1 m . ^Mnrg Nem ^atk S»tate (^allege of Agriculture At Qotnell UntDecaitg itifuta. s. f . Sltbracg HG 8771.D282" """""^'*y Library The original of tliis book is in tine Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31924013780287 ELEMENTS OP LIFE INSURANCE Third Edition with Definitions of Life Insurance Terms MILES MENANDER DAWSON Counsellor-at-Law and Consulting Actuary PRICE, - $2.00 19U THE SPECTATOR COMPANY Chicago Office : 1 35 William Street insumnoe exchange new york H a^n 1 COPYSIGHT 1911 BY THE SPECTATOR COMPANY New Yokk First Printing igii Second Printing 1914 ;^Gb./\/^> PREFACE TO THE THIRD EDITION. The demand for this little book calls for a new edition, and the changes in life insurance as practiced in the United States which have taken place during a decade past have rendered it necessary to make this a revised edition as well. The surprising thing is that the princi- ples of sound life insurance are so well established and so universal that even the great, and indeed startling, de- partures in recent years from the former methods result in but few alterations of the text — and these relatively unimportant — and in yet fewer additions. An earnest attempt has been made to make the book yet simpler and more explicit than in the previous editions, and to exclude all that is mere opinion. A glossary has been added, giving the definitions of life insurance terms which are in common use, with references to pages of the book which discuss the subject more fully. In revising the book, its employment as a text-book in schools and colleges has been kept in mind, and especial efforts have been put forth to make it accurate and defini- tive throughout. New York, September i, 191 1. TABLE OF CONTENTS. INSURANCE IN GENERAL Page 15 Insurance, equalization of fortune. Indemnity. Spreads financial loss. Application of solidarity. Encourages enter- prise. Not altruism but enlightened selfishness. Indemnity, fundamental. Distinguished from gambling. A "hedge." Not gambling for companies. Reliability of averages. Over- insurance or insurance without insurable interest, gambling. Unknown to ancients. Marine insurance first. SOME FEATURES PECULIAR TO LIFE IN- SURANCE Page 19 "Policy" and "Premium.'' Rates of premium "'guessed." Effect of high and low "guesses" — life, health, annuity. Laws of average. Variations of hazards. Increasing hazard of death with ultimate certainy. Likeness to hazard of sickness. Insurance against death at any time seemingly impossible. Company the stakeholder. How accomplished. "Self-insur- ance." Premiums based on statistics. Life insurance com- panies may not cancel, must renew if desired and cannot alter premiums at will. Consequences of this. Insurable interest; over-insurance. Gradual reduction through increase of "self- insurance." VITAL STATISTICS AND MORTALITY TABLES Page 24 Comparison of fire and life insurance. Need for reliable statistics. Table from freshly selected lives not suitable. After insured five years, not better than average. Getting 5 death rates from population statistics. Observing lives from birth. Equivalence of methods. Ulpian's table. Graunt's table. DeWitt's table. Breslau table. London Experience table. Northampton table. Carlisle table. Actuaries' or 17 Offices' table. American Experience table. Farr's English Life tables, i, 2 and 3. British government's tables of an- nuitants. 20 Offices' tables. 30 American Offices' tables. 23 German Offices' tables. Duvillard's and Deparcieux's tables. French Companies' tables. Fraternal Congress table. New British tables. New American "special risk" tables. Select and Ultimate. Actuaries' table not intended to be permanent standard. Elizur Wright's statement. How far justified. Wisdom of conservative table. Actuaries' and American Ex- perience tables standard. THE ELEMENTS OF PROBABILITIES Page 33 History of science of probabilities. Almost unknown to an- cients. First modern appearance. Pascal's Letters. Bernoulli's Ars Conjectandi. DeMoivre. Thomas Simpson. La Place. DeMorgan. Quetelet. "Choice and Chance." Certainty equals. Illustration that chance is a fraction. Application to future events. Illustration. A priori and a posteriori methods. Latter safer. Application of same. Like conditions necessary. Com- pound probabilities. Product, not sum of simple probabilities. Illustration. Last survivor probability. RATE-MAKING— ONE- YEAR TERM OR NATURAL PREMIUM Page 38 Premium changing each year. Assumption of uniform deaths. Error on safe side above age 10. Assumption of death claims payable at end of year. Custom elsewhere. Error unimportant, with conservative table. One-year term net pre- mium computed. An alternative process. A more general rule. Historically not the earliest form. Championed by Sheppard Homans. His experiment. Description of plan and its opera- tion. Departures. Adverse selection at higher ages. Neces- sarily so. Probably no mortality table would answer. Yet under all plans all the actual insurance is paid for at natural premium rates. 6 RATE-MAKING— PURE ENDOWMENTS AND LIFE ANNUITIES Page 45 Why here introduced. Definition pure endowment. Illus- tration. Alternative rule. Life annuity, series of pure en- dowments. Rule, life annuity and life annuity due. Alterna- tive rule. Rule, temporary life annuity and temporary life annuity due. Illustrations, life annuity and temporary life annuity. Annual premiums are life annuities due or temporary life annuities due. Net annual premium for pure endowment. Illustration. RATE-MAKING— TERM, WHOLE LIFE AND LIMITED PAYMENT Page 50 Term insurance earliest form. Illustration. Alternative rule, general. Special explanation. When term is life, equals highest age in table, plus i, less age at entry. Illustration. Net annual premiums equivalent in value to net single premium. Rule, net annual premium, whole life. Rule, net annual pre- mium, term. Net annual limited premium. Limitations. Also apply to net annual premium from age o. When whole life in- surance introduced. RATE-MAKING— ENDOWMENT INSURANCES. . .Page 56 Definition. Illustration. Rule, for net single premium. Alternative rule. Rule, net annual premium. Alternative rule. Semi-endowment. Double endowment. Partial endowment. Application to special forms. When endowment insurance in- troduced. Favorable selection. Misconception. Illustration. A second illustration. RATE-MAKING RETURN PREMIUM IN- SURANCES Page 61 Definition. Net single and annual premiums, increasing in- surance. Illustration. Illustration, return premium. Why algebraic. Extra premium loaded. Half premium return. Re- turn of premiums paid in last of period. RATE-MAKING— INSTALMENT AND CON- TINUOUS INSTALMENT INSURANCES. "MONTHLY INCOME" POLICIES AND "INCOME" BONDS Page 64 Ordinary instalments. Definition. "Monthly Income" poli- cies. Value of instalments. Commutation of instalments. Reversionary annuity. Definition. Net single premium. Rules, life annuity and joint life annuity. Reversionary annuities favored by actuaries but not by the public. Defects. Con- tinuous instalments. Definition. Advantages. Invented by Emory McClintock. Net single premium. Illustration. Rule. Continuous instalment provisions. Definition. Rule. Income bonds. When wholly interest income. Higher incomes. Illus- tration and rule. Alternative rule. Special form. Income until death. Partly reversionary annuity. Rule for approxi- mation net single premium. Annual premiums. When joint life annuity due is used. Extra premium dropped if beneficiary dies first. RATE-MAKING— JOINT LIFE INSURANCES Page 73 Definition. Called partnership insurances. Name not ex- clusive. Analogy to one life. Rule for net single premium. Rule for probabilities. Rule for net single premium joint life pure endowment and endowment insurance. Present values, joint life annuity and temporary joint life annuity. Net annual premium, joint life; net annual limited premium, joint life. RATE-MAKING— LOADING— PRELIMINARY TERM Page 76 Meaning of "net premiums." Need for "loading." Premiums not always "loaded." Non-participating premiums. "Loading" not split into parts. Expense not limited to loading. Exceeds it for several years. Loading by percentage — ^by a constant. Uni- form loading favored by some. Effect of commissions. Scien- tific loading in France. Separation by purposes. Modes of ad- justment. First year's loading. Making loading function of cost of insurance. French plan explained. Effect on net pre- miums. Preliminary term plan. Its effect. Apparent net premiums. Modification of plan. Apparent net premiums. 8 Whole life endowment. Justification of plan. Other modifica- tions. Loading of single premiums. Deemed at once available. Limited premiums and endowment premiums loaded more than whole life. Select and ultimate method of determining extra loading recognized by laws of New York. Limitations in New Jersey. Minimum reserve standard in Canada. European countries. RATE-MAKING— PREMIUMS PAYABLE MORE FREQUENTLY THAN ANNUALLY .Page 84 Mode of exact computation. Usual mode. What is assumed. Deferred premiums, owed. Usual rule for semi-annual, quar- terly, bi-monthly and monthly premiums. Exact addition to make good the interest lost, at 4 per cent. RATE-MAKING— SOME MISCONCEPTIONS Page 86 Not based on expectancy. What is expectation of life? Curtate expectation. Identity of curtate expectation and value of an annuity without discount. Effect of discount. Net single premium. Probable life. Most probable after-lifetime. Test of net single premiums and present values : Will they work out? Component parts of premiums. "Three elements," cor- rect first year only. Mortality and deposit "elements" com- plementary variables. Mortality "element" may exceed entire premium. Reserve used to pay claim. Elizur Wright's illus- tration. UNEARNED PREMIUM OR RE-INSURANCE RESERVES Page 93 Basis. "Unearned premiums." "Re-insurance." Equiva- lent. When "retrospective" gives correct results. Illustrations, single and annual premiums. When retrospective and prospec- tive methods give same results. When they do not. Illustra- tions, mean reserves. Common approximation. Initial reserve. Sufficiency of reserves only true of aggregates. Individual re- serves are pro rata parts. Two rules. "Gross" values ; "net" values. Meaning of "net reserve." "Loading*' disregarded. Inaccuracy of assumption. Effect of so-called "scientific load- ing." Level gross premiums imply level net premiums? Is preliminary term valuation net? SURPLUS, WHENCE DERIVED Page loi Sources of gain, three. One, additional. Conservative as- sumptions assure margins from interest and mortality. "Load- ing" originally intended to provide dividend. Usually little margin nowadays. Salvage on mortality expected. "Suspended mortality." Accretions from forfeitures. Extravagant esti- mates. Causes of disappointment. Relaxation of harsh con- ditions. Little or no profit. False pretenses. Surplus for- feited at death. Gains from lapses, why illusory. SURPLUS, HOW AND WHEN APPORTIONED. . .Page 106 Variety of modes. Contribution plan. Sheppard Homans and David Parks Fackler, authors. Mr. Homans' explanation. Expenses charged. First idea of cash dividends. Equitable's Deed of Settlement. Plan not carried out. "Reversionary bonuses." "Bonus" English name for dividend. Idea and name of cash dividend revived by American companies. Popu- larity of contribution plan. Generally adopted here. Dis- tributing lapse and other forfeiture gains. Mr. Homans' for- mula. Elizur Wright's savings bank system. Surplus indi- vidual account. Gains from forfeitures, how treated. General average percentages usually employed. Five-year and seven- year distributions. Annual dividends. Tontine plans. No surplus from loading for several years. Not always apparent. Advantages claimed for deferred dividend periods. Disad- vantages. Legislation in New York and elsewhere requiring annual distribution. Its effects. SURPLUS, HOW APPLIED Page 115 Cash. Paid-up additions. Interest-bearing script. Bonuses on bonuses. Cash dividends the rule in the United States. Dividend additions with privilege of cash. Cash, with privilege of additions. Proof of good health. Usually but once re- quired. Temporary additions. Options. Accelerated ma- turity. To purchase pure endowments, 10 SURRENDER VALUES Page ii8 Insurance originally forfeitable. Inconsistent with funda- mental idea. Old-time practice of Equitable. Use and abuse of discretion. Demand for surrender conditions in policies. In United States first recognition, as to dividend additions. First agitation by Elizur Wright in so's. As commissioner, urged automatic extended insurance. Massachusetts non- forfeiture law of 1861. Wright's table of temporary in- surances. Presbyterian Ministers' Fund issued non-forfeitable policies in 1856. New York Life introduced paid-up surrender values in i860. Attitude of Massachusetts companies. Early course of Mutual Benefit and National of Vermont. Tontine reaction. Massachusetts cash surrender law of 1880. Nature of surrender charge. Foundation, adverse selection. Effect of adverse selection. Costs of insurance. Insurance value. Per- spicacity of Elizur Wright's presentations. Subsidence of ton- tine reaction. Demand for surrender privileges. Adverse selection theory discounted. The new view. Action of New York Life in 1892. Equitable's cash value policy. Mutual Life's. Nature of its excess guaranties. Excessive guaranties. Reasonable limits of same. Elizur Wright's alternative measure for surrender charge. Three forms of values generally — of equivalent value. Automatic extension usual. Grace clauses. LOANS ON POLICIES Page 127 "Loan note" plan. Description. For from 25 per cent, to so per cent, of premium. Elizur Wright contrasts with refusal to pay surrender values. Distinction important, however. Loans often to maintain insurance. Loans and cash values usually in company. Same circumstances caused two companies to act differently. Strong disinclination to lend. Disrepute of "loan note" plan. Loans to pay premiums only. Nearly all companies now lend. Amount loaned. Next year's terminal re- serve plan explained. Special loans to pay premiums for re- mainder of period. Lending part of each premium. Automatic non-forfeiture by loans. Some abuses. INSURANCE OF IMPAIRED LIVES Page 133 First tried in the United States in 1865. Elizur Wright's comments. Failure of company. Discrimination among "good II lives.'' Lien system introduced by Actuary Fouse in 1892. Now taken up by several companies. Classification. "Rating-up" and "extra premiums." Special dividend class. "Rating-up" more frequent since deferred dividends prohibited. Uses of various plans. Lien plan preferred for agency reasons. Suc- cess of "rating-up" alone demonstrated. DEPARTMENTAL VALUATIONS Page 138 Original form of company statement. Usually "gross" pre- miums valued. Sometimes provision made for expenses. Elizur Wright's modifications. Simplification by offset. Valuations on December 31. Approximation. Mean for year. Reserve for excess guaranties or deficient premiums. Valuing policies with impairment liens. Valuing "rated-up" policies. Net unpaid and deferred premiums. Preliminary term valuation. Indus- trial policy values. Correct offsets on policies "dated back with liens." Elizur Wright on the same issue. Abuses of "dated back with liens." Is not excess an "impairment lien"? Ab- sorbs future cash payments. Comity in accepting valuations. Elizur Wright on this. Loans against renewal commissions once accepted, later thrown out. Not net valuation. Effect on small companies. Changes of standards. THE POLICY CONTRACT Page 147 The application. Effect of a warranty. What constitutes fraudulent misrepresentation? What is breach of warranty? Waived by incontestable clause. The promise to pay. An unilateral contract. Explanations. Place of payment. Con- venience of insured and beneficiary really consulted. Annual or more frequent premiums. Prepayment of premiums, two modes. Time of payment of premiums. Grace-time insur- ance is payable. Usually at once. To whom payable. Various plans. Privilege to change beneficiaries. Conditions of pay- ment. Usually unconditional after one year or more. Cor- rection for mistake in age. Incontestable provisions. Intro- duced 1879 by Equitable. President Hyde's comments. Does it hold in case of fraud? Assignments. Power to assign. Re- quirements. Validity. Instalments. Commutation. Con- version into instalments. Dividends. Usual agreement. 12 Options. Variations. Deferred dividends. After deferred period. Change to other forms. Usual in renewable term poli- cies. Other changes. Special conditions. Preliminary term provisions. Non-discriminating method. Guaranteed interest provisions. Surrender provisions. Non-forfeiture. Loan pro- visions. When next year's reserve. DEFINITIONS OF LIFE INSURANCE TERMS. . . .Page i6i 13 ELEMENTS OF LIFE INSURANCE. INSURANCE IN GENERAL. Insurance is the equalization of fortune. The degree to which it accomplishes that end is, of course, limited by its sufficiency and the contingencies to which it applies. But, by indemnifying one set of men for their losses through misfortune out of funds contributed by them- selves and others who, like them, in advance seemed sub- ject to the danger of a like misfortune, it tends to spread the loss over all and thus to equalize their fortunes in the one regard. By means of insurance, a large number of men arrange to lose small sums, the premiums which they pay. Their reward is that such of them as would otherwise lose great sums through a particular sort of mischance, shall be in- demnified in whole or in part, as may be the agreement. Thus all have the benefits of the protection, though to only a part do the misfortunes actually come which are indemnified. The first known form of insurance, there- fore, was giving a bond for another, a form even now not always recognized to be insurance at all. Insurance is the alliance of prudent men against mis- fortune. It is a peculiarly significant, important and even vital invention of civilization and a practical application of the principle of solidarity or community of interest. In this broader sense, the organization of the family, fol- lowed by the community, by society and the State, was the first manifestation of- the same principle.- 15 Insurance, so far as it applies, prevents the crushing of the individual by disaster of a financial nature, through apportioning his loss among persons who appear to be subject to the risk of such disaster. Each, charged with a sniall part of the loss, determined in advance, carries no more than he can bear. Business men, though prudent and not wildly venturesome, who are freed in this manner from the fear of disaster, dare to essay that which would otherwise be most dangerous; and thus great enterprises are encouraged. The practice of insurance was brought about not by an appeal to altruistic sentiment, but by purely business con- siderations. It is worthy of note that even the most of the insurances upon lives were at first for security of cred- itors. Sentimental charity had interpreted "Bear ye one another's burdens" to mean "Bear ye others' burdens." Insurance came about by a recognition of a truer inter- pretation of the command, and one that made it a practical rule for wise living. The new meaning, which was per- haps all along the true meaning, is : "Bear your share of the common burden and your own burden will be borne by you and the others." This principle has by some been thought to be applicable to a scheme of general co-opera- tion, perhaps too repressive of individual freedom of action. Business men have recognized its applicability through insurance to the sharing of unexpectedly heavy financial burdens under given contingencies ; and in a per- fectly practical way, for purposes of enlightened selfish- ness only, they co-operate in insurance, as they co-operate in the State, for mutual protection. Indemnity is the fundamental idea of insurance. It replaces, in whole or in part, in kind or in equivalent, that which is lost. This it does by what is a reversal of gambling, though it bears much similitude to gambling in form. Thus gambling is- to bet upon ascertain contin^ i6 gency. If it happens, you get back your stake and also the stake of your opponent; if it does not happen, you lose your stake. In insurance, so far as the surface of the thing goes, you also bet upon a contingency. If it hap- pens, you get the stake of your opponent, that is, the amount of the insurance if the loss is so much; but you do not get your stake back. It it does not happen, you lose your stake. The only diiference appears, on the sur- face, to be that you do not get your stake back and that your opponent is also stakeholder. But when you go deeper into it, the case is otherwise. It would not be gambling, though it seems so, if another had ventured your money for you on a certain contin- gency, for you to bet a like sum on the other side, so that in any event you would come out even. That is what gamblers call a "hedge" and speculators a "wash sale." Nature exposes men to certain risks of loss. To permit that risk to remain uncovered is really to gamble; to cover it by insurance is to "hedge." An illustration of this is the case of a miller buying a large quantity of grain in order to grind it, at the same time selling a like amount for future delivery, in order to protect himself against a fall in price. It may also be shown that the company does not gamble. If you make one bet on the tossing of a coin, you either win or lose. But if you make ten thousand such bets, the laws of average come in to limit your loss or gain ; and, if you make an unlimited number of such bets, you cannot lose or gain at all, because the chances are even. Nothing is more reliable than the laws of average when a large number of risks are combined. Insurance, as conducted by prudent companies, is a business, with reasonably reliable margins of profit, and not a speculation. The total loss on a large number of insurances within a given period can be foretold with remarkable accuracy. 