 8,89488-08 8.89346-82 8,89215-84 8.89094-35 .ysoSi 64 8.8«877 05 8,88779-< 8,88689' Log. a*. 8.88r23507-44 1,2725009 1.3099274 1.34735-39 1,3847804 1,42220-69 '.45963-34 '.4970599 '.5344864 1,57191-29 1.60933-94 1,64676-59 1,68419*24 1,72161-89 '.75904-54 ''Z9647-19 ^13389-84 1.87132-49 Log. <»■. 0,03742-65 9.75470-67 9.59665-73 9,48949-26 9,41008-93 9,34814-86 9,29817-72 9.2568966 9,22219*29 9,19262*35 9,16715-98 9,14504-29 9,12569-77 9,10867-72 9,00362-78 9,08026-53 9,06835-74 9.0577' 28 9,04817-14 9.0395984 9,03187-94 9,02491 -64 9,01862*51 9,01293*22 9,0077744 0,00309-57 8,99884*72 8.99498-57 8,99' 47 30 8,98827-51 8,9853618 8,98270-62 8.98028-40 8.97807-36 8,97605-57 8,97421*25 8.97252-83 8,9709890 8,96958-15 8,96829*43 8,96711-67 8,96603*91 8,96505-28 8,96415*00 8,96256 ■63 8,96187-29 8,96123*78 8,96065-5 8,96012-2 Log. a" 8.95963-42 8.959 '»-65 8,9587761 8,9584000 8.95805-52 8,95773-9' 8.9574493 8.957'8-36 8.9569401 8,95671-67 8.95651*19 8.95632-40 8,95615-18 8.95599-38 8,95584-89 8.9557' -61 8,95559-43 8.95548-24 8.9553799 8.95528*59 8.955'9*96 8,95512-06 8,95504-80 8,95498- 14 8,9549204 , 8,95486-44 8,95481*29 8.95476-59 8,95472-26 8.95468*29 8,9546465 8.95461-32 8.95458-26 8,95455-45 8,95452-87 8,95450-50 8,95448-34 8,95446-35 8.95444-52 8,95442-85 8,95441 •31 8.95439-9' 8.9543»-6i 8.95437-42 8,95436-34 8,95435*.?4 8,95432". 8,95432-11 8*95424*21? For explanation see pp. 216-228 (314) PerCwit. Log. f*. (rears 1,90875-14 '.94617-79 1,98360-44 2,02103-09 2.0584574 2,09588-39 2, '333' -04 2,17073-69 2,20816-34 2,24558-99 2,28301*64 2,32044*29 2.35786-94 2.3952959 2,43272*24 2,47014*89 2.50757-54 2.54500*19 2,58242-84 2,61985*49 2,65728-14 2,69470-79 2.73213-43 2,7695608 2,80698-73 2,84441-38 2,8818403 2,91926-68 2.95669-33 2,99411*98 3.03154-63 3,06897-28 3,10639-93 3,14382-58 3,18125-23 3,21867-88 3,25610*53 3.29.^53- '8 3.3309583 3.3683848 5» 52 53 54 5 57 58 19 3,40581-13 3.4432378 3,48066-43 3,51809*08 3.5555' -73 3,59294*.38 3.6303703 3,66779-68 3,70522*33 3,74264-98 61 62 ^^ % 69 70 7' 72 73 74 75 76 80 81 82 84 8 81 1^ 89 90 91 92 93 94 v> 97 98. 99 100 Perp. -fmrnrnmaam Teaa I 2 3 4 i I 9 10 II 12 '3 '4 \l '7 18 '9 20 21 22 23 24 29 30 31 32 33 34 % % 39 40 4» 42 43 44 t 49 SO Log. r*. 0,04130-27 0,08278-54 0,12417-81 o,i6«7-o7 0,2069634 0,24835-61 0,28974-88 0.33 "4- '5 0,37253-42 0,41392-69 0,45531-95 0,49671-22 0,53810-49 0,57949*76 0,62089-03 0,66328-30 0,70367-57 0,74506*83 0,78646- 10 0,82785-37 0,86924-64 0,91063*91 0,95203*18 0,9934244 ,03481*71 ,07620-98 ,11760*25 .'5899-52 ,20038-79 ,24178-06 ,28317*32 .32456-59 .36595 -86 .40735- '3 .44874-40 ,49013*67 .53152-94 ,^7292 -20 ,61431*47 .65570*74 ,69710-01 ,73840*28 ,77988-<5 ,82127-81 ,86267*08 ,90406-35 2,02824-16 2,06963-43 10 Per Cent Log a". 0,04139-27 9,76056-60 9,6043501 9,49895*92 9,42(27-07 9,3609859 9,31261*21 9,27287*16 9,23965*11 9,21150*87 9,18741*68 9,16661*75 9,14853-64 9,13272-77 9,11883-91 9,10658-73 9,09574-15 9,08611-14 9.o77.'