17 From these considerations, it must be evident that to insure for more than the amount of the loss converts in- surance into gambling. This has long been recognized. In a like manner, to permit a person to have an insurance against that which involves no financial loss to him, is seen to be gambling. Both are discountenanced by the laws. Insurance, except in the form of fidelity or surety bonds, was unknown among the ancients, though some- thing like insurance was practiced in marine loans. Thus money was advanced at higher than the current rates of interest, upon ships and cargoes, on condition that, in case the same were lost, the loan was not to be repaid. Marine insurance was also the earliest form of modern insurance. Next came fire insurance and after that life insurance and other forms. i8 SOME FEATURES PECULIAR TO LIFE IN- SURANCE. The contract of insurance is called a policy. The word is from the Italian word for lottery ticket. The monetary consideration for the insurance is called a premium, which word, in Latin, means "bonus" or "prize." The fixing of rates of premium in all branches of insur- ance was at first necessarily pure guess-work. -In some cases, fortunately, the rates were guessed high enough or too high, in which latter case nothing was required but to adjust the premiums suitably ; and in either case there was no interruption of the successful course of the business. In other instances, the first rates were guessed too low, and, such is the perversity of human nature, the displeas- ure and distrust of men were visited on those forms of insurance, instead of merely upon the poor guessing. This was because failure attended the first companies that essayed such branches of insurance. Life insurance premiums, fortunately, were guessed high enough by the first regular company, the "Old Equitable," of London, that undertook whole life insur- ance for a level premium. On the contrary, the prices of life annuities were guessed too low; and, if the institu- tions guaranteeing them had not been solvent govern- ments and life insurance companies which earned on their life insurance policies sufficient profit to offset annuity losses, the sale of annuities would doubtless have been seriously checked. The rates for sickness or health insur- ance — it is known by both names — were also guessed too 19 low at first, and the business has suffered from the results of that circumstance to this day. In all branches of insurance, it has come to be recog- nized, though in some much earlier than in others, that proper rates of premium are to be found by combining statistics and by applying the laws of average. Variations of the hazard are found in all the subjects of insurance. Thus the hazard of fire varies with exposures, with occupancies, with the seasons of the year. But in most branches of insurance, there is no force or tendency constantly at work to diminish or increase the risk. In this respect, two forms of insurance, life and health, stand alone. The risk of death is great during the first year of life and then subsides slowly. At about the age of puberty it begins slowly to increase, and this rate of in- crement itself increases slowly. In extreme old age it becomes no longer a risk but, instead, a certainty. The time lost by disablement due to sickness tends to vary in a similar manner, also ; and, indeed, it is what mathema- ticians call a "function" of the mortality — that is to say, in some mysterious manner and according to an ill-defined law, the liability to sickness accompanies the risk of death, though low mortality rates and high sickness rates often concur. Death is a certainty and not a chance. The man would be accounted a fool who should put up a stake with third parties that he would never die; for it would be certain to be lost. Insurance against death, therefore, so far as insurance against its ever happening is concerned, it is plain, would be impossible, were not the company the stakeholder, as well as the bettor on one side. That death will come within a year, however, is a chance. Against this it is possible to make an insurance, quite as against any other contingency. Insurance may then be furnished for another year if one survives the first, and so on, but not without the limitation that the company must receive an adequate premium for each year's insurance. The risk is an increasing one, converg- ing into certainty ; and, when whatever age is considered the extreme limit of life is attained, the premium must be equal to the amount insured — discounted for one year, if the premium is paid at the beginning of the year and the insurance is treated as if payable at the end of the year. How, then, can a company supply insurance for the whole of life and for equal annual premiums or for premiums limited in number and amount or for a single premium, much less in amount than the sum insured ? The explana- tion is that the company is the stakeholder as well as one of the bettors. It collects more than is needed to cover the current risk, and it accumulates the remainder. This diminishes the actual amount to be paid at death out of the contributions of other policies; and, when the final age is reached, this produces a sum sufficient at the end of the year to pay the death-loss, deemed then to be certain. This accumulation is known as the reserve because it needs to be reserved in order that the company may fulfill its obligations, and was called the "self insurance fund," a self-explanatory name, by the great actuary, Elizur Wright. Because of these peculiar features of life insurance, the study of the subject is attended with somewhat greater difficulties than the study of other branches of insurance. The same considerations impelled life insurance compa- nies to begin collecting statistics from the outset, which would enable them to cope successfully with these diffi- culties, and they have proceeded much further in this re- gard than other insurance companies. Upon the results of these statistics, they predicate their premiums, and without such a basis life insurance would perhaps be an unsafe speculation. Two other facts lead life insurance companies to exer- cise great care in determining rates of premium. In other branches of insurance, the companies may cancel the in- surance by returning a pro rata portion of the premium. They may also refuse to renew when the term for which the premium was paid has elapsed. And they may make their own terms about renewing. But a life insurance company must not reserve the right to cancel or to refuse to renew or to alter the rate of premium. In other branches of insurance, as has been said, an insurance payable to a person who has no interest in the thing insured is recognized to be a gambling transaction. The same thing applies with yet greater force to a life insurance, and it would clearly be against public policy to permit gambling where a human life was made the contingency. Insurances, effected by one man on the life of another, are, therefore, viewed with suspicion, unless the nature and the amount of the insurable inter- est are clear. The question, what constitutes insurable interest, remains to be discussed, however, in its proper place. The amount of insurance is, as has been said, also an item of importance; for even a contract of indemnity, based upon a valid insurable interest, can be made a gambling contract if the insurance is for an amount in excess of the financial loss. The difficulties of determin- ing what is over-insurance upon a life, however, when insured in favor of persons who are dependent upon the person whose life is insured, coupled with the fact that the sum payable to persons whose insurable interest is limited, such as creditors, is usually limited to the amount of such interest, have made this question of little im- portance in life insurance. Moreover, under-insurance has been the rule and over-insurance the rare exception ; and the natural course of a whole life insurance, as has 22 been seen, whether purchased by level premiums for life, by limited premiums or by a single premium, is toward the reduction and ultimate extinction of the insurance, by the "self -insurance" fund growing until equal to the sum insured. Thus a gradual reduction takes place as the value of the life diminishes because its probable duration is less. Few men, also, can afford an outlay sufficient to supply premiums for an amount of insurance that exceeds the values of their respective lives. 23 VITAL STATISTICS AND MORTALITY TABLES. Where, as in fire insurance, policies are issued for a year only or at most for three or five years, it is sufficient to know approximately what the average annual hazard is for the class of risk covered. In fact, fire insurance companies have done with less than this; that is, with merely knowing that, on the whole, the business pays a margin, without knowing that this or that class of hazard has been profitable by itself. If a fire insurance company were, by the nature of the business, compelled to issue policies, without reserving the right to fix the premium on renewal or to refuse to renew, much greater care would, of course, be taken in determining the rates; but even then, the hazard dealt with would not be inherently an increasing one. The problems of classification would per- haps be serious and difficult; but, when they were once solved, the annual risk would not change, the conditions remaining the same. Life insurance policies usually cover, either for a long term or for the whole period of life, and are issued either for a level premium, or, in any event, for definite premi- ums. Even in assessment insurance, where the total amount of assessments per annum may vary, the power is not reserved to vary them as to a particular life, because that life is likely to fail soon. Life insurance cannot be canceled by the company, and it is nearly always renew- able at the pleasure of the insured. If life insurance were issued for a year at a time and the company were free to refuse to renew, the problem would be merely to ascertain in what ratio men, beginning 24 the year in perfect health at each given age, die before its expiration, which could easily be determined by the experience of companies. Of course, in that event the sickly and moribund would be refused the privilege of continuing their insurance. But the rates of a life insurance company must provide, at age 40, for instance, not merely for lives newly insured at age 40, but also for lives which were taken on at age 39 one year ago, at age 38 two years ago, etc. Such lives will be in an average condition only. Therefore, the statistics of a young company, or of any company with a very large proportion of freshly selected lives, would not be a reliable guide. After the benefit of the selection of the lives by medical examination has worn off, which is estimated to be in about five years, it is usually the case that the insured are at best in no better health than the average of the general population at the same ages; in- deed, at the higher ages they may often not average to be in as good condition. It is evident from the foregoing that great care is requisite to determine just what statistics may be relied upon to gauge the mortality likely to be realized among insured lives. The effects of medical selection, the possi- bly persistent effects of selection on account of family history and personal constitutional history, the ill effects of what is known as adverse selection by persons who are conscious of diminished vitality remaining in and others going out more freely, and the disinclination of men to carry insurance to an advanced age, unless convinced that death is near, must all be taken into account. Though, during extended periods, some companies have had very favorable experiences, it is not considered safe or prudent to expect that after the benefits of fresh selection have worn away, the mortality will be materially lower than obtains in the general population. 25 If, then, an accurate count could be kept of all persons in a nation as they enter upon a certain year of age and of those who die during that year of age, a reasonably reliable death-rate for that age would be the result. This repeated for each age, we would have the death-rate for every age when the work was completed. From this we could readily construct a mortality table, starting with any assumed number of persons, newly born, and dimin- ishing that number annually by applying these respective death-rates. The ideal method of making a mortality table, if it were possible, would be to take a large number of persons under observation from their birth and keep account of the diminution of their number each year by death. This is not practicable, however, for it would not be possible to keep them all under observation. But, if one has already ascertained, by observing a large number at each age, what the rate of mortality is at each age, he can, as has been said, construct a table which will show how the lives would fail, quite as well as if he had been able to keep a large number of persons under observation from their births. The first trace of anything like a mortality table is dis- covered at about the year 364, A. D., when Ulpian, a Roman praetorian prefect, introduced a table of probable life, in order to enable annuities upon lives to be valued. Upon what data it was based is unknown. John Graunt, in a book published in 1662, gives a crude mortality table, proceeding by decades from birth, instead of single years, derived from the baptismal and mortality records of the city of London. John de Witt, the famous Grand Pensioner of Holland and West Friesland, in a state paper bearing date about 1671, suggested a mortality table. This was in a discus- sion of the sale of life annuities by the State as a means of raising money. ^6 In a contribution to the Philosophical Society, in 1693, Edmund Halley published the first complete mortality table, deduced from the mortality records of the city of Breslau, Germany. This table was based on reports of deaths only, and it was assumed that the population was stationary, the births and deaths balancing. In 1762 the Equitable Society for the Assurance of Lives and Survivorships was organized in London through the efforts of Thomas Simpson and James Dodson. Is was the first life insurance company to issue policies for the whole period of life at level or other fixed premiums, and for fixed sums payable at death. The computations were based on a mortality table, deduced from the vital statistics of London by Simpson and Dod- son, and published in 1752. In 1780 Dr. Richard Price, a Scotch clergyman, pub- lished several mortality tables which he had constructed, including the famous Northampton Table, derived from the mortality records of two parishes in Northampton. This table, which, like the Breslau, was based upon returns of deaths only, was adopted by the Equitable as its stand- ard, and also by the British government as a standard for annuities. Dr. Price also gave tables, deduced from the vital statistics collected by the Swedish government at the suggestion of the philosopher, Menander. In 1815 Joshua Milne published a mortality table which he had constructed from the mortality statistics of the city of Carlisle, England. This was the first mortality table graduated so as to smooth out accidental variations from age to age; unlike the Northampton, it was con- structed from census returns as well as records of deaths. It exhibited much lower mortality rates than the North- ampton, and a great debate ensued as to the comparative merits of the tables. The Northampton table had shown much higher death rates at the younger ages than were 27 experienced by the companies as to insured lives or by the government as to annuitants. For insurances, the error proved to be on the safe side, for the premiums had been higher than was necessary; but for life annuities, the error was on the wrong side, and in consequence they had been sold at prices quite too low. The Carlisle table, since it accorded more nearly with the actual experience on insured lives, after a time super- seded the Northampton table for computing premiums and values of insurances ; but a table of mortality, con- structed from the experience of the British government as to annuitants, by the government actuary, John Fin- laison, and published in 1823, became the standard for life annuities. In 1843 the first "combined experience" table, derived from insured lives, appeared. It was deduced from the experience of 17 British life insurance offices, male and female lives combined, and accordingly was called in England the "17 Offices Table." In that country it never became standard ; but it was adopted by Elizur Wright, Insurance Commissioner of Massachusetts, as the stand- ard table for the valuation of life policies in that State, and under the name "Actuaries' Table" or "Combined Experience Table" it became the leading and recognized standard in the United States. In 1868 Sheppard Homans, then actuary of the Mutual Life Insurance Company of New York, published a table, which has since been known as the "American Experience Table," deduced from the experience of that company, adjusted by reference to the "17 Offices Table" and cer- tain arbitrary assumptions. This table was adopted as the standard of the State of New York, and has also been of great reputation in this country. It is now the table most frequently used in life insurance computations and also the usual standard for valuation. It is what is known 28 as an "ultimate" table, i. e., the data of the period during which mortality is most markedly affected by fresh medi- cal selection were excluded in constructing the table. Certain famous population tables, known as English Life Tables I, II and III, were constructed by Dr. William Farr from British census statistics, and were puiblished between 1845 and 1865. A second table deduced from the British government experience with annuitants appeared in i860, and a third in 1883. A second "combined experience" table was published in 1869. It was deduced from the experience of 20 lead- ing British offices, and is known as the 20 Offices Table. It consists really of three tables, a male life table known as the H^, a female life table known as the H^, and one, from male lives, omitting the first five years after entry, known as the H*^^ table. The H^ table soon became the recognized standard in Great Britain generally. In the United States a "combined experience" table, representing the combined experience of 30 American companies, was published in 1870. It is known as the "30 American Offices' Table" or "Meech's Table," from the name of the chairman of the committee which had charge of the work. It never became standard, being objected to as including too large a proportion of freshly selected lives, and on other grounds. In 1883 a "combined experience" table was published, based upon the experience of 23 German companies. This is known as the "23 German Offices' Table," and is the usual standard in Germany. A new mortality investiga- tion is now in progress there. In France, there were early tables, as follows: Duvil- lard's Table for annuitants and Deparcieux's Table for insured lives, each named for its author. The former was published in 1806 and was deduced during certain 29 investigations of the effect of small-pox upon mortality, and the latter was published in 1746 and was deduced from the experience of certain religious houses. In 1895, "combined experience" tables, both for insured lives and annuitants, were published in France, being con- structed from the experience of the leading French com- panies. The table from insured lives is known as A^ and the table from annuitants as R^. Both are from male and female experience combined. A mortality table, known as the Fraternal Congress Table, was adopted by the National Fraternal Congress as a standard for fraternities, and, upon its recommenda- tion, has been rnade the state standard for such societies pretty generally. Published in 1898, it was derived from the actual experience of two American fraternal societies, with certain arbitrary adjustments and modifications. New "combined experience" tables of the British com- panies, giving the experience as to assured lives and an- nuitants, and also for males and females separately, were brought out by the Institute and the Faculty of Actuaries jointly in 1903. Tables showing experiences under differ- ent kinds of insurance and also for different years of in- surance, i. e., on a "select" basis, are also given. The British government annuity tables also set' forth male and female experience separately, as do the English Life Tables and the 30 American Offices' Table. The combined experience of the leading American com- panies as to lives accepted otherwise than as first class, has been analyzed by a committee of the Actuarial Society in its "Specialized Mortality Investigation," published in 1903. This gives the mortality rates, as influenced by certain features of personal or family history, personal condition when accepted, residence, occupation, etc. A similar and more extended investigation is now in pro- gress. 