>3-82 9,06988-86 9,0630495 9,05692-41 9,05142-97 9,04649-44 9,04205-57 9,03805-07 9,0344586 9,03121-05 9,02827-87 9,0256304 9,02323-69 9,02107*23 9,01911-38 9,01 734- 10 9.o'57.VS6 9,01428-13 9,01296*35 9,01176*08 9.01068-57 9,00970*32 9,00881-21 9,00800*36 9,00726-99 9,00660-40 9.00599-94 9,00545-06 9,00495 22 9,00440-07 9,00408-87 9.00371-54 Log. cT. 9,00337-03 9,00306*83 9,00278-85 9,00253-42 9,00230*32 9,00209-33 9,00190-26 9,00172-93 9,00157-18 9,00142-87 9,0012986 9,00118-04 9,00107-30 9,ooo97*e3 9,00088-65 9,00080-59 9,00073*26 9,00066-59 9,00060-53 9,00055-03 9,0005003 9,0004547 9,00041-34 9,00037-57 9.00034-16 9,00031*05 9,00028-23 9,00025-66 9,0002333 9,00021*21 9,00019-28 9,00017-53 9,00015-93 9,00014*48 9,0001317 9,0001 1 -97 9,00010-88 9,00009-89 9,00009-00 9,00008*17 9,00007*43 9,00006-76 9,00006*14 9,0000558 9,00005*08 9,00004-61 9,00004*19 9,00003-81 9.0000347 9.00003- 1 5 ^,00000-00 Log. 1*. 2,11102-00 2,15241*96 2,19381-33 2,23520-50 2.27659*77 2.3179904 2.35938-31 2,40077*0 2,44216-84 2.48356-11 2.52495-38 2,56634-65 2.60773*92 2,64913-19 2,69052-45 2,73'9'72 2,77330-99 2,81470-26 ^♦§5609-53 2,89748-8o 2,93888-06 2,98027*33 3.02166-60 3,0630587 3, 10445- 14 3,14584-41 3, '872368 3,22862-94 3,27002*21 3,31141 48 3,35280-75 3,39420-02 3,43559 2Q 3,47698-56 3.5'837-8a 3.55977-09 3,60116-36 3,64255-63 3,68394-90 3.72534- »7 3,76673-43 3,80812-70 3,84951 97 3,89091-24 3,93230-51 3.97369-78 4,0150005 .4.05648-31 4.09787-58 4,13926-85 Yean 51 52 53 54 S I 61 63 69 70 7' 73 73 74 \l 81 82 % 89 90 9» 92 93 94 ^ 97 98 99 100 Feipt. (315) LOGARITHMIC TABLES I ill I Yean I 2 3 4 i I 9 lO II 12 '3 M \i [I 20 21 32 23 24 Log. I*. % 2 2 29 30 31 32 33 34 35 36 I? 39 40 41 42 43 44 45 46 47 ^8 49 50 0,04021-80 o>09»43 6o o»M76s-4i 0,19687-21 0,24609*01 O' 29530-81 0*34452-62 o»39374'42 0,44296-22 0,49218-02 «>.54'39'82 0,59061 63 0,63983-43 o, o. =>'03983*43 3,68005-23 3,73827-03 0,78748-84 0,83670-64 0,8859:^ -44 0,9351434 o>98436o5 »*o^357-85 1,08279-65 »' '3201-45 I,i8l23-2K 1*2304500 i,27o66-86 1,32888-66 1,37810-46 1,42732-27 J.4765407 ' i»52575-87 i»57497*67 1,62419-47 1,67341-28 1,72263-08 1,77184-88 1,82106-68 1,8702849 1,91050-29 1,9687209 2,0179389 2,06715-70 2,11637-50 2. 165^9-30 2,21481-10 2,26402-90 2,3132471 2,36246-51 2,41168-31 2,46090-11 12 Log. a-. For explanation see pp. 216-228 Per Cent. 0,049:11-80 9,772iiO*02 9,61945-76 9,5«75o-S3 9,4431 21 7 9,3860c -95 9,34067-76 9*30384 '99 9,27341-55 9>24793-44 9,22638-18 9, 20800- 26 9,19222-50 9,i786o-65 9,16679-78 9*15651 69 9,14754-25 9*13968-18 9,1327815 9,12671-17 9.12136-31 9,11664-26 9* "247 08 9,1087796 9, 105 CI 01 9,10261*16 9,10003-99 9.09775-65 9,0957278 9,0939245 9,09232*07 9,09089*38 9,08962*36 9,08840-27 9,08748-55 9,o86s8-8i 9,0857884 9*08507-57 9,0844403 9*08387-38 9,08336-86 9.0S291-80 9,08251-61 9,08215*76 9,08183*77 9,08155-23 9,08129*76 9,08 1 07 04 9,08086-76 9,0806866 Log. or. 9,0805250 9,08038-09 9,08025 -22 9,08013-73 9,0800348 9,07994-32 9,07986- 1 c 9,07978-86 9,07972-35 9,07966-53 9,07961*35 9*079567' 9,07952 -50 9*07948 -88 9,0794559 9,07942-64 9.07940-02 9.07937-67 9,07935-58 9,07933-71 9,07932-04 9*07930-55 9,07920-^1 9,07928*03 9,07926-97 9,0792601 9,07925- 1 7 9,07924-42 9,07923-75 9,07923*14 9,07922*60 9,07922-12 9,07921*70 9,07921*31 9,0792097 9,0792067 9,07920-39 9,07920-15 9,07919-93 9,07919-74 9,07919-57 9,07919-41 9,07919-27 9,07919-15 9,07910-04 9,079 > 8- 9,079'8- 9,07918-78 9,07918-71 9,07918*65 9,0 '918-12 Log. r". 2*80542*73 1,85464-53 2,51011*92 2*55933-72 2,60855-52 2*65777-32 2,70699-12 2,75620-93 2," 2, 2,90386-33 2,95308-14 3,00229-94 3.05151-74 3,10073-54 3. 14995 35 3,i99»7-i5 3,24838-95 3*29760-75 3.34682- 3,39604- 3,44526-16 3,4944796 3.54369-76 3,59291-57 3,64213-37 3,69135-17 3,74056-97 3,78978-77 ^'!J2°°S8 3,88822-38 3*93744-18 3,98665-98 4,0358779 4,0850959 4,13431-39 4,18353-19 4,23274-09 4,28i96-8o 4,33"8-6o 4,38040-40 4,42962-20 4,47884-01 4,52805-81 4,5772761 4,62649-41 4,67571-22 4.7249302 4,77414-82 4»82336*62 4,872c8-42 4,92180*23 Yean SI 52 53 54 5 5 9 61 62 69 70 71 72 73 74 81 82 83 ?4 85 86 87 88 89 90 9» 92 93 94 99 100 Perp (316) TABLE II. SHOWING A. For every rate contained in the preceding table the logarithms, to 10 and 7 decimals, of f, t being the interest of ;^i per annum or the rate ; of /-, r being ^1 increased by interest for one year ; and the logarithm of log' r. B. For every rate between o and 10 per cent, proceeding by loths, the logarithms of t and r. C. For every fractionary rate between o and to per cent., pro- ceeding by 1 2ths, the logarithms of / and r. The rate of interest which M. Thoman calls / is in modern notation denoted by /, and the amount of i in i period is now expressed by i + / instead of by /•. (317; i LOGARITHMIC TABLES OF Table II This table shews the Logarithms of (<), (r), and (Log'.r), i being the rate of interest per cent, and r £1 increased bj its interest for one jear. Rate per Cent. V. •/a Vs 't 8 * /« 2 * . I'/s 3 3 Vs 3> 3% 3 % 3% . 3'/i 4 A'U ^> 1;/. S'/s sy. 5% 6 6 V, 7 7 V. 8 9 lO Log. fc 7.6989700043 8,0000000000 8,17609-12591 8. 2*085 33653 8,24303-80487 8,27300-12721 8,30102-09957 8.32735-89344 8,35218-25181 8,37566-36140 8,3979400087 8,4191293072 8,4393326938 8,4S863-78490 8,47712-12547 8,49485 002 1 7 8,5« '88-33610 8,52827-a7772 8.54406-80444 8,55930-80109 8.57403«2677 8,58827-17068 8,60205-99913 &J^§^«'39529 8,62638-89301 8.64097-8057^ 8,6<32i-35i38 8,66 /lO '/le 7,. 7,. I ■ y.. • 7ie I 7,0 • 7i« 1 7,0 2 2 v.. 27,. 2 7l. »!/'• 2 7,e 27,. 2 7,o 27.. 2 7lO 3 3 v.. 3 7i. 3 7.. 3 7io Log. r. 3 7.0 3> 3> 3 7,. 3 7io 4 J?:: 4 7,. 4 7,. 