30 In 1905, a modification of the American Experience Table was made by the author of this book, so as to show approximately the benefits of fresh selection by medical examination. It is known as "select and ultimate" and has been adopted in New York as a table by which to compute minimum reserves. It is constructed on the as- sumption that mortality rates during the first five years will be the following percentages of the "ultimate" or table rates for the same ages : Year. Percentage. Year. Percentage. I 50 4 85 2 65 5 95 3 75 and thereafter the full "ultimate" rates. The introduction of the Actuaries' or 17 Offices' Table as the standard of valuation in the State of Massachusetts was not regarded by Commissioner Wright as more than tentative. He expected and desired that a new standard should be adopted when the actual experience of Ameri- can companies could be compiled. Accordingly, for sev- eral years, he printed in the reports of that department tables showing the actual mortality of companies report- ing to it, compared with the expected by the Actuaries' Table, and thus showed that the actual experience was much more favorable than the table. Concerning this he remarked, in his last report, 1865 : "Of course this favor- able difference of experience cannot be permanently held by companies whose business is chiefly life policies ; for, if the death rate is slower on the earlier ages, it must be faster on the later, the limit of human life being pretty certainly fixed." Population statistics do not bear out Mr. Wright's gen- eralization, and there is reason to believe that the same influences which make mortality lower at earlier ages 31 work in a diminishing but always sensible degree to extend also the ultimate limit of life. But his conclusions do agree remarkably well with the experience as to insured lives generally; the phenomenon is, however, ascribed mainly to the disinclination of old men, who feel that their chances of life are as good as, or better than, the average at their ages, to continue to carry life insurance, which is usually no longer needed. The wisdom, also, of continuing to employ a conserva- tive table, giving somewhat redundant premiums, is justi- fied by the fact that, while the death-losses of companies are each year, on the average, materially less than the expected by either the Actuaries' or the American Ex- perience table, individual companies have more than once showed mortality equal to the expected by the table or exceeding it. Accordingly, the Actuaries' and the American Experi- ence Tables have continued to be standards in the United States. The Actuaries' Table has generally, though not always, been the standard where the rate of interest was set at 4 per cent., and the American Experience Table has always been the standard where the rate of interest has been set at four and one-half, three and one-half or three per cent. 33 THE ELEMENTS OF PROBABILITIES. An understanding of the simpler elements of the science of probabilities is desirable before proceeding further; for, of course, life insurance, indeed all insurance, deals with probabilities. The history of the science of probabilities is short. It was virtually unknown to the ancients, although traces of it are found in practice, as in the loans upon ships and cargoes, already referred to, and also in Ulpian's attempt to value life annuities. Traces are also found in the writ- ings of Pythagoras and in the works of mathematicians of India. Its first modern appearance is in 1663, in a pamphlet published in Italy by Cardan, and entitled "De ludo aleae," i. e., "upon the game of dice." The next is in a series of letters written by Pascal, the great French savant, from 1654 to 1679, in which he discussed the chances at play. The next great work, and the first to put the subject into treatise form, was Jacob (or James) Bernoulli's "Ars Conjectandi," published in 1705. Then came Augustus de Moivre's "Doctrine of Chances," published in England in 171 1, followed by Thomas Simpson's "Nature and Laws of Chance," published in 1740. The next great work was La Place's "Analytical Theory of Probabili- ties," written and published by the French Government, under the patronage of the great Napoleon, in 1812. After this came De Morgan's "Probabilities," in England, in 1838, and Quetelet's "Letters on Probabilities," in French, in 1845. Whitworth's "Choice and Chance" is the best English text-book. 33 The fundamental discovery was that certainty could be represented by unity and a chance by a fraction, the value of which can be computed, the requisite data being pro- vided. Thus suppose it were known that one out of 36 persons known to have been on board a vessel had been lost, but not which one. Plainly it is an even chance, one with another, that a particular person was lost ; and since there are 36 such equal chances, the chance as to any one per- son is in the ratio, i to 36, which is %6. The chance that he was not the person lost is in the ratio, 35:36, which is ^%e. Suppose that 6 were passengers and 30 were the crew ; the chance that the person lost was a passenger is evidently 6 times as great as that he was a certain pas- senger. Now let the news be received that the person was a passenger, which then becomes a certainty. The chance that it was a particular passenger now becomes Vt, i. e., one-sixth of unity ; but the probability that it was a pas- senger, we have found to be six times as great, t. e., 6 X % = I. That is, certainty is unity and all probalities are fractions. That reasoning is clear and conclusive as applied to past events. Now let us assume that it is known that out of 36 trials, a thing will happen once and fail to happen 35 times. It is again evident that the chance of its hap- pening is %6 and the chance of its failing to happen is ^e. This applies to the first trial. Whether it would apply to further trials or not would depend upon whether its happening is exclusive of its recurrence or not. For instance, suppose it is drawing balls from a box which contains one black and 35 white balls. If a black ball is drawn the first time and is not replaced, nothing but white can be drawn afterward; if a white ball is drawn the first time, and is not replaced, the chance of a black ball the next time is not i :36 but i :35. 34 But in either case, if the first ball is replaced, the chance remains the same, viz., i :36, or ^Se, for each trial. Probabilities as to future events may be deduced in either of two ways, viz., by a priori reasoning or by knowl- edge of what has happened before under conditions pre- cisely similar. The infirmities of the human mind are such that reasoning from the nature of things is perilous unless supported by experiment or by observation. It is also in most matters very difficult to assure that past oc- currences took place under conditions precisely similar to those which will hereafter obtain. Yet induction from the facts of experience affords in almost all things a safer basis for predictions of the future than does deduction from assumptions as to the nature of things. This is true, also, though the conditions be but approximately the same, and not exactly so. Another principle of the science of probabilities, only second in importance, then, is that, if out of a very large number of trials under conditions nearly alike, an event has been observed to take place a certain number of times, then, under like conditions, the probability that it will occur may be expressed by a fraction of which the number of times it happened is the numerator and the number of trials — i. e., the number of times it happened plus the number of times it failed to happen — is the denominator. And the chance that it will not occur may be expressed by a fraction with the same denominator, of which the num- ber of times it did not happen is the numerator. Thus, if out of 100,000 persons, at age ten, 676 have died in one year, we consider that the chance that a person, aged 10, will die in one year is-jg^^, and the chance that he will not die is^^, while the chance that he will die, plus the chance that he will not die is ^^^1^0000'* = ^S= I, or certainty. In the application of this important principle lies the pos- 35 sibility of computing in advance, within reasonable limits of error, the cost of insurance. The value of the risk or probability is estimated as closely as possible by means of averages drawn from past experience. The utmost care is, of course, necessary to ascertain that the condi- tions of the past experience, from which the averages are derived, and of the future as to which insurance is to be given, are alike in all essential regards. In life insurance alone are compound probabilities sometimes employed; as, for instance, in an insurance payable upon the failure of the first of two or more lives or an annuity continuing during the life of the last sur- vivor of two or more lives. The chance that two events will happen — the first neither including nor excluding the second — is not the sum of the chances that they will severally happen, but the product of those chances. Thus suppose the chance that one thing will happen is j^, that a second will happen is^g- and that a third will happen is-^. Then out of 1,000,000 persons, as to each of whom these chances are equally valid, the first thing will happen to 1,000; and out of this 1,000, to each of whom the second chance is equally valid, the second thing will happen to 10 ; and out of these 10, to each of whom the third chance is equally valid, the third thing will happen to i. Therefore, all these things will happen to but one out of the original 1,000,000; and the chance that all will happen to a particular one of them is ^^^^^ This is equal to the several chances multiplied together, i e to •^ V ^ v-^ 1 ' 1000 '^ 100 '^10 — 1000000 • In a similar manner it may be proved generally that where events are not mutually inclusive or exclusive, the probability that two or more will happen is the product of the probability that each will happen separately. So, the chance of incurring a claim within a year on a 36 life insurance on two joint lives is the chance that one will die plus the chance that the other will die, less the chance that both will die, i e., less the product of the two chances, for the amount of the policy is paid but once. Or it may be given as certainty, which is i, less the chances that both will survive the year, which is the product of the chance that one will survive and the chance that the other will survive ; for, if both do not survive the year, one at least must have died within it. An annuity payable during the life of the survivor of two lives, for instance, will yield a payment at the end of the year if either life survive ; that is, if both lives survive, or if the first life survive and the other expire, or if the first life expire and the second survive. The total probability, then, is the sum of these three separate probabilities. No attempt will be made in this volume to develop these principles into mathematical formulas; but the reader will not fail to find the foregoing principles both interest- ing and useful if he will give their statement in non- mathematical language his careful attention. ^1 RATE-MAKING— ONE- YEAR TERM OR NAT- URAL PREMIUM. Because of its simplicity the method of insuring lives which naturally first suggests itself is insurance from the date of the payment of one premium to the date when another premium becomes due, collecting just sufficient to cover the current cost of the protection. Thus, if pre- miums are payable annually, this will be an insurance for the term of one year, renewable, if at all, by the payment of a premium varying with the risk as the age increases, the premium for each year just taking care of the insur- ance for that year. Of course, the annual probability of death does not remain the same throughout life, but must be conceived of as constantly varying in a more or less regular man- ner. From birth to age lo, for instance, it is usually found that it constantly diminishes, though at a diminishing ratio. Then it usually begins to increase, very slowly at first, but at a constantly increasing ratio. The custom in life insurance, though it is not without exceptions, is to deal with the deaths as occurring uni- formly throughout the year, and with the death-rate as changing at the end of the year, so that the deaths then occur uniformly at the new rate throughout another year. This, as applied to renewable term or current cost insur- ance, involves no material error when premiums are paid annually; and at age lo and over the error is also not material from a financial standpoint when premiums are paid at intervals of less than one year because, as the risk 38 is actually increasing, to charge a pro rata part of an annual one-year term premium, representing the risk of the entire year, yields in the aggregate of premiums paid more than current cost for all parts of the year until the whole year's insurance is paid for. This assumption that the risk does not vary throughout the year is called the assumption of uniform deaths throughout the year. On the basis of this assumption, insurances at current cost, with premiums more frequent than annual, may be treated as one-year term insurances, with premiums adjusted to the varying cost at the begin- ning of each year and the remainder of the year's pre- mium as a deferred premium. Another assumption, also common in British and Amer- ican life insurance companies, is that death-claims are payable on the average at the end of the policy year in which the deaths occur. This was probably very nearly true when claims were not payable until three months after approval of proofs of loss ; for deaths occur on the average in the middle of the year, and if we allow three months within which to make claim and complete proofs and then three months for payment, the claims would be paid on the average at the end of the year. But in these days, when proofs are made promptly and claims paid almost at once, it would doubtless be more nearly correct to assume that death-claims are payable at the middle of the year. Such is the assumption in France and in some other countries ; and doubtless the change would be made also in Great Britain and America if it were not, first, that there are so many valuable working tables based on the former assumption, and, second, that the large margins in the standard mortality tables make the distinction of minor importance. Let us then compute the annual premium, payable at the beginning of the year, for one year's insurance from 39 age lo. And let us assume that deaths will be according to the Actuaries' Table, and that money in hand will earn 4 per cent, interest per annum until required. For convenience, assume, also, that 100,000 such insur- ances start at the same moment, each for $1,000 and each on a life aged 10. Then there will be altogether $100,000,- 000 of insurance running for one year. According to this table 676 persons out of the 100,000 will. die during that year, calling for $676,000 to be paid at the end of the year. The sum which must be on hand at the beginning of the year to meet payments of $676,000 at the end of the year, 4 per cent, interest being realized, is $676,000 -^ 1.04^ $650,000. If each of the 100,00 persons insured were to pay his proportionate part of this sum in advance, he would pay a premium of $6.50 for an insurance of $1,000 for one year. The same result may be reached thus : The contribution of each towards the. amount required to pay the total losses of $676,000, is $6.76. But this would not need to be paid until the end of the year — in which case the premiums of those who had died could be deducted from the amounts of their insurances — and since it is to be paid at the be- ginning of the year, it must be discounted at 4 per cent. and the net amount becomes $6.76-=- 1.04^ $6.50, as before. Or that result may be reached by a more general pro- cess, thus : for each the risk of dying during the year is j5j^. This, then, would be the premium, payable at the end of the year, for an insurance of i ; therefore, the premium payable at the beginning of the year for an insur- ance of I iSi^H-i.04=^5g, and the premium, payable at the beginning of the year for an insurance of $1,000, is-j^X $1,000 = $6.50, as before. This last method is most instructive. It shows that, on the assumption of losses payable at the end of the year, 40 the value, at the beginning of the year, of the year's insur- ance is the product of the probability of death, the dis- counted value of $1 due at the end of the year and the sum insured. From that fact many rules are derived. In the foregoing we have dealt with "net premiums" only, i. e., premiums sufficient merely to provide for the mortality expected according to the table employed with- out addition for expenses and contingencies. Historically, one-year term or natural premium insur- ance was not the earliest, though, because of its simplicity, it will here be considered first. Current cost insurance came earliest, to be sure, but no care was taken to appor- tion the cost correctly. Insurances for short terms, such as less than a year, a single year or a short terms of years, were granted at an early period, but without developing the method of computing the premiums for such insur- ances. Even whole life insurance, paid for by level pre- miums or by a single premium, preceded whole life insur- ance divided up into renewable one-year term insurances, each paid for by its own appropriate premium. The late Sheppard Homans, an eminent American actu- ary, devoted a large part of his life to an attempt to in- troduce and popularize renewable one-year term life in- surance, which he named the "natural premium" system. The demand for low-priced insurance was then, as always, very great ; and numerous societies and orders, operating under inequitable plans of apportioning the costs, had sprung up to supply this demand. The history of Mr. Homans' experiment, which was undertaken by the Provident Savings Life Assurance So- ciety, which he founded and which survived until this year, 191 1, when it was reinsured and merged with another company, though the natural premium plan which it at first employed was long ago recognized to be a fail- ure, is as follows: The gross premiums were computed 41 by adding one-third to the net premium as a contingency and reserve provision, and then $4 per each $1,000 in- sured, for expenses. This was on renewal premiums ; the first year the entire margin over the net premium was available for expenses. Savings in mortuary cost were to be apportioned at the end of each year in reduction of the next year's premiums. The premium was to advance each year to the premium for the attained age. At the end of ten-year periods the unused reserve was to be applied to reduce subsequent premiums. The dividends derived from mortality savings were at first large and served to disguise the increase in rates of premiums ; and the reserve provision, together with this fact, enabled uninformed and unscrupulous agents to represent that premiums would not increase. When, owing to the wear- ing off of fresh selection and to the advancing ages, the cash payments had to be rather sharply increased, the pro- tests of agents and the defections of policyholders caused the company to abandon the original plan so far as to employ the reserve portion to oflfset the increase in the one-year term premiums and to return the remainder in increased dividends in the form of reductions of current premiums. Thus, it will be seen, the pure natural premium, or one- year renewal plan, sold for what it was and then rigidly adhered to, did not get a fair trial, in spite of the re- nowned actuary's good intentions. The same company offered a non-participating, pure natural premium plan at low rates and in two forms, viz. : one with the amount of insurance fixed and the premiums increasing and one with the amount of the premium fixed and the amounts of in- surance decreasing. Neither of these found a ready sale, but it is not clear whether this was due to the plan itself or to these facts : A larger commission was paid for selling insurance on the other plan; the latter seemed, also, in 4a view of the dividends, to be even cheaper, while the