4 7i. 4 7m 4 7,. Log. i. 0,00043-40775 0,00086-77215 0,0013009330 0,001 73*37 » 28 0,00216-60618 0,00259-79807 0,00302-94706 0.0034605321 0,00389-1 1662 0,00432-13738 0,00475-11556 0,0051805125 0,00560-94454 0.00603-79550 0,00646-60422 0,00689-37079 0,0073209529 0,00774-77780 0,00817-41840 0,00860 01 7 18 0,00902-57421 0,00945-08958 0,00987-56337 0,01029-99566 0,01072-38654 0,01114-73608 o.oii 57-04436 0.01 199-31 147 0.01241-53748 0,01283-72247 0,01325-86653 0,01367-96973 0.0141003215 0,0145205388 0,0149403498 0,01535-07554 0,01577-87564 0,01619-73535 0,01661-55476 0,01703-33393 0,0174507295 0,01786-77100 0,01828 43084 0.01870-04987 0.01911-62904 •.01953* »6845 0,0199^-66817 0,02036- 12826 ©.•2077-54882 •,02118-92991 Log. f. 7,00000-00 7,30103-00 7,477i2'3 7,60206-00 7,6989700 7,778i5-»3 7,8450980 7,9030900 7,95424-25 8,0000000 8,04139-27 8,0791812 8,11394-34 8,14612-80 8,17609-13 8,20412-00 8,2304489 8,25527-25 8.27875-36 8,3010300 8,32221 93 8,34242-27 8.36172-78 8,38021-12 8,3979400 8,4«497-33 8,43'36-38 8,447«S-8o 8,4623980 8,477»2i3 8,49136- 1 7 8,50515-00 8,51851-39 8, 53 « 47 89 8.5440680 8. 556.30-25 8,56820-17 8.57978-36 8,59106.46 8,6020600 8.61 278-* 9 8.62324- 8,63346 . 8,64345-27 8.65321 -25 8,66275- 78 8,67209- 79 8,68124-12 8,69019- tl 8,69897*00 r93 V85 Log. r. 8,70757-02 8.71600-33 8,72427-59 8,73239.38 8,74036-27 8,74818-80 8,75587-49 8,76342-80 8,7708520 8,778iS->3 8,7853298 8, 79239-' 7 8,7993405 8,80618-00 8.81291-34 8,81954-39 8.82607-48 8.83250-89 8,83884-91 8,8450980 8.85125-83 8.857.33-25 8,8633229 8,86923*17 8,87506- '3 8,88081-36 8,88649-07 8.89209 46 8,89762-71 8,90309-00 8,90848-50 8,9'38»*.39 8,91907-81 8,92427-93 8,92941-89 8,9344985 8.9395'-93 8,9444827 8,949.39-00 8,95424-25 8,95904*14 8,96578-78 8,96848-29 8,973' 2*79 8,9777236 8,98227-18 8.98677*17 8,99122-61 8.9956352 ^00000-00 Bate I 0,02160-27160 0,02201*57398 0.02242-83712 0,02284-06109 0,02325-24506 0,02366-39182 0,02407-49873 0.02448-56677 0,02489-59601 0.02530-58653 0,02571-5.3839 0.02612-45167 0,02653-32645 0.02694-16280 0,02734-96078 0,02775-72047 0,02816*44194 0,02857-12527 0,02897*77052 0,02938-37777 0,02978-94708 0,03019-47854 0,03059-97220 0,03100-42814 0,0314084643 0,03181-22713 0,03221-57033 0,03261 87609 0,03302- 14447 0,0334237555 o,03.:i82-56940 0,03422-72608 0,03462-84566 0,03502 92822 0,0354297382 0.03582-98253 0,036229544' 0.03662 8895ii 0,03702-78798 0.0374264979 0,03782-47506 0,03822-26384 0,03862-01619 0.03901-73220 0,03941 *4"92 0,03981 05541 0,04020-66376 0,04060-23401 0,0409976024 0,04139*26852 /I. 7,0 7,. 7,. 6V,. 7.. 7.. > J'* 7.. 7.. 7.. 7i. H s 7' 7' 7 7 7 7 7 7 7 1. /I. 7.. 7i. 7i I. .1. I. •/. 7i« 8 8 8 7;. 8 7i. 8 8 8 1. 1. 8 7ie 9 9 y- 7i. t 7.. 7.. 7 10 10 (319) LOGARITHMIC TABLES ^'g^^i; ^' ^v:.rj.*te-.