policy- holders did not expect the premiums to increase ; and cur- rent cost protection was furnished much cheaper by assessment societies and orders, though on unscientific and ultimately unsafe plans. The practicability of the plan, then, was not put directly to the test ; but for certain reasons, now to be considered, it is believed that the result of such a test, if attempted, would have been and must be unfavorable. First, the participating plan actually employed by the Provident Savings becomes pure natural premium at about age 60 and upward, the dividends not availing to hold the rate level ; second, the discontinuances of good lives were per- haps not greater before those ages under the plan actually used than they would have been under a pure natural premium plan; and, third, statistics as to mortality at advanced ages on current cost plans, though unscientific and calling for much less than the true one-year term premiums at these ages, strongly confirm the experience of the Provident Savings that under this plan excessive mortality must be expected at the older ages. Consideration of the nature of the plan shows that ad- verse selection at advanced ages is to be expected, because the continually increasing premiums more and more dis- pose all who do not feel the need for the insurance, to with- draw. Persons who expect to die very soon always consider that they need the insurance. Of course, at age 95 under the American Experience Table and age 99 under the Actuaries' Table, where the one-year term premium for $1,000 insurance is $1,000 -h 1.04 = $961.36 on the basis of 4 per cent, interest, no person would pay the premium at all, and the premiums for many ages before that are prohibitive, also, for all lives except such as are consciously moribund. Yet such are one-year term premiums, if based on the 43 usual tables, for average lives at these ages. If, say from age 60, higher mortality were assumed to cover the ad- verse selection caused by the increase of premiums, would they not drive out the best of the lives which might have remained at rates computed on the lower mortality as- sumptions ? In other words, is there not a force at work in natural premium insurance, when continued in force at the older ages, which renders it impracticable, and perhaps even impossible, to have a mortality table making a sufficient provision, because the larger the rates, the greater the adverse selection ? On a priori grounds, this is now believed to be the case, and actual experience, so far as available, bears out that conclusion. It will be shown, hereinafter, and may now be stated, that on sound plans under all forms of life insurance the insured really pays for all the protection he receives, over and above the reserve or "self-insurance" fund, at the natural premium or one-year term rate for the attained age. If this were fully understood by everyone, perhaps the natural premium plan — especially if with decreasing benefits instead of increasing premiums — might be more popular and also might not exhibit so marked adverse selection at the higher ages. 44 RATE-MAKING— PURE ENDOWMENTS AND LIFE ANNUITIES. It would be possible now to pass directly to the single premium rates for other forms of insurance; but, since, as will be seen, the method of computing annual premiums cannot be explained without first explaining how to com- pute pure endowments and annuities, these fall first to be considered. After this, single and annual premiums can be taken up together. A pure endowment is a promise to pay a sum of money at the end of a given period, to a person, if then surviving, the purchase money to be forfeited in case he dies during the period. The net single premium for this — that is, the premium that would need to be collected in one sum in advance, without adding anything for expenses and con- tingencies — is found as follows : Taking age lo and the Actuaries' Table again and as- suming that funds will earn 4 per cent, interest until dis- bursed, let us consider the case of 100,000 pure endow- ments of $1,000 each, payable in 10 years to each survivor of that period. According to the table there will ibe 93,268 surviving at age 20 out of the 100,000 setting out from age 10. Therefore, $93,268,000 would be required to pay each survivor $1,000; and, if it were not for interest, each of the original 100,000 would need to deposit $932.68 in order to make up a fund large enough to pay $1,000 to each survivor. But $1 accumulates at 4 per cent, annually com- pounded, to $1.4802 in 10 years. Therefore, if the 100,- 000 persons altogether deposit in advance, the sum of 45 $93,268,000 -T- $1.4802 = $63,010,000 nearly, they will ac- cumulate enough to amount, with interest, to $93,268,000 at the end of 10 years and thus to pay all the endowments. So that, if each deposits $630.10, in advance, instead of $932.68, the accumulation will be sufficient. Therefore, $630.10 is the net single premium at age 10 for a pure endowment of $1,000, due in 10 years. The process we have followed is self-explanatory. It is equivalent, however, to this: Multiply the probability of surviving (93,268 -4- 100,000) by the discounted value of $1,000 ($1,000 H- 1.4802). And, generally, for the net single premium for a pure endowment of $1, this would be: Multiply the probability of surviving the en- dowment period by the value of $1 certain, due at the end of the endowment period, discounted to the beginning of the same. The probability of surviving is always a fraction, of which the "number living" in the mortality table at the original age of the endowment holders is the denominator and the "number living" at the age attained at the end of the endowment period is the numerator. If the promise is to pay $1 at the end of each year, in case a certain person survives, this evidently is equivalent to a series of pure endowments ; that is, a pure endowment of $1 due at the end of one year, plus a pure endowment of $1 due at the end of two years, etc. If it is to continue to be paid at the end of each year until the person dies, the last possible payment is at age 95 according to the Ameri- can Experience Table, and at age 99 according to the Actuaries" Table. That series of pure endowments is called a life annuity. If $1 is also to be paid at the outset, it is called a life annuity due, or sometimes, less accu- rately, an immediate life annuity. Technically, the latter term means an annuity with the first payment at the end of the first of the intervals at the end of which 46 the payments are to be made, as the first year, first quarter, etc. The net single premium for a life annuity of $i at age lo then, is the sum of the single premiums for a pure en- dowment of $1 in one year, a pure endowment of $i in two years,etc.,up to and including a pure endowment of $i in 85 (t. e., 95 — 10) years, if by the American Experience Table, and 89 (i. e., 99-10) years, if by the Actuaries' Table. And the single premium for a life annuity due is just $1 more than this; since, in addition to these pure endowments, there is $1, also, to be paid at once. The method of finding the net single premium for a life annuity of $1 may, then, be given this general form : Multiply the probability of surviving one year by the dis- counted value of $1, due in one year; multiply the prob- ability of surviving two years by the discounted value of $1, due in two years; and so on, including the number of years which is equal to the highest age in the mortality table less the present age; then add together these prod- ucts. If the net single premium is for a life annuity due, add $1. If the life annuity is payable for a certain number of years only, as 10, for instance, then, of course, the process stops at 10 years and the sum of the first 10 years' pure endowments only is taken ; this is the net single premium. If it is a life annuity due of $1 for a certain number of years only, then take the sum of the pure endowments for one year less, and add $1. Thus a life annuity due of $1 for 10 years is a life annuity for 9 years, plus an immedi- ate payment of $1. All net single premiums are also known as "present values;" as, for instance, the present value of an insur- ance, an endowment or annuity. They are also sometimes called "values," but that is likely to cause confusion, as the same word is used for "reserves." 47 To find, for example, the net single premium or the present value of a life annuity of $i from age 90, Actu- aries' Table and 4 per cent., assume 1,319 such annuities at that age, involving payments and values as follows : End of 1st year $892.00 2nd 3rd 4th 5th 6th 7th 8th gth 1892.00 Discounted i year. . .$857.6919 570.00 2 years. . 526.9969 339.00 3 . 301.3696 184.00 4 . 157.2839 89.00 5 . 73.1515 37.00 6 . 29.2417 1300 7 . 9.8789 4.00 8 2.9228 I. DO 9 .7026 $1,959.2398 Dividing by 1,319, the number of annuitants at the out- outset, age 90, we have $1,485 as the net single premium or present value of a life annuity of $1 from age 90. If it were a life annuity due, the present value would be increased by the $1 immediately payable, and would be $2,485- The foregoing mode of calculation can also be em- ployed to illustrate the computation of a life annuity due limited to five years, thus : End of 1st year $892.00 Discounted i year $857.6919 " " 2nd " 570.00 " 2 years . . . 526.9969 " " 3rd " 339.00 " 3 " ... 301.3696 " "4th " 184.00 " 4 " ... 157.2839 $1,843.3423 Dividing by 1,319, the number of annuitants at the out- set, age 90, we have $1,398 as the present value of life annuity of $1 for four years at age 90. Adding $1 to this we have the present value of a life annuity of $1 due for five years at age 90, $2,398. Annual premiums are paid in advance each year if the 48 insured is surviving and, tiierefore, are life annuities due. Thus, if a pure endowment of $i,ooo were issued at age 90 due in five years, and to be paid for by five annual premiums in advance these premiums would constitute a life annuity due from age 90 for the amount of the pre- mium. This annuity due must be equivalent in present value to the net single premium for the pure endowment ; that is to say, the annual premium must be for as many dollars as the present value of a life annuity due of $1, at age 90 for five years, is contained in the net single premium for the pure endowment. We have seen that if 1,319 of these pure endowments were issued at age 90, for $1 each, $89 would need to be paid to the 89 survivors at the end of five years ; the value of which, discounted five years, is $73.1515. If the amount payable to each were $1,000 this would be $73, 1 5 1. 50, which, divided by 1,319, gives $55.46 as the net single premium at age 90 for a pure endowment of $1,000, payable at the end of five years. Remembering that the annual premium is a life annuity due, at age 90, for five years, we have seen that each $1 of it has a present value of $2,398. But the present value of the whole of it must be equal to $55.46, the net single premium for the endowment, because both are equivalent to the same thing, viz. : the value of the endowment itself ; so that the net annual premium is equal to $5546 -^ 2.398, that is, $23.13. 49 RATE-MAKING— TERM, WHOLE LIFE, AND LIMITED PAYMENT. The very earliest form in which is found what is now known as regular life insurance, that is, life insurance of a fixed amount and for a fixed premium, is that of term insurance or insurance for a limited period. For a long time such policies were always issued without the privi- lege of renewal and either for one premium or for annual or other periodical premiums. How to compute the net premium for an insurance of one year has already been shown. To find the net single premium, payable in advance, for an insurance of $i,ooo for two years from age lo, assume that there are 100,000 such insurances ; that deaths will be as per the Actuaries' Table; that money will earn interest at 4 per cent, per annum, until disbursed ; and that death claims are payable at the end of the year in which death occurs. Then the payments will be $676,000 at the end of one year and $674,000 at the end of two years, or $1,350,000 in all. If no interest were earned, each would need to pay in his share of this sum, or $1,350,000 -=- 100,000 = $13.50. But since the funds are to earn 4 per cent., annually com- pounded, the aggregate sum required to be paid in advance to accumulate to sufficient to pay the claims as they fall due, is $676,000 -f- 1.04 and $674,000-=- 1.0816 — ^that is, these sums discounted for one and two years, respectively. The total is $576,000 -=- 1.04 =$650,000 $674,000 -^ 1.0816 = 623,151 $1,273,151 so If, then, each of the 100,000 entrants deposits his share in advance, he will only need to pay in $1,273,151 — 100,- 000 = $12.73 instead of $13.50; that is, $12.73 will be the net single premium for an insurance of $1,000 for two years from age 10. If the net single premium for an insurance for three years is desired, it is only necessary to add the claims pay- able at the end of three years, discounted three years ($672,000-=- 1. 1 249), before dividing by 100,000. And in like manner to get the net single premium for an in- surance for four or five or any number of years. This rule may be stated in a general form, thus : The net single premium for a term insurance of $1,000 for three years is found by multiplying the probability of dying the first year (676 -=- 100,000) by the value of $1,000, discounted one year ($1,000 -f- 1.04); by multi- plying the probability of dying the second year (674 -r- 100,000) by the value of $1,000 discounted two years ($1,000 -f- 1.0816), and by multiplying the probability of dying the third year (672 -f- 100,000) by the value of $1,000, discounted three years ($1,000 -f- 1.1249) and by adding the products together. And, generally, the net single premium of an insurance of $1 for a term of years may be found by multiplying the probability of dying the first year by the discounted value of $1 due in one year ; by multiplying the probability of dying the second year by the discounted value of $1 due in two years, and so on for the term ; and by adding these products together. It must be noted that by the probability of dying the second year, that is, at age 11 ; or the third year, that is, at age 12, etc., the probability that one who is 11 or 12, or as the case may be, will die within one year, is not meant ; but, instead, the probability that one who is now 10 will die in his nth year of age, or his 12th year of SI age, or as the case may be. Thus the probability, by the Actuaries' Table, of one who is ii years of age dying within one year is 674 -H 99324 ; but the probability of one who is now 10 dying in his nth year is 674 -=- 100,000. If the term is life, these computations must be made for every year up to the highest age in the table, plus 1, less the age at admission; that is, for age 10, up to 86 (i. e., 96 — 10) years by the American Experience Table, and 90 (i. e., 100 — 10) years by the Actuaries' Table. It will be observed that this is one year more than in a life annuity. The reason is that of the entire number none survives by one year the extreme age to whom an annuity payment would be made ; but, on the other hand, there are deaths in the year of the extreme age, so that on the assumption of all deaths at the end of the year, in- surance payments would be made at the end of that year. As an example of the manner of computing the net single premium for whole life insurance, let us take 1,319 insurances of $1,000 each, age 90, and employ the Actu- aries' Table and 4 per cent, interest. The amounts payable and their values are : End of 1st year $427,000 Discounted i year. .. .$410,577 ' 2nd ' 3rd ' 4th ' Sth '■ 6th ' 7th ' 8th 9th loth 322,000 231,000 i5S>ooo 9S.0OO 52,000 24,000 9,000 3.000 1,000 2 years.. 3 4 5 6 7 8 9 10 297,707 205,358 132,49s 78,083 41,096 18,238 6,576 2,108 676 $1,192,914 Dividing this sum by 1,319 the net single premium is found to be $904.41. A whole life insurance is thus seen to be a term insur- ance for the term of possible life ; that is, for a term of S3 years equal to the highest age of the table, plus i, less the age at entry. If one desires to pay premiums otherwise than once for all in advance, he must, of course, pay sums that will be equivalent in value to the net single premium. Thus, if he wishes to pay by means of an annual premium, it must be an annual premium equal in present value to the net single premium for the insurance. In the case of a whole life insurance from age go, for instance, the following is the way to find the net annual premium, equivalent to the net single premium of $904.41, the first premium payable in advance, and subsequent pre- miums at the beginning of each year if the insured has survived. Such is precisely the character of a life annuity due ; that is : a sum payable at the 'beginning of each year in case one survives. Therefore, the net annual premium is a life annuity due ; and if we know the present value of such an annuity of $1 per annum, it will be the present value of such a net annual premium of $1. But since the net single premium and the net annual premium are to be equivalent in present value, the number of dollars and cents in the net annual premium may be found by dividing the net single premium for the insurance by the present value of the annuity of $1. The present value of a life annuity due of $1 from age 90 has been found to be $2.485 ; the single net premium at age 90 is $904.41. The net annual premium then becomes $904.41 -=- 2.485 = $363-9S- In like manner the net annual premium for a term insurance may be found by dividing the single premium for the same by the present value of a term annuity due of $1 for the same period. In computing the present value of the term annuity due of $1, it is to be remembered that it is a life annuity for one year less than the term, with $1 added for the advance payment. S3 The net annual premium, payable for a limited number of years, such as five, ten, fifteen or twenty payment life, may be found by dividing the net single premium for whole life insurance by the present value of a term an- nuity due of $1. The principle is the same in all cases ; the net annual premium, whether for the same term of years as the insurance, or for a shorter term, must be equivalent in present value to the net single premium ; that is, the net annual premium must be as many dollars as the present value of a life annuity due of $i for the payment term, is contained in the net single premium. So far as the mathematics of it goes, there could be a. premium for a term insurance, payable during a longer term than that covered by the insurance ; but two things make this impracticable, except under extraordinary con- ditions: During the term of the insurance not enough would in such case be collected to pay claims ; and, if the deficiency were advanced from other funds, security would need to be taken that the premiums falling due after the insurance expired would be paid, since there would no longer be any incentive to pay them. The same reasoning applies, almost without change, to the case of furnishing insurance from birth at a net level premium for life, since such premium will be smaller the first year than the current cost, which would occasion a deficiency. Therefore, insurance at the earliest ages is sold on the natural premium plan, the premium being level but the amount of the insurance increasing each year. Whole life insurances, with both amounts and pre- miums definitely fixed in the contracts whether at single or at annual premiums; were first offered by the Equitable Society for the Assurance of Lives and Survivorships, of London, which was organized for that purpose on the mutual plan in 1762, through the efforts of Thomas Simp- son and James Dodson. Limited premiums were a later 54 development. The plan was at first deemed so dubious, notwithstanding its mathematical demonstration, that by the advice of a parliamentary committee a charter was re- fused the Society, which, in consequence, became a mere voluntary association. 55 RATE-MAKING— ENDOWMENT INSURANCE. Endowment insurances are often called endowments, but that name is more appropriately applied to pure en- dowments. An endowment insurance is payable to the insured at the end of a fixed period if he survives, or to the beneficiary if he dies within the period. It will readily be seen, then, that an endowment insur- ance consists of two things combined, viz. : A life insur- ance for the term with no return on survival, and a pure endowment on survival of the term with no return in event of prior death. Were each made a separate contract, one would pay in event of death and the other in event of survival. To illustrate, the following is the method for finding the net single premium for an endowment insurance of $i,ooo issued at age 90, payable at the end of five years or at prior death. Assume that 1,319 such endowment insurances are is- sued ; then to pay the death-claims the following amounts will be required : 1st year... ..$427,000 Discountec I year. .. • -$410,577 2nd " . . . . . 322,000 *' 2 years. . .. 297,707 3rd " ... .. 231,000 11 3 " ■• .. 205,358 4th " ... .. 155,000 It 4 " .. • • 132.495 Sth " ... . . 95,000 It s " .. .. 78,083 $1,124,220 Dividing by 1,319, we get $852.25 as the net single pre- mium for the five years' insurance of $i,ocx) from age 90. S6 At the end of the five years, in addition to paying $9S,ooo to the beneficiaries of those who die during that year, there must be $89,000 paid to the 89 survivors, the discounted value of which is $73,151.50. Dividing this by 1,319, we have $55.46 as the net single premium at age 90 for a pure endowment of $1,000 due in five years. Adding together the net single premiums for the insur- ance and for the pure endowment we have $852.25 + $55.46^ $907.71, as the net single premium for a five- year endowment insurance of $1,000 issued at age 90. Or we might have reasoned thus: Since $1,124,220 is the discounted value of all the insurances, and $73,151.50 the discounted value of all the endowments, $1,124,220 + $73,151-50 = $1,197,371-50 is the discounted value of the 1,319 endowment insurances of $1,000 each, whence $1,197,371.50 -f- 1,319 = $907.71, the net single premium for an endowment insurance of $1,000 at age 90. We have seen that $2,398 is the present value at age 90 of a life annuity due of $1 limited to five years. The net annual premium for a five-year endowment insurance for $1,000, issued at age 90, is a life annuity due, at age 90, limited to five years, and the problem is to determine the amount of it. Its present value must be equal to the net single premium of such an endowment insurance, which is $907.71. Therefore, the net annual premium is as many dollars as $2,398 is contained in $907.71, which is $378.53. Instead of thus deriving the net annual premium for the endowment insurance from the single premium for the same, and the latter from the net single premiums for the temporary insurance and the pure endowment, we might get the net annual premium for the endowment in- surance by first computing the net annual premiums for the temporary insurance and for the pure endowment separately, and then adding these together to make the net annual premium for the endowment insurance. S7 Semi-endowment insurances provide for the payment of a certain sum in event of death during a certain period, or of one-half as much on survival. Thus, for a semi-endowment insurance for five years at age 90, of $1,000, we would combine the net single pre- miums for $1,000 insurance for five years and for $500 pure endowment in five years to get the net single pre- mium for the semi-endowment insurance, thus : $852.25 + $27.73 = $879.98 ; and in like manner for the net annual premium or by dividing this net single premium by the present value of a life annuity due of $1 at age 90 limited to five years. A double endowment insurance means an insurance for a certain sum in event of death during a certain period, and a pure endowment for double that sum payable in event of survival of the period. The mode of arriving at net single and annual premiums is identical with that already described. Any policy which, at the end of a given period, pro- duces a certain accumulation upon survival, besides car- rying an insurance during the period, may be considered a partial endowment insurance, and the net single and annual premiums may be computed in accordance with the foregoing principles. Thus a limited-premium life insurance may be con- sidered to be a term insurance for the premium-paying period, and a pure endowment maturing at the end of the same period for the amount of the net single premium at the age attained for the insurance to be furnished there- after; for, in addition to furnishing insurance during the period, a limited-premium policy accumulates by the end of the period to the credit of the policy of each survivor, a sum equivalent in value to the insurance to be furnished thereafter, i. e., at least the net single premium for such paid-up insurance. "At least," because some companies accumulate more than this under limited-premium policies in order to cover expenses and contingencies, including adverse selection, after the premium-paying period ex- pires. In such cases, the net annual limited premiums must be computed on the basis that the policy is a partial endowment, and the rule already given for computing limited premiums would not apply unless supplemented by a net pure endowment premium for the extra guarantee. Endowment insurance was introduced much later than the other usual forms. It was expected of it that it would induce many to insure through the hope of individual gain, who might otherwise have refused to do so. Appar- ently persons who are conscious of superior vitality have selected these forms, for the general experience is that the death rates on lives, insured on endowment plans, are very low. A frequent misconception is that an endowment insur- ance premium consists of a term insurance premium plus an annual instalment the same each year and sufficient, when improved at compound interest, to accumulate to the amount payable at the end of the period. Instead there is added to the term premium only that smaller annual in- stalment which will suffice to mature the amount of the endowment only for those who survive. Thus at 90, the net annual premium for a pure endowment of $1,000, due in 5 years, is only $55.46 -f- 2.398 = $23.13 a year. This improved at 4 per cent, compound interest would only amount to $130.29, whereas $1,000 is payable if one sur- vives it. At the same rate of interest the sum payable annually in advance required to accumulate to $1,000 at the end of five years would be $177.53. At younger ages the difference is not so great because the number of survivors is much larger in proportion to 59 the entrants, but it is always considerable. Thus, at age 20, the net annual premium for a pure endowment of $i,ooo due in 20 years is $29.03 by the Actuaries' Table, and 4 per cent., while it requires $32.29 deposited annually in advance and improved at 4 per cent, interest, annuallv compounded, to accumulate to $1,000 in 20 years. 60 RATE-MAKING— RETURN PREMIUM ANCES. INSUR- A variation from the usual forms of life insurance is a policy which promises the payment of a sum equal to a part or of all the premiums paid, together with the face of the policy, at death. Usually this promise is limited to ID, 15 or 20 years, but policies have been issued with all premiums returnable at death, whenever occurring. This proposal is at first a little bewildering, but all that is neces- sary in order to grasp it is to observe that it is merely an increasing life insurance with a level premium. Let us first consider how we should go to work to find the net single premium for an increasing insurance of $1 in event of death the first year, $2 in event of death the second year, etc., and let us again make use of age 90 and make the term 10 years, in which case it will also be for life. Using the Actuaries' Table, we have the following death payments and their discounted values for 1,319 such insurances issued at age 90 : End 1st yr., 427 < leath claims @ $1 = $427, disc't'd I yi -., I410.58 " 2nd " 322 @ 2= 644 2 yrs., 595.41 " 3rd " 231 @ 3= 693 3 ' 616.07 " 4th " ISS @ 4= 620 ' 4 ' 529-98 " 5th " 9S @ 5= 475 5 ' 390.42 " 6th " 52 @ 6= 312 6 ' 246.58 " 7th " 24 @ 7= 168 7 ' 127.66 " Sth " 9 @ 8= 72 ' 8 52.61 " 9th " 3 @ 9= 27 9 ' 18.97 "loth " I @ 10= 10 10 6.76 $2,995.04 Dividing by 1-319 we have $2,995.04 -f 61 - I.319 = $2.27 as the net single premium for an insurance at age 90 of $1 in event of death the first year, $2 in event of death the second year, etc., to the end of Hfe. The net annual pre- mium is found by dividing this by $2,485, the present value of a life annuity due of $1 at age 90; that is, $2.27 -=- 2.485 = $.913. For an increasing insurance of $10 this would be $9.13 per annum, and in order to return a premium of $10, this amount, $9.13, must be paid as a net extra premium each year. To find the entire premium when the whole of it, in- cluding the extra premium, is to be returned in event of death (the extra premium not "loaded" for expenses or contingencies), resort must be had to the following simple algebraic transformation : Let P" = entire premium, in- cluding extra, P' = premium before extra is added, and TT = net annual premium for an increasing insurance of $1 for the desired term. Plainly the extra premium will be the net annual premium for an increasing insurance of P", which is, however, an unknown value ; and, there- fore will be P" (w). Plainly, also, the entire premium, P", will be equal to P' plus this extra premium. Whence, we have: P" = P' -f- P" (tt) P" — P" (tt) = P' P"(i— ^)=F P' P" = I IT In other words, to arrive at the entire premium, divide the premium before the extra is added, by $1, less the net annual premium for an increasing insurance of $1 for the desired term. The foregoing is more algebraic in form than is desired usually for this book; but the subject awakens so much curiosity and even incredulity in the minds of many who 62 are interested in life insurance that, since it is next to impossible to explain the matter otherwise, it is thus pre- sented. When the extra premium is itself loaded for expenses and contingencies, the analysis of the process is yet more complex and will not be attempted here. It proceeds, however, upon very similar lines. When only half or some other portion of the premium is to be returned, the sole alteration is that the original premium, not involving the return of premiums, is divided by $1 less the half or other portion of the net annual pre- mium for an increasing insurance of $i for the desired term, instead of less all of it. When only the premiums paid in the last lo years of a 2o-year deferred dividend period are to be returned, for instance, the net annual premium payable for 20 years for an insurance of $1 beginning in 10 years and increasing each year by $1 for 10 years, is found as follows : The net single premium is a net single premium for a pure endow- ment in 10 years, equal to the net single premium at an age 10 years higher for an increasing insurance for 10 years ; divide this by the present value of a 20-year term annuity due. 63 RATE-MAKING— INSTALMENT AND CONTIN- UOUS INSTALMENT INSURANCES— "MONTHLY INCOME" POLICIES AND "INCOME" BONDS. Ordinary instalments. Another variation from the usual forms of life insurance, is to make the proceeds payable at death or on maturity as an endowment, or both, by instalments, payable annually, semi-annually, quarterly or even monthly, instead of by one lump sum. Thus there may be ten annual instalments of $ioo each, 15 annual instalments of $66.67 each, 20 annual instalments of $50 each, 25 annual instalments of $40 each, etc. When the benefits are to be paid in monthly instalments, such a policy is nowadays known as "Monthly Income." Of late, since so-called investment insurance on de- ferred dividend plans is less in demand, and more atten- tion is given to the virtues of life insurance, "Monthly Income" policies are becoming increasingly and deserv- edly popular, providing, as they do, an income for the beneficiaries as needed for their support. In order to compute the net premiums for such policies, it is first necessary to find the value of the instalments when discounted to the date of the insured's death. The instalments are usually, though not always, payable in advance, and their values at various rates of interest are as follows : s 3% 4 4% b 6 per ct, per ct. per ct. per ct, per ct. per ct. JIOO.OO yearly in advance for 10 yrs., J878.61 $860.77 $843.53 $826.88 $810.78 $780.17 66.67 yearly in advance for IB yrs., 819.74 794.70 770.88 748.18 726.58 686.34 50.00 yearly in advance for 20 yrs., 766.19 735.49 706.70 679.67 654.27 607.90 40.00 yearly in advance for 25 yrs., 717.42 682.34 649.88 619.82 591.94 542.02 When these annual sums are paid in equal monthly in- 64 stalments, the value is less, by approximately half a year's interest on the whole amount. Then, to find the net premium, compute, in the proper manner for that form of policy, the net premium for an amount of insurance, payable in one lump sum, equal to this discounted or commuted value. Sometimes it is provided that the beneficiary may with- draw the commuted value instead of receiving the instal- ments as they become due ; but this is not usual, because the purpose in taking such an insurance is to provide the beneficiary an assured income. It is frequently provided, however, that in event of the death of the beneficiary be- fore the death of the insured, the insurance becomes one for a lump sum equal to the commuted value, and also that in event of the death of the beneficiary before all the instalments have been paid, the remaining instalments may be commuted. Reversionary Annuity : A much earlier form of instal- ment insurance was the reversionary or survivorship an- nuity, providing that if the insured die before the bene- ficiary, a life annuity, first payment immediate, becomes payable during the subsequent life of the beneficiary. If the beneficiary die first, the insurance is at an end and all premiums paid are fully earned. The mode of computing the net single premium for this is not so complicated as might be thought. For, suppose the beneficiary now has a life annuity; this will pay her $i, for instance, as long as she and the insured both live, and then, if she survives him, through all her subsequent life- time. It is composed, then, of an annuity payable for their joint lifetime and then of an annuity, beginning at the insured's death, and payable during her after lifetime. Therefore, if we compute the present value of a life an- nuity for the beneficiary's life and deduct the present value of an annuity for the joint lives of the insured and 6S the beneficiary, we shall have the present value of what remains of the life annuity, viz. : a reversionary life an- nuity for the after-lifetime of the beneficiary. How to compute the present value of a life annuity has already been explained. In short, it is to multiply the probability of living one year by the value of $i discounted one year, and so on to the end of the table, adding to- gether the products. The mode of computing the present value of a joint-life annuity is very similar. Multiply the probability of both living one year by the value of $i discounted one year and so on to the end of the table, remembering that the prob- ability of both living is the product of the probabilities that each will live. Then add together the discounted products as before. Theoretically, the first payment on the reversionary annuity will be due at the end of the policy year in which the insured dies, provided the beneficiary is then surviv- ing. This is analogous to the usual assumption that death- claims are payable at the end of the year. Practically it is always paid upon receipt and approval of proofs of death. The reversionary annuity has always been favored by experts in life insurance, but never by the public, because of the uncertainty whether the beneficiary will survive to realize much, and also because of the possibility that noth- ing at all would be realized by reason of the beneficiary dying before the insured. To remedy the latter disadvantage an increasing insur- ance on the life of the beneficiary in favor of the insured, promising in event of the death of the beneficiary before the death of the insured, a return of all premiums paid, has been combined with the promise of a reversionary an- nuity. The mode of computing the extra premium for such a return premium insurance is the same as that de- 66 scribed in an earlier chapter. The addition so consider- ably increases the premiums as to prevent the plan from becoming popular. Among the distinguished life insurance men who long ago showed a preference for this plan in selecting insur- ance for themselves was the late Sheppard Homans. When he left the service of the Mutual Life Insurance Company of New York, more than forty years ago, it was disclosed that his only insurance was a large policy of this character. At the present time the most distin- guished American actuary, Emory McClintock, shows his preference for this form of protection in a like manner. No small part of the neglect of survivorship annuities in former years was due, no doubt, to the over-emphasis upon life insurance as an investment. They have recently become more popular. Continuous Instalment Insurance : The objection to or- dinary instalment insurance is that the beneficiary may outlive the instalment period and be left without the in- come in old age when it is most needed ; the objection to the reversionary annuity that the beneficiary might die so soon after the insured as to realize very little. The "con- tinuous instalment" plan, invented by Emory McClintock, obviates both. It provides for the payment of instalments for a fixed period in any event — usually for twenty years — and as much longer as the beneficiary may survive. The policy promises a fixed amount yearly for a definite period of years after the death of the insured and there- after during the lifetime of the beneficiary. The net single premium is the sum of the net single premium for an insurance of the commuted value of the 20 instalments and the net single premium for a reversionary annuity for the after-lifetime of the beneficiary, the first payment 20 years after the death of the insured. The mode of computing the net single premium for a 67 life insurance payable in annual instalments has already been explained. To ascertain the net single premium for the contin- gent benefit, let us first compute its value twenty years from now. If twenty-one years from now the beneficiary were living and in receipt of an annuity for her lifetime, its then present value would be that of a life annuity for an age twenty-one years older than the beneficiary's pres- ent age. But the beneficiary will not then be in receipt of this first payment of the contingent annuity unless the insured shall have died the first year, nor the next year after that, i. e., the twenty-second, unless the insured shall have died the second year; and so on. That is to say, an instalment of this contingent annuity will not be paid the first, second, etc., year after the expiration of twenty years from now if the insured survives the first, second, etc., year after the policy is issued. We must, therefore, deduct the value of payments due in one year, two years, etc., conditioned upon the benefi- ciary living one year (after surviving twenty years al- ready), two years, etc., and the insured living one year, two years, etc., from his original age. But this is a joint- life annuity, based upon the joint lives of the beneficiary at an age twenty years older and the insured at his orig- inal age. " The value, then, twenty years from now if the benefi- ciary then survives, of the benefit beyond the twenty in- stalments certain is the present value of a life annuity for the life of the beneficiary at the attained age less the pres- ent value of an annuity for the joint lives of the benefi- ciary at the attained age and of the insured at the age of entry. This is the value twenty years from now and on the condition that the beneficiary then survives ; its present value, which is the net single premium for the contingent 68 benefit, is the net single premium for a pure endowment for twenty years, for the amount of the present value twenty years from now, such endowment being based on the life of the beneficiary at age at entry. Add to this the net single premium for an insurance of twenty instalments certain to obtain the entire net single premium. Continuous Instalment Provisions : Of a much simpler character is the computation of the amount of instalment for twenty years certain and for the after-lifetime of the beneficiary, in lieu of a lump payment of $i,ooo, for in- stance, the amount of the instalment to be determined by the age of the beneficiary at the time of the death of the insured. Such provisions, with a table of such values per $i,ooo insured, are frequently found in policies nowadays. First find the present value of twenty instalments of $1 each, payable annually in advance, and add the pres- ent value of a life annuity of $i at the present age of the beneficiary, less the present value of a life annuity at the same age limited to 20 years. Since this is the pres- ent value of an instalment of $1, and the sum of $1,000 is to be employed to purchase the instalment benefits, divide $1,000 by this present value; the quotient will be the amount of continuous annual instalment which can be paid in lieu of a lump sum of $1,000 if the insured die this year — that is, while the beneficiary is at her pres- ent age. The amount of the instalment if the insured dies the second, third, fourth, etc., year is computed in a similar manner. If desired, the amounts for each age may be computed and a table of such amounts may be endorsed upon the policy. Income or Guaranteed Interest Bonds: If a company makes its computations at 3 per cent, interest, for instance, and is really willing to guarantee that rate of interest in- 69 definitely, it can, if it chcwse, without any addition to the net premium, permit