-:^- s 7 IS V, IS I 0,00036-1761^ 0,00072-32216 0,00144-52409 0^00180-58009 0,00252 60240 0,00288-56882 0,00360-41243 0,00396-28971 It V. 2 2 7,2 0,00467 0,00503 0,00575 0,00610 0,00682 0,00717 0,00788 0,00824 •95548 74407 •23289 ■93322 •24596 •85M 99599 531 10 6,92081 -88 7,2218487 7.52287-87 7>6i978 88 7,76591-68 7,8239087 7.92081 -88 7,96221-14 8,03476-21 8,06694-68 8,1249387 8,15126-77 8,19957-24 8,2218487 8,26324 «% V, 3 3 . IS 0,00895 0,00930 0,01001 0,01037 0,01 107 0,01142 0,01213 0,0124^' •48427 92241 -71208 •06368 -68060 •94618 •39136 S7"5 3'h 3> 3 »Vi, V. 18 ^ J* 4»Vu IS 0,01318-84536 0,01353-93986 0,0142404391 0,0145905355 0,01528-98826 0,01563-91343 0,01633-67963 0,01668-52074 0,01738-11923 0,01772-87670 0,01842-30828 0,01876-98249 0,019^6-24798 0,01980-83934 0,02019-93051 0,02084-44841 ,26324-14 1,28254-66 8,31875-88 8,3357921 8,36797 68 8,38321-68 8,4121804 8,42596-87 5'45229-77 8,4648868 8,48902-05 8,50060-24 8,5228787 8,53360-26 8,55428-72 8,56427-14 8,58357-66 8,59291 -66 8,61101-48 8,6197888 8,63682-21 8,64500-46 8,66118-14 8,6690068 8,68424-67 8,6916708 8,70614-86 8.71321-04 8,7269987 8,73373*21 8,74689-36 8.7533277 8. 7059* -68 8,77207-71 8,78414-16 8,79005-05 8,80163-23 8,80730-9^ 8,81844-^8 8,82390-87 1 8,83463-26! 8,83989-68 0,02IC3 0,02187 0,02256 0,02290 0,02359 0,02393 0,02462 0,02496 •38405 -81089 ■58279 ■536 •80075 •24749 •43045 8,85023-77 8.8CS3I-72 8,86530-14 8,87020-88 8,87986-01 8,88460-66 8,8939466 8,89854-24 8,9075905 8,91204-48 8,92081-88 8,92514-01 8.9336560 8,93785-21 8,94612-46 8,95020-25 0,02564 0,02598 0,02666 0,02700 0,02 r68 0,02802 0,02870 0,02904- -81^20 •94283 •96512 -92984 87236 67791 54103 ^,95824-53 8,96221-14 8,97003-68 8,9738972 8.98151-66 8,98527-67 8,99270-08 8.99636-57 0,0297218816 0,03005-97225 0,03073-46170 0,03107-16713 0,03174-49962 0,03208-12676 o,0327K-?o303 0,0330885224 0,03375-87300 0,03409-34464 o, 034 762 1063 0,0350960505 0,03576-31697 0,03609-63453 0,03676 19309 0*03709-434 i 5 0,03775-84005 0,0380900496 0,03875-25890 0,03908-34800 0,03974-45068 0,04007-46^32 0,0407^-41642 0,04106-35495 5 5 5 5 5 5 5 5 6 6 6 6 6 6 7i. I 7, 4 6 7 6'»/ ;.. 7 . " 7 /« 7 7. 7 7,« 7 ;/,. 7'Vi 8 > 8'V. if 9 ;/„ 9 /• ^ I* 9 7i. 9 7u 9 7* 9% 9'V« For explanation see pp. 216-228 (320) . IMPORTANT BOOKS ON VALUATION^ Thh'ii Edition Enlargectf Demy 8vo, cloth, 334 pages. 78. 6cl. net. Valuation of Real Property. A Guide to the Principles of Valuation of Land and Buildings, &c., for Various Purposes, including the Taxation of Land Values. By CLARENCE A. WEBB, P.A.S.I. Valuer and Rating Surveyor, Author of ' The Law and Practice of Rating and Assessment,' Joint Author of 'Rates and Taxes.' Third Edition. Revised and Enlarged. By ALFRED HUNNINQS, F.S.I. Rating Surveyor to the Hackney Borough Council, &c. ' The book will prove a capital vade mecum to all who are called upon to value land or buildings, as well as to owners or stewards of real estate. It is a valuable contribution to a difficult and intricate subject.' — Property Market Revieiu. Demy Svo, cloth, 168 pages. 