the proceeds of an endowment to remain with it, paying interest at 3 per cent, annually thereon during a life or lives — such as the life of the insured or the lives of the insured and the beneficiary — or for a definite term of years, and paying over the prin- cipal sum upon the termination of the life or lives or of the agreed period. In like manner, upon the death of the insured it could hold the sum insured, paying inter- est at such rate to the beneficiary during her lifetime and upon her death paying over the principal sum. Poli- cies with such provisions — i. e., for the payment of in- terest at the rate assumed by the company in computing its premiums and reserves — are sometimes issued with- out increase of premium. Frequently, however, the income or guaranteed "in- terest," so called, on the nominal amount of the bond or insurance — usually $1,000 — is higher than the company really counts upon earning. Then, in order to find the net single premium, the present value, at the moment of the death of the insured, of all the sums actually to be paid, must be computed and be taken as the true and full amount of the insurance. Suppose the bond provides that, beginning at the death of the insured — or also at the policy's maturity, if en- dowment insurance — ^$50 shall be paid at the end of each year for 20 years, and then $1,000. Suppose the com- pany really counts upon earning only 3 per cent, interest. The present value, at the death of the insured (or on maturity, if an endowment), of all the payments to be made is, at 3 per cent, annually compounded, present value of principal, $553.67 ; of "interest," $743.88. Total, $743.88 + $553-67 = $1,297.55. Compute, then, in the ordinary manner, the net single premium for an insur- ance or an endowment insurance, as the case may be, of 70 $i,297-55> ^nd you have the net single premium for this bond. The effect is that the bond is really sold at a pre- mium over par of about 30 per cent. The same result may be arrived at in another manner, as follows : The nominal principal sum of $1,000 pro- duces $30 a year income at 3 per cent, interest, leaving $20 a year for 20 years to be provided for. The dis- counted value of $20 a year is, at 3 per cent, interest, an- nually compounded, $297.55, which sum, being added to $1,000, produces $1,297.55 ^s the actual principal sum insured. A special form of this bond is to pay $1,000 immedi- ately upon death or maturity, $50 a year at the end of each year for 20 years, and then $1,000. This is, of course, worth just $1,000 more — i. e., it is an insurance, on a 3 per cent, basis, for $2,297.55. There remains the case of a policy which pays $50 at the end of each year for the after-lifetime of the bene- ficiary, if surviving the insured, and $1,000 at the death of the beneficiary. The interest which $1,000 would actually yield at 3 per cent, is $30 a year ; provision, there- fore, must be made for $20 a year additional for the re- maining lifetime of the beneficiary after the death of the insured. Remembering that the present value of a sur- vivorship or reversionary annuity is the present value of an annuity for the life of the beneficiary, less the pres- ent value of an annuity for the joint lives of the insured and the beneficiary, we have : The entire net single premium is the net single pre- mium for an insurance of $1,000 on the life of the in- sured (which, as has been said, can be treated as produc- ing $30 interest per annum during the beneficiary's after- lifetime and being still worth $1,000 at the time of her decease) plus the present value of an annuity of $20 on the life of the beneficiary, less the present value of 71 an annuity of $20 on the joint lives of the insured and the beneficiary. This would yield $1,030, however, at the death of the beneficiary, as a year's interest would be earned, and so would need to be slightly modified in practice. All of the foregoing are on the basis that the payments are at the end of the year; in practice they are usually at the beginning or in instalments throughout the year, in which cases suitable adjustments must be made. Annual Premiums : The net annual premium for any of these insurances, if involving one life only, is com- puted by dividing the net single premium or present value by the present value of a life annuity due of $1 for the life of the insured when premiums are payable through- out life, or the present value of the corresponding tem- porary life annuity due if premiums are payable for a lim- ited term only. Where the insurance involves survivorship, it is usually assumed that payment of premiums will not continue be- yond the lifetime of either the insured or the beneficiary, and the net single premium is divided by the present value of a joint-life annuity due or a temporary joint-life an- nuity due, as the case may require. If only a part involves survivorship, that part of the entire net single premium should be divided by a joint- life annuity due and the remainder by the annuity due for the life of the insured; and in such case the part of the annual premium arrived at by dividing by the joint-life annuity is not required after the beneficiary's death, if it takes place before the death of the insured. Thus, a continuous instalment policy becomes a mere insurance of twenty instalments certain when the bene- ficiary dies before the insured, and, therefore, from that time forth the net annual premium should be only the net annual premium for an insurance of twenty instal- ments certain. 72 RATE-MAKING— JOINT-LIFE INSURANCE. Life insurance is sometimes conditional upon the fail- ure of joint-lives and becomes payable upon the first death. Such are called joint-life insurances. They are sometimes taken by husband and wife in favor of each other or of their children. At one time joint-life insur- ances of husband and wife, payable to the survivor, were somewhat common in the United States. More fre- quently, however, these insurances have been taken by firms upon the joint lives of the partners, running to the surviving partners to aid in paying out the interest of the deceased partner. For this reason, joint-life insurance is sometimes known as partnership insurance. That name, however, is not applied to it exclusively ; separate insurances on the individual lives of the partners, if made payable to the other partners, are sometimes known likewise as part- nership insurances. The method of computing the net single premium for a whole life insurance of $i,ooo has already been de- scribed as follows: Add together the following present values: $r,ooo discounted one year and multiplied by the probability of dying the first year; $i,ooo discounted two years and multiplied by the probability of dying the sec- ond year ; and so on to the end of the table. In like manner the method of finding the net single premium for a joint-life insurance of $i,cx30 is as fol- lows : Add together the following present values : $r,ooo discounted one year and multipled by the probability 73 that the joint lives — i. e., at least one of them — will fail the first year, and so on to the highest age in the mor- tality table; when the oldest life reaches this age it must be assumed that it certainly fails, and, therefore, that the joint-lives certainly fail. All that remains to be explained is the mode of find- ing the probability that at least one life out of the joint lives will fail the first year, the second year, and so on. If we go to work to get this directly, it will become a very complicated matter. Thus, if there are only two lives, it evidently consists of three separate probabilities — viz.: (i) that both lives will fail, (2) that the one life will fail and the other survive, and (3) that the other life will fail and the one survive. Where more lives are involved, the probability can be separated into a larger number of distinct, separate probabilities in an increas- ing ratio for each life added. But, remembering that certainty is unity and that all probabilities are fractions, we can very easily get the probability that at least one of any number of lives will fail ; because it is certainty, less the chance that none of them will fail, which, in turn, is the chance that all will survive. And the probability that all will survive is the product of the probability that one will survive and the probability that another will survive, and so on. In computing the net single premium for a joint-life insurance for a certain number of years only, all that is necessary is to add together the present values computed in accordance with the foregoing for that number of years only. To determine the net single premium for a joint-life endowment insurance, add the net single premium for a joint-life insurance and the net single premium of a joint-Hfe pure endowment, both for the desired term. A joint-Hfe pure endowment is a promise to pay a sum 74 of money at the end of the term if all the lives involved have survived. The net single premium for a joint-life pure endowment is the amount of the endowment dis- counted for the term of years and multiplied by the probability that all will survive the term, which, as has been explained, is the product of the probabilities that each will severally survive the term. The present value of a joint-life annuity is the sum of the net single premiums for joint-life pure endowments of $1 due in one, two, three, etc., years up to the number of years by which the present age of the oldest life falls short of the highest age in the table. A joint-life an- nuity due is a joint-life annuity with one payment imme- diate, and its present value is, therefore, greater by the amount of the annuity payment made in advance. The present value of a joint-life annuity for a term of years is the sum of the net single premiums for joint-life pure endowments of $i due in one, two, three, four, etc., years up to the number of years in the term. The present value of a joint-life annuity due for a term of years is the present value of a joint-life annuity for a term one year shorter plus $i. The net annual premium of a joint-life insurance is found by dividing the net single premium by the present value of a joint-life annuity due. The net annual premium, limited to a term of years, for a joint-life insurance, is found by dividing the net single premium by the present value of a joint-life an- nuity due for the payment term. The net annual premium for a joint-life insurance for a certain term, or of a joint-life endowment insurance for a certain term, is found by dividing the respective net sin- gle premium by the present value of a joint-life annuity due for the same term. 73 RATE-MAKING— LOADING— PRELIMINARY TERM. What has been said in previous chapters on the gen- eral subject of rate-making has been concerned with net premiums only — that is, only premiums which will be precisely sufficient, interest and mortality being as as- sumed, to enable the company to furnish the promised benefits. Possible deficiencies because of errors in the assumptions regarding mortality or interest, used in com- puting these premiums, are not taken into account ; neither are possible losses on investments, nor the expenses of carrying on the business. All of these are provided for by means of an addition to the net premium, which is called the loading. The loading and the net premium together compose the gross or office premium. Life insurance companies have not always made an addition to net premiums for loading, nor do they now in every case. The premiums of non-participating policies, where no part of the gains is apportioned to the insured, are sometimes net or nearly so. This means that the company looks to the margins of interest over the rate assumed, and the salvage on the provision for mortality, to be expected according to the table employed, to cover all expenses and contingencies and produce a satisfac- tory profit. The premiums of policies which grant the insured participation in the profits are always loaded. And, though this loading is also to provide for expenses and contingencies, it is, in large part, a direct provision for 76 dividends for policyholders. The portion for each pur- pose is not usually separated from the portion for the other purposes by American actuaries, though in other countries the contrary is sometimes the case. In prac- tice here, all is treated as available for any or all of these purposes ; and, in fact, as will be seen more fully here- after, in some companies the expenses more than absorb the loading, as usually computed, for several years. There are two modes of loading premiums which are frequently and several others that are occasionally em- ployed. The plan most commonly used is to add a fixed or varying percentage of the net premium, the loading thus becoming what mathematicians call a "function" of the net premium. Somewhat less common is the addi- tion to the net premium of some sum per $i,ooo of in- surance, no matter what the age or the net premium; this loading is a "function" of the sum insured. A com- bination of the two is also sometimes used, the net pre- mium being first loaded a fixed amount per $ 1,000, in- sured, and the sum of these a percentage; or. the order may be reversed. Some have argued that in strict theory the loading ought to be the same amount for all ages, and that the burden of the net premium, increasing inevitably with age, should not be augmented by imposing also a heavier loading. But in practice the apparent necessity for pay- ing commissions upon the gross premium has usually out- weighed such considerations. Moreover, at best this could apply only to loading for expenses ; the same argu- ment has no relevancy as regards mortality contingencies, for fluctuations in the mortality would not be the same in value for each age, regardless of the probability of death, but would usually be treated as varying with the tabular mortality rates and proportionately thereto. In other countries, France and Switzerland especially, n efforts have been made to separate loadings into distinct parts, each deemed sufficient for its particular purpose. Expenses might obviously be divided into six classes at least : expense of procuring insurances, medical expenses, expense of renewing insurances, managerial expenses, investment expenses and expense of adjusting claims. Of these, the first two are mainly incurred the first year of insurance, the third wholly after the first year, the fourth and fifth every year, and the last only when in- surances are terminated. It is now a common opinion, however, that as the expense of medical selection brings lower mortality for several years, and as expenses of ad- justment are incident to paying claims, one or both should be provided for and be met out of the mortality provi- sion. In the same way, many think that investment ex- penses should be met out of surplus gains on investments over the rate of interest assumed, quite as investment losses are taken care of ordinarily. Managerial ex- penses, some maintain, should be provided for by a charge of a certain amount per $i,ooo of insurance; in other words, as a function of the sum insured. The expense of renewing insurances is composed chiefly of renewal commissions, and these are usually calculated as percent- ages of the gross premiums; in other words, such ex- penses are functions of the premiums. A well-known American actuary urges a method of loading which takes no account of the incidence of the expense, but charges it as a percentage of the aggregate annual costs of insurance — i. e., for each policy, of the net one-year term premium at the attained age for an in- surance equal to the total sum insured, less the reserve or "self-insurance." This gives an increasing loading for a whole life premium. While no other American actuary goes so far, many urge that there is no occasion for adjusting the loading to meet the incidence of ex- 78 penses, and that it should be the same amount each year. This means that expense of procuring insurances is met by borrowing from surplus accumulated from the earn- ings upon other policies or paid in by stockholders for the purpose, and such borrowings are made good ultimately out of margins of future loading. This, of course, is impossible for new companies, and results in very slow growth for small companies. The most eminent actuary of the United States is authority for the statement that under such conditions, rigidly en- forced, to establish a new company is "a well-known im- possibility, not challenged by a single instance to the contrary." A favorite mode of dealing with this matter, in the United States and other countries, has been to make the gross premiums level, as usual, and then to take for the first year's loading as large a proportion as may be re- quired, up to the limit that enough is left of the gross premium to contribute the policy's share of the losses. The portion of the first year's premium remaining after such deduction for first year's expenses is made is the net premium for that year. The net premiums after the first year are increased by an amount equivalent to the de- ficiency thus created in the first year's net premiums. It has been the opinion of many that the use of such a system is not contemplated by the valuation laws of many of the States of this country. Accordingly, com- panies that have desired to have a larger loading the first year have made use of what is known as the preliminary term plan; that is to say, the policies provide that the premium the first year shall be for a term insurance of one year only, and that the whole life, or limited payment life or endowment insurance, shall commence at the end of that year upon the payment of the premium due at the beginning of the second year. 79 The effect of this is to give a very much larger loading the first year. Usually all the premiums, including the first, are for the same amount; and in this manner pre- miums as large as the subsequent nine-year endowment premiums have been taken as premiums for a single year's insurance. In some cases, indeed, under certain endow- ment schemes, as large a premium as $ioo has been charged, ostensibly for $500 insurance for a single year or even for a less amount. The net premiums under such a preliminary term plan are as follows : The first year, the net premium for one- year term insurance ; after the first year, the net level an- nual premium for an insurance, maturing as promised in the policy, issued at an age one year higher, at a date one year later and for a term one year shorter. The extravagance of the loading sometimes under the preliminary term plan, as described, has led certain com- panies to make modifications first introduced in this coun- try by the author of this book in 1897. Before consider- ing these modifications, however, it may well be remarked that if sums so large as these are actually expended in pro- curing the insurances, the extravagance is present, no matter how the loading is computed. The modification consists in making but one rate for one-year preliminary term insurance for each age, which rate is equal to the whole life premium at the next age. This, of course, gives a level gross premium each year. The net premiums on the whole life plan are the net one- year term premium the first year and the net whole life annual premium for an age one year higher the next year and all subsequent years. But net premiums for plans which involve the cessation of premium payment after ten, fifteen or twenty years are based upon these whole life preliminary term net rates, by adding each and every year, including thfe first, a net pure endowment premium So sufficient to produce a fund at the end of the payment period equivalent to the then present value of the sub- sequent net ordinary life premiums, which are thus pre- paid. Occasionally, companies have accumulated enough to prepay the gross premiums; but usually, as stated, merely enough to prepay the net premiums. For endow- ment insurances this net additional premium is a pure en- dowment annual premium, sufficient to produce an en- dowment at the end of the period equal to the excess of the sum payable as an endowment over and above the then reserve on a whole life preliminary term policy issued at the same age. The justification of this system, which has been offered, is first, that it provides merely the funds which an eco- nomically conducted company requires in order to procure new business, and, second, that it is a system of loading as nearly scientific as the present laws and conditions ad- mit of. The greatest living actuary of Great Britain, Dr. Thomas Bond Sprague, first advocated a similar system in that country, and asserted that in even the most carefully conducted companies preliminary expenses and losses ex- haust pretty much all the first year's premiums, especially on whole life insurances. Emory McClintock has ex- pressed similar views as regards the United States. Other methods of modifying the full preliminary term method have since been introduced, as confining the extra first year's loading to not more than the excess of the net twenty-payment life premium over the net one-year term premium. It is customary also to add a percentage loading to net single premiums, and sometimes also a fixed amount per $i,ooo insured. In this country, with few exceptions, all the loading on single premiums and on limited premiums is considered to be immediately available when received, and no part of the same is reserved to cover expenses after 8i the policy becomes paid-up. Companies in some other countries adopt the contrary practice. Under the prevailing customs, limited-payment policies during their payment period and endowment insurance policies contribute more, per $i,ooo insured, for expenses, than do whole life policies issued at the same age. In con- sequence, insurance under such contracts really costs the insured more, currently. There have been cases of load- ing on a ten-year endowment premium as much as, or even more than, the entire whole life premium for the same age. Such are the peculiarities of loading systems which have grown up under the spur of competition, and, until within a few years, without much careful scientific con- sideration of the real nature of the problems to be solved. The laws of New York now recognize the "select and ultimate" method of determining the extra loading the first year, as the maximum provision; this confines the amount to the "present value of assumed mortality gains for the first five years of insurance" according to the fol- lowing assumptions : Mortality, first year, 50 per cent, of rates according to American Experience Table; second year, 65 per cent. ; third year, 75 per cent. ; fourth year, 85 per cent; fifth year, 95 per cent. This method requires the special allowance to be made good within the five years. This method was introduced to the attention of actuaries by the author of this book, in co-operation with Emory McClintock and Henry Moir, in 1905. The laws of New Jersey limit the allowance to the straight modified preliminary term loading plus half the mortality provision for that year, according to the Ameri- can Experience Table, and require it to be made good in seven years. The minimum reserve standard of Canada limits the 8a allowance to the straight modified preliminary term load- ing and requires it to be made good in five years. In some of the European countries, as in Sweden, the allowance is also limited. In Sweden it must be made good in five years, in Denmark in six years and in France in seven years. In the last two countries, the amount of the allowance is not otherwise limited. 83 RATE-MAKING— PREMIUMS PAYABLE MORE FREQUENTLY THAN ANNUALLY. Premiums are sometimes payable more frequently than once a year; for instance, semi-annually, quarterly, bi- monthly, monthly, or even weekly. It would be possible, of course, by extending the prin- ciples already laid down, to compute net premiums pay- able in this manner. All that would be requisite would be to divide the net single premiums by the present value of a life annuity of $i per annum, payable (in equal parts in advance) two, four, six, twelve or fifty-two times a year, as the case may be, instead of by the present value of a life annuity due of $i. But, unless payable weekly, or sometimes monthly, premiums are not usually dealt with in this manner. The policy usually contains a provision that, in event of death during the year, premiums for the year, not yet paid, are to be deducted from the claim. This transforms the insurance into one with annual pre- miums payable in instalments. On this basis it is customary to make an arbitrary addi- tion to the gross annual premium and divide it^ thus in- creased, into the desired number of parts. The following are the usual rules : For semi-annual premiums, add 4 per cent, of itself to the gross annual premium and divide by two. For quarterly premiums, add 6 per cent, of itself to the gross annual premium and divide by four. For bi-monthly premiums, add 8 per cent, or 10 per cent, of itself to the gross annual premium and divide by six. 84 For monthly premiums, add 20 per cent, of itself to the gross annual premium and divide by twelve ; or divide the gross annual premium by ten, which gives the same result. There is no rule as to weekly premiums, which are usually based upon true net weekly premiums. The mor- tality table employed in computing net weekly premiums — and sometimes monthly premiums as well — is some- times different from the mortality table employed in com- puting net premiums for ordinary insurances, because the lives are not upon the average so good. The greatest part of the increase over the annual pre- mium, made in computing premiums payable more fre- quently, is to cover the added expense. Thus, upon the basis of 4 per cent, interest, the following rates of increase only would be necessary to make good the interest lost by deferring the receipt of part of the premiums : Semi-annual : 2 per cent, on half the annual premium due in six months, equal to i per cent, on the annual premium. Quarterly : 3 per cent, on one-fourth of the annual pre- mium, due in nine months, 2 per cent, on one- fourth due in six months, and i per cent, on one-fourth due in three months equal to li per cent, on the annual premium. Bi-monthly: 3J per cent, on one-sixth of the annual premium due in ten months, 2f per cent, on one-sixth due in eight months, 2 per cent, on one-sixth due in six months, ij per cent, on one-sixth due in four months, and f per cent, on one-sixth due in two months, equal to i§ per cent, on the annual premium. Monthly: 3! per cent, on one-twelfth due in eleven months, and so on down to ^ per cent, on one-twelfth due in one month, equal to 1% per cent, on the annual pre- mium. Weekly : About 2 per cent, on the annual premium. 85 RATE-MAKING— SOME MISCONCEPTIONS. Premiums and Values Not Based on Expectancy: Every now and then some one conceives the idea, either that the net single premium for a whole life insurance is equal to the sum insured, discounted for the average num- ber of years the insured may expect to live, which is called the expectancy or expectation of life, or that the present value of a life annuity is equal to the present value of an annuity certain for the expectancy. These ideas once had earnest advocates ; the plan of valuing annuities, introduced by Ulpian and adopted by the Roman courts, was based upon this theory. The expectation of life is the aggregate number of years that, according to the mortality table, all the persons in a large group, setting out from a given age, survive, divided by the number in the original group. Thus, those who die the first year live a half-year on the average; those who die the second year live a year and a half, and so on to the end of the table. Add all these years together and divide by the original number and you have the average number of future years of lifetime. Or, since the number living at the end of one year have each survived a year or that number of years altogether, the number living at the end of the second year have each survived another year or that number of years more alto- gether, and so on, we may obtain the number of complete years survived in the aggregate by all, by adding together the number who survive one year, the number who sur- vive two years, etc. ; and we may get the average number 86 of complete years su^^f)l#d33 eiflKfo'' ^1^* ^^ called the curtate expectampn^ Ijy dividing thi^ tota/by the original number of lives. >^^^'|*I»3iMeWfe^ianMj»e average half the year in vsrhich they OTB»«agg|]iM£aS^r€ar to the curtate ex- pectation and the sum is the complete expectation. Suppose each of the original group was in receipt of a life annuity of $i, the dollars payable at the end of the first year would be equal to the number living at the end of that year ; the dollars payable at the end of the second year would be equal to the number then living, and so on. The total number of dollars paid out in annuities would be equal to the number living at the end of one year, added to the number living at the end of two years, and so on. The average number of dollars paid each person in an- nuities would be this total, divided by the original number of lives. In other words, the average number of dollars paid would be precisely equal to the number of years in the curtate expectation ; and half the money paid to the entire group will have been paid before the end of the expectation and half will be payable after- ward. That is, the present value of a life annuity would be precisely equal to that of an annuity certain for the curtate expectation, if in both cases no interest earnings were taken into account. But when interest is taken account of, the dollars of annuity payable at the end of the years late in life are discounted, to bring them to their present value in a much larger proportion, than the dollars payable earlier in life. Therefore, the half, payable after the end of the expec- tancy, will be discounted much more, compared with the same discounted for the term of the expectancy, than the discount on half, payable before the end of the expectancy, is less than the discount for the term of the expectancy. But the value would be exactly equal to that of an annuity certain for the term of the expectancy, only in case the 87 values of these two halves continued to be equal as when no interest is earned. On this account, the present value of an annuity certain for the term of the curtate expecta- tion is greater than the present value of the life annuity. The excess, also, is greater, the larger the rate of interest ; and is greater, also, the younger the age. The net single premium for a whole life insurance is larger than the present value of the face of the policy discounted for the term of the complete expectation of life, if the insurance is payable at the moment of death. In no case can the net single premium be accurately found by reference to the expectation. The expectation of life is not the probable after-lifetime or the period of probable life which fixes the date at which it will be equally probable, according to the table, that a life, setting out from a certain age, will have died or will have survived. This may be found from the mortality table by observing at what moment of age the number, setting out from a certain age, is reduced just one-half. This period is also not of use in computing net single premiums or present values of annuities. "The most probable after-lifetime" is yet another ex- pression, signifying the period extending from the origi- nal age to the age when the number of deaths is greatest in the group. The test of all net single premiums and present values is this : Will they work out by paying all claims as they fall due? To test this, take a large number and carry their net premiums, less disbursements for claims, for- ward with interest at the assumed rate, on the basis that deaths will be according to the mortality table, to the termination of the policy when nothing should be left if it is insurance or annuity that is dealt with, and if it is endowment insurance, a sum sufficient to give each his endowment, with nothing over. 8a Component Parts of Premiums: Another unfortunate misconception was created some years ago by the publica- tion in a popular little book on life insurance of a division of premiums into their "elements" or component parts. The division showed the loading and the net premiums and also separated the latter into what were termed "mor- tality" and "reserve" elements. The partition of the pre- miums showed how much money was required, the first year of insurance only, to pay the current cost, at a net one-year term premium, of the actual insurance for that year — that is, of the whole insurance, less the reserve or "self-insurance" at the end of that year — and also showed how much of the net premium remained after this was deducted, which was called "reserve" element. If the net premium is properly computed, it is, of course, precisely adequate; and in such case, what is left after providing for the current cost the first year, will, when accumulated at interest for one year, be just sufficient to make good the reserve at the end of the first year. In like manner for the second year, if the net premium is precisely adequate, the remainder, after deducting the one-year term premium at the attained age for the actual insurance for that year, will also be just sufficient, when added to the reserve at the end of the previous year, the sum being improved at the assumed rate of interest, to produce the reserve at the end of the second year; and so on. But the "net one-year term premium at the attained age for the actual insurance for that year" is not the same each year. It varies each year; and, as the "deposit for reserve" is the remainder after the "cost of insurance" or so-called "mortality element" is deducted, it must also vary from year to year. Indeed, these are what mathe- maticians call "complementary variables," i. e., they vary inversely, their sum always remaining the 89 same, viz. : the level net premium. And in whole life insurances and term insurances, there comes a time when the "cost of insurance" exceeds the whole net premium and absorbs part of the interest earned upon the already accumulated reserve or even absorbs part of the reserve, besides all of the interest ; and, in the last year of a term insurance the "cost of insurance" ab- sorbs the entire reserve, the current premium and the in- terest. When death occurs, the reserve of the policy goes toward paying the death-claim thereunder, and only the remainder of the claim is paid out of the "costs of insur- ance," contributed for that purpose by the premiums of that policy and of other policies. The following illustration of the varying proportions of the component parts or elements of a premium is taken from "Savings Bank Life Insurance," by Elizur Wright, who first called especial attention to the subject. Whole Life, Age 32. Actuaries' Table. 4 per cent. Net Annual Premium, $24.10. DIVISION OF PREMIUMS. Policy. Cost of Deposit for Years. Loading. Insurance. Reserve. 1 $6.06 $8.33 $9.71 2 6.06 8.40 9.64 3 6.06 8.47 9.57 4 6.06 8.55 9-49 5 6.06 8.63 9.41 6 6.06 8.70 9.34 7 6.06 8.78 9.26 8 6.06 8.86 9.18 9 6.06 8.93 9.11 10 6.06 9.01 9.03 11 6.06 9.10 8.94 12 6.06 9.24 8.80 13 6.06 9.44 8.60 14 6.06 9.68 8.36 15 606 9.98 8.06 90 Policy. Cost of Deposit for Years. Loading. Insurance. Reserve. i6 6.06 10.09 7.9s 17 6.06 10.66 7.38 18 6.06 11.02 7.02 19 6.06 11.41 6.63 20 6.06 11.83 6-21 21 6.06 12.27 S-77 22 , 6.06 12.74 5-3° 23 6.06 13.22 4.82 24 6.06 13.74 4-3° 25 6.06 14.27 3.77 26 6.06 14.81 3.23 27 6.06 15.38 2.66 28 6.06 15.98 2.06 29 6.06 16.64 140 30 6.06 17.33 -71 31 6.06 18.06 — .02 32 6.06 18.81 — .77 33 6.06 19.60 —1.56 34 6.06 20.41 —2.37 35 6.06 21.26 — ^3.22 36 6.06 22.13 — ^4.09 37 6.06 23.01 —4-97 38 6.06 23.89 — S.85 39 6.06 24.79 —6.7s 40 6.06 25.69 — 7.65 41 6.06 26.60 — 8.56 42 6.06 27.51 — 9.47 43 6.06 28.43 —10.30 44 6.06 29.34 —11.30 45 6.06 30.24 — 12.20 46 6.06 31.14 — 13.10 47 6.06 32.06 — 14.02 48 6.06 32.93 -14-89 49 6.06 33-79 —15-75 50 6.06 34.58 —16.54 51 6.06 35.29 —17-25 52 6.06 35.95 —17.91 53 6.06 36.52 —18.48 54 6.06 37.08 —19.04 55 6.06 37.64 —19.60 91 Policy. Cost of Deposit for Years. Loading. Insurance. Reserve. 56 6.06 57 6.06 58 6.06 59 6.06 60 6.06 61 6.06 62 6.06 63 6.06 64 6.06 65 6.06 66 6.06 67 6.06 68 6.06 At the end of the 68th year, according to the table, the insured must certainly have died; and the reserve therefore amounts to the face of the policy and is ready to be paid over. 38.18 —20.14 38.78 —20.74 3948 —21.44 40.18 — 22.14 40.99 —22.9s 41.98 —23.94 4314 -25.10 44.44 -^6.40 46.40 —28.36 48.17 —30.13 46.6s —28.61 40.7s — 22.71 .00 18.04 92 UNEARNED PREMIUM OR RE-INSURANCE RESERVES. If no interest were counted upon, if mortality were precisely according to the mortality table, and if losses were payable at the instant of death, a company which had insured 100,000 lives at age 10 for $1,000 each, just six months ago, receiving net premiums in the aggregate of $676,000, ought to have on hand just $338,000. For, on the basis of uniform deaths throughout the year of age, 338 would already have died out of the 100,000 per- sons insured, and 338 more would die in the ensuing six months. This sum, then, would be the aggregate "unearned pre- mium" reserve for these insurances, because it is what would remain of the original net premiums, after the in- surance already furnished had been paid for. It would also be the aggregate "re-insurance" reserve because another company, counting upon experiencing mortality precisely as per the table employed, could afford to accept this sum as a re-insurance premium and assume the liabil- ity under the policies for the ensuing six months. Because, by looking at the past receipts and disburse- ments calculated as per the original assumptions, we may find the value or reserve, we call that method the retro- spective method of valuation, i. e., of computing the re- serve ; and, because by looking at the future requirements, on the same assumptions, we may also find it, we call that the prospective method. The "retrospective" method, setting out with the net premiums actually received, will produce the reserve actu- 93 ally required, only in case the net premiums are precisely sufficient according to the mortality table and rate of in- terest assumed. The real test of the sufficiency of a re- serve is the "prospective" method, as we shall see here- after. Thus, if the net premiums actually collected had been $600,000 there would remain at the end of six months only $600,000 — $338,000 = $262,000, which would not be enough to meet the $338,000 of claims that would accrue in the next six months ; the actual reserve would then be $262,000, but $338,000 the required re- serve. Suppose that the losses were not really payable until the end of the year, in such case no claims would have been paid and the whole $676,000 would be in hand. We should still call $338,000 the "unearned premium" or "re- insurance" reserve, however, and the remaining $338,000 would be offset by a liability of $338,000 for death-claims, already accrued but not paid. Suppose, now, that instead of an insurance for one year and of assuming that no interest is earned, we consider 100,000 term insurances for two years from age 10, of $1,000 each, paid for by aggregate net single premiums of $1,273,151, and that the funds earn 4 per cent, per annum until disbursed ; and it is desired to ascertain the "unearned premium" or "re-insurance" reserve at the end of the first year. By the "retrospective" method, first, at the end of the first year, the aggregate net single pre- miums amount, with one year's interest at 4 per cent., to $1,324,077, out of which $676,000 is immediately payable because of deaths the first year, leaving the sum of $648,- 077 as the reserve to provide for paying the claims of the second year — i. e., to cover 99,324 insurances of $1,000 each, for one year from age 11. By the "prospective method" we have: $674,000 will be due at the end of one year to pay the death claims of 94 the 99,324 insured for $1,000 each at age 11. Its value at the beginning of the year is $674,000 -^ 1.04 = $648,- 077, i. e., the same amount. Suppose, however, that the 100,000 insurances for two years for $1,000 each from age 10 have been paid for by annual premiums in advance, aggregating $651,211. At the end of the first year the premiums paid at the begin- ning of that year, improved at interest, would amount to $677,269, out of which $676,000 is immediately payable for first year's death losses, leaving $1,269. There now remain 99,324 persons living to pay the second year's pre- mium, which is for each person $651,211 -=- 100,000^ $6.51211, which makes $646,808 for the 99,324 persons. We have found that, on the basis of no premium payable at the beginning of the second year, the reserve should be $648,077 in order to meet the $674,000 death losses pay- able at the end of that year ; but premiums amounting to $646,808 are now payable, leaving $648,077 — $646,808 = $1,269 to be supplied by the reserve. This sum, then, is the aggregate reserve, by both the "retrospective" and the "prospective" methods. We may now state this general proposition : When the net premiums have been correctly computed and calcula- tions are made on the same assumptions as to interest and mortality, as in computing the premiums, the "retrospec- tive" and the "prospective" methods will bring out the same reserve, which means that there will have been saved and accumulated out of past premiums just enough, so that this sum, together with net premiums payable in future, accumulated at the expected rate of interest, will enable the future claims to be met as they fall due. In other words, the accumulations at interest from past net premiums which form the "unearned premium" re- serve balance the discounted deficiencies of future net pre- miums, which form the "re-insurance" reserve. 