7s. Bd. net. The Valuation of Mineral Property \ Rules and Tables. By T. A. O'DONAHUE, M.E., F.G.S., Editor of * Mining Engineering,' First Class Certificated Colliery Manager, Member of the Institution of Mining Engineers, Author of ' The Colliery Engineer's Pocket Book,' 'Colliery Surveying,' 'Mining Calculations, * Mining Formulae,' &c. * The Author has endeavoured to be as brief and simple as possible, and in the result has produced a thoroughly useful book.' — Ne7vcastle Daily Chronicle. Crown Svo. Cloth. 5S. net. Tabular Aids to Valuation. For Ascertaining the Purchase Price of Building Estates : Percentages required to Cover Interest and Sinking Fund ; Cost of Buildings ; Deductions for Maintenance ; Comparative Site Values, &c. By GEO. TYRRELL M*CAW, B.A.L. M.A. (T.C.D.), Fellow of the Surveyors' Institution, AND F. OLIVER LYONS, B.A.I., M.A. (T.C.D.), Valuer and Surveyor, General Valuation Office, Ireland ; Fellow of the Surveyors' Institution. London: CROSBY LOCKWOOD & SON, 7 Stationers' Hali Court, E.G. 4, and 5 Broadway, Westminster, S.W.I Complete Catalogue on Application, USEFUL BOOKS FOR VALUERS. Demy 8vo, cloth, 258 pages. 7S. 6Cl. net. The Law and Practice of Rating and Assessment. A Handbook for Overseers, Members of Assessment Committees, Surveyors, and others interested in Rating and Valuation. By CLARENCE A. WEBB, P, A.S.I. Valuer and Rating Surveyor ; Author of ' The Valuation of Real Property,' &c. 'This book is one of the most authoritative and exhaustive yet issued on the subject.'— City Press. Mr Webb may be congratulated on having carried out with success a difficult piece of work. ' —Economic Journal, Fifth Edition Enlarged. Crown Svo, cloth, 300 pages. 6S> net. Agricultural Valuer's Assistant. A Practical Handbook on the Valuation of Landed Estates; including Example of a Detailed Report on Management and Realisation ; Forms of Valuations of Tenant Right ; Lists of Local Agricultural Customs ; Scales of Com- pensation under the Agricultural Holdings Acts, and a Brief Treatise on Compensation under the Lands Clauses Acts, &c. Fifth Edition, with Appendix containing a Digest of the Agricultural Holdings Act, 1908, together with the Full Text of the Act, and Practical Commentary thereon. By TOM BRIGHT. Agricultural Valuer; Author of 'The Agricultural Surveyor and Estate Agent's Handbook.' Fcap Svo, leather, 450 pages. 7«. 6cl. net. Agricultural Surveyor and Estate Agent's Handbook Of Practical Rules, Formulae, Tables, arid Data. A Comprehensive Manual for the use of Surveyors, Agents, Landowners, and others interested in the Equipment, the Management, or the Valuation of Landed Estates. Second Edition. Revised. By TOM BRIGHT, Agricultural Surveyor and Valuer, Author of * The Agricultural Valuer's Assistant," &c. London: CROSBY LOCKWOOD & SON, 7 Stationers' Hall Court, E.C.4, and 5 Broadway, Westminster, S.W.I Complete Caimlogne on AppUcmtlon. Date Due '^T'C^- ^n \ i^ — / — j- ¥■ r- i \ \ ^ ^^ ' -^ ii i^-^U ipp wfm. ^^Ztn'5> Inwood Tables of interest L ^if'i cr«? NEH *iM23m COLUMBIA UNIVERSITY LIBRARIES 0044243324 END OF a TITLE