95 If the net premiums are not adequate, the two methods will not produce the same results. The "retrospective" method will bring out a lower reserve and the "prospec- tive" method a higher reserve than if the net premiums were precisely adequate; in such case, the latter will be the reserve, required under the actual circumstances, to enable the claims to be met. Likewise, if the net pre- miums employed were redundant (i. e., larger than neces- sary) the "retrospective" method would bring out a higher reserve and the "prospective" method a lower reserve than if with precisely adequate net premiums ; but, again, the latter will be the correct reserve under the actual circumstances. It is the custom, however, to treat all in excess of the usual net premium as surplus and value on the basis of the usual net premiums ; but this would not be proper if no part of the future net premiums could be used otherwise than to pay death claims, unless the pur- pose be to over-state the reserve required. Suppose it were desired to find the reserve at the end of six months, instead of at the end of one year, for the loo,- ooo insurances at age lo, paid for by aggregate net single premiums of $1,273,151. This sum would have accumu- lated at 4 per cent, to $1,298,614 by the end of six months. Death claims to the amount of $338,000 would have been incurred ; but, as these are not deemed to be payable until the end of the year, only $338,000 -=- 1.02 = $331,372 is set aside to meet them. This leaves $1,298,614 — $331,- 372 = $967,242 as the reserve at the end of six months, by the retrospective method. By the prospective method we have $338,000 of claims to accrue in the next six months, payable at the end of that time, and $674,000 of claims to accrue during the year following, payable at the end of that year, or eighteen months from this date. The present values of these re- spective sums are: $338,000 -4- 1.02 = $331,372, and 96 $674,000-^(1.04 X 1.02) = $674,000 -^ 1.0608 = $635,- 370, and the sum of these is $966,742, the aggregate re- serve by the prospective method. These reserves thus approximately computed, are $500 apart, owing to the assumption that the accumulated and discounted values for six months at 4 per cent, interest, annually com- pounded, are found by multiplying and dividing by 1.02 respectively, which is not quite accurate. An approximation to the correct reserve at the end of six months may be made as follows : Assume that changes in the reserve, by death claims diminishing the fund and interest increasing it, take place uniformly throughout the year. Then, since, we start the year with $1,273,151 and close it with $648,077, which we have found to be the aggregate reserve at the end of the first year, in six months the reserve will have diminished by half of ($1,273,151— $648,077), i. e., by half of $625,074 = $312,537; that is, the reserve will be $1,273,151 less $312,537 = $960,614. This approximation would be ac- curate if the claims for the first six months were paid at the end thereof ; for, in that case, we would have the accu- mulation $1,298,614 less $338,000 = $960,614. As, not- withstanding the assumption in computing net premiums, claims are usually paid very soon after the deaths take place, this is usually taken as the reserve at the end of six months ; and the initial reserve, that is, the fund on hand at the beginning of the year, modified by the proportionate change, whether it be an increase or decrease, which it undergoes during the year, is considered to be the reserve at a given time during the year. Thus the reserve at the end of six months is called the mean reserve ; that is, the mean between the initial reserve and the terminal reserve, between the reserve at the beginning of the year and at its end. It may be computed, in the case we have been considering, in the following manner: ($1,273,151 + Q7 $648,077) -;- 2 = $1,921,228 -=- 2 = $960,614, as before. When premiums are paid annually in advance, the last terminal reserve, plus the premium due at the beginning of the year, constitutes the initial reserve. Take the case of the 100,000 insurances of $1,000 each for two years from age 10, with annual premiums. At the end of the first six months the reserve is the sum of the premiums paid — which alone constitute the initial reserve the first year — and the terminal reserve, the sum divided by two, $651,21 1 + $1,269) -^ 2 = $652,480 ^ 2 = $326,240. At the end of a year and six months it will be : The terminal reserve plus the premiums then paid — that is, taken to- gether, the initial reserve — plus zero, because nothing is reserved at the end of the second year, since the insurance then expires, the whole divided by two, ($1,269 -{- $646,- 808) -f- 2 = $648,077 -f- 2= $324,038.50. When it is said that the reserve is that sum which, to- gether with future premiums, will enable the company to fulfill its promises, mortality and interest being as as- sumed, it can only be meant that the reserve is the aggre- gate sum which enables the company to fulfill its aggre- gate promises. When the aggregate reserve is apportioned to individual insurances, this statement is not true, as to each of them taken separately. An individual who is about to die will require much more than the premiums he will pay — which may be none at all — ^plus his portion of the aggregate reserve, in order to meet the claim under his insurance; and, of course, others — which of them it would be inconvenient or even impossible to determine — will require corresponding less. The minimum may be taken as the reserve on the basis that, paying net pre- miums as per the original computations, the insured is really to be taken as a first-class life, i. e., equal to one who passes a fresh examination for life insurance. The so-called individual reserve, then, is merely an average, 98 found by partitioning the aggregate reserve; and the sufficiency of reserves is really determined by the aggre- gates. At the same time, the aggregate, of course, may at any time be reconstituted by merely adding up these individual portions. That is the usual course. Two general statements of the prospective view of the reserve are very useful, viz. : First, it is the difference between the net single pre- miums for the insurance yet to be furnished and the pres- ent values of the net premiums yet to be received. Second, it is the present value of the excess of the ag- gregate net premiums that would be charged for the in- surance yet to be furnished, if beginning now, over the aggregate net premiums, which are actually payable and which are fixed according to the ages at the time the in- surances were originally taken. If the gross premiums are assumed in these computa- tions to be receivable for the purpose of paying future claims, this is called "a gross premium valuation"; and unless the gross premiums are smaller than the net, the reserve will be smaller than if the net premiums were em- ployed in the computations. When net premiums are employed, it is called "net valuation" or "net premium valuation." A net premium valuation is required in all or nearly all the States of this country as a standard of solvency; it assumes that all the loadings realized upon renewal premiums will be needed to cover future expenses and contingencies. This assumption is, of course, not ac- curate ; and, as we have seen, it is wholly invalidated if the loadings have been so computed that the margin on renewal premiums is not only to take care of future ex- penses and contingencies, but also to make good a defi- ciency due to the loading on the first year's premiums being a less amount than the policy's share of the actual expenses of the first year of insurance. But it is the effect 99 of requiring net valuation unless a method of loading, calling for a lower net premium the first year with higher net premiums thereafter, though with gross premiums the same each year, is recognized as admissible. The usual implication, when gross premiums are level, is that net premiums are also level ; and by some actuaries of very high standing it is held that this implication is neces- sary and subject to no exception, i e., that it applies in all cases, no matter what the conditions of the policy, even though calling for preliminary term insurance or in some other manner attempting to set up varying net premiums, but with the gross premiums the same each year. It is not denied that valuation on the preliminary term basis — that is, with a lower net premium the first year and larger net premiums thereafter — will assure solvency; but these actuaries declare that it is in no proper sense "net valua- tion" if made by employing such "net premiums" when the gross premiums are in fact level. 100 SURPLUS— WHENCE DERIVED. In the conduct of a life insurance company, profits or salvages may be made in all or at least in some of three ways, viz. : higher returns from investments than at the rate of interest assumed in computing net premiums and reserves, a lower amount of mortality claims than was expected, according to the table employed, and expenses and disbursements less in the aggregate than the load- ings of the premiums received. But one of these, the excess of returns from invest- ments over interest at the required rate, is genuinely a profit. Both the others are really salvages. Yet the three are usually grouped together and called surplus earnings. A due regard for prudence dictates that the rate of in- terest assumed in computing net premiums and reserves shall be so low as to assure that it can be realized through a long term of years, and that the mortality table shall represent mortality which may reasonably be expected by the average company, operating under like conditions, with a moderate margin for safety. These precautions make it all but certain that, for a time at least, there will be gains from excess interest and salvages on the expected disbursements for death losses. In other words, net pre- miums, when so computed, are certain to be slightly re- dundant. Originally, one of the declared purposes in loading participating premiums was to provide for a definite bonus or dividend to be returned to the insured, in addi- tion to other gains and salvages. This is still true in Great Britain and some other countries; but, owing to competitive conditions in the United States as to agents' first-year commissions, it was until recently deemed that a company did well to keep its expense disbursements just within the aggregate loading, even though the business were large and on the full-participating plan. A few companies saved a fair percentage of the loading by con- tenting themselves with a very moderate new business. As has been shown, however, unless preliminary term or some substitute for it has been adopted, the expense in- curred the first year of insurance is greatly in excess of the loading on the first year's premiums. This excess alone absorbs the margins in the loadings on renewal pre- miums, if new insurances, equal to about one-third the insurances in force at the beginning of the year, are se- cured at the then prevailing rates of commissions. The rates of commissions payable under the restrictions of the Armstrong laws would admit of nearly one-half being written, if all the margins of old and new premiums could be and were so applied. The difference between the aggregate "costs of insur- ance" — that is, the sum of the net tabular mortality costs of the actual insurance — and the actual death losses, less reserves released at death, is accounted a clear gain or salvage. This salvage is sometimes called suspended mortality, meaning that all must die some day; payment is merely deferred. The assumption involved in calling the salvage on mortality a true gain is this : The lives which complete the year, no matter if there have been fewer losses than as per the table during the year, have as good vitality and as good chances of life as the persons at their attained ages, from whose lives the experience was taken which made up the mortality table. Therefore, their future 102 premiums, with their present reserves, assure the payment of their claims ; and the premiums which have been re- ceived in excess of the needs of the past and of the rein- surance reserve, may therefore be considered a true sur- plus. Another source of gain to individual policyholders, but at the cost of others, which was once paraded as likely to yield very large returns, is from forfeitures and sur- render charges. Estimates of enormous profits, based ufMDn conditions as to lapsation that were passing away, were indulged in a few years ago. Usually these esti- mates were honestly made, and were not larger than at the time appeared, both to prudent business men and to experts in life insurance, to be reasonable. Thus the first figures employed by one of the leading companies which issued these "tontines" were submitted to the lead- ing American actuary of that day, Sheppard Homans, and were endorsed by him as conservative ; though in the event they proved to be preposterously high. The gains were of this nature : The reserves of poli- cies which were terminated by lapse during a term of ten, fifteen or twenty years, which had been selected by the insured in advance, were forfeited to the persistent policyholders. These gains proved to be much smaller than was expected, partly because interest was not at so high a rate as was anticipated, but chiefly because the gains from forfeitures were much smaller and were, per- haps, almost wholly offset by the increased expense in- curred in procuring applications for policies which were subject to so harsh conditions. The accumulated gain from forfeitures in some instances, as to which detailed statements were furnished, added but two or three per cent, to the total accumulations of surplus. The harsh and unfair character of the "full tontine" insurance provisions was relaxed after a time as regards 103 new policies ; and the condition was substituted that only the surplus, if any, over the reserves should be forfeited, liberal surrender values being allowed from the reserve. The deceptive nature of gains from forfeitures is suffi- ciently indicated by the fact, attested by the managing actuary of one of the largest companies, that of two policies of the same kind, age of insured and year oi issue, the one with full tontine provisions completed its twenty-year term with a smaller accumulation of surplus than the one which provided for forfeiture of surplus only. • The disappointing character of the tontine gains actu- ally realized was soon so far forgotten that certain com- panies, organized for the purpose, were able for a time to make representations that accumulated profits of from 66§ per cent, to loo per cent, could be realized on en- dowments maturing in ten years, because of gains from forfeitures ; whereas the largest gains, under more favor- able conditions, both as to interest and economy of man- agement, had been only from one-third to one-half of the lowest of these percentages. The actual returns on poli- cies sold by these representations were about lo per cent. Under accumulated surplus plans, as applied to endow- ment insurances, with the distribution term the same as the endowment period, the accumulation, including re- serve, exceeds the sum insured during the last years of the period, so that there is a positive gain to the sur- vivors because of deaths during these years. In com- parison with plans where surplus is withdrawn annually or is applied to increase the sum insured, there are such gains in event of death at any time, for the surplus that would have been paid to the deceased policyholder dur- ing his lifetime or to his beneficiaries in increased benefits is forfeited to the survivors. The reason these gains were illusory, even when they 104 should have been considerable, is that they were fully absorbed by the larger expenses incurred by the com- panies, largely in the form of wasteful expenditure to se- cure new business. los SURPLUS— HOW AND WHEN APPORTIONED. There have been many different methods of distributing the surplus earnings of participating policies. A com- mon method in Great Britain, where, as has been said, the loading is frequently computed with a view to re- turning part of it in bonuses or dividends, is to divide the surplus earnings aside from excess interest over the rate required to maintain the reserves, in proportion to the loading on the premiums ; or, if the loading is a uniform percentage of the premium, then in proportion to pre- miums. Another method, also at one time somewhat common, was to divide the surplus in proportion to sums insured. And there have been all sorts of variations of these. In 1863, Sheppard Romans, then the actuary of the Mutual Life Insurance Company of New York, brought to the attention of actuaries and other life insurance men a system of apportioning surplus, devised by himself and David Parks Fackler, then the assistant actuary of that company. To this method was given the name "Con- tribution Plan" ; it is succinctly and accurately described in the following extract from a communication by Mr. Homans to the "Journal of the Institute of Actuaries" : "Credit each policyholder, first, with the amount actu- ally reserved at the last preceding distribution of surplus, as the then present value ; and, second, with the effective (or full) premiums paid since that time, both sums be- ing accumulated at the actual current rate of interest to the date of the present distribution; and charge him, 106 first, with the actual cost of the risk to which the com- pany has been exposed during the interval, determined by means of a table representing the rates of mortality and interest actually experienced; and, second, with the amount now reserved as the present value of the policy. The difference between the sum of his credits and the sum of his debits determines the overpayment or contribution from the policy proper." This formula neglected to provide for charging for expenses. Mr. Homans at that time found it possible to pay all expenses out of gains from forfeitures. The prac- tice, however, has been to charge the expenses and credit gains for forfeitures. The idea of apportioning the surplus in cash dividends is an old one, dating back, indeed, to the foundation of che Equitable Society in 1762; for in its deed of settle- ment appeared the following: /'That, when and as often as it shall appear to a Gen- eral Court of the said Society that the Stock of the said Society arising from premiums is more than sufficient to pay the claims made or liable to be made, upon the said Society, then and so often the said Society shall, in a General Court, declare a dividend of the surplus or of such part thereof as shall, by the said General Court, be thought and judged convenient, amongst the members of the said Society who shall be assured with the said So- ciety upon (and for the whole continuance of) their re- spective lives." Instead of cash dividends as contemplated, the actual division was made in the form of additions to the sums payable at death ; the actuary puts it thus : "By extend- ing the allowance to Claimants after a certain rate to be computed upon the sums assured, for every year's pre- mium paid upon their respective Policies prior to a certain day in such several Orders specified." 107 It has more than once happened since that time that actuaries have in learned and obscure language concealed departures from what was promised. These additions to the sums insured were called "bonuses," and accordingly that name, instead of "divi- dend," became, and yet remains in Great Britain, the com- mon expression for apportioned surplus which is usually in the form of paid-up additions. When the surplus is thus applied to increase the insurance it is called in Great Britain a "reversionary bonus," and, when paid in cash, a "cash bonus"; while, when paid in cash, it bears in America the name "dividend," and when applied to in- crease the insurance, "dividend additions." The system contemplated by the Equitable's Deed of Settlement was to divide the total surplus so that one part was given for one premium paid, two parts for two premiums, etc. The same system was employed in de- termining the "reversionary bonuses," first declared by that company — i. e., one whose policy was ten years old got ten times as much bonus as one whose policy was only a year old. It was reserved for American companies to revive and establish the name "dividend," to reintroduce and popu- larize the distribution of surplus in cash and to perfect and exemplify a just and equitable system of distribution. The contribution plan became at once popular in the United States and has been employed by all American companies, though sometimes with modifications so great as to render it almost unrecognizable. The most com- mon modification has been to distribute excess interest upon the reserves according to the amounts of the re- serves and all other profits in proportion to the loadings on premiums. Another, to distribute practically all the gains in the same form as excess interest, in which case about all that remains of the contribution plan appears to io8 be such veneration for the name as influences one not to acknowledge that it is discarded. The original contribution plan made no provision for apportioning accretions of surplus from forfeitures, but it was long ago modified so as to distribute such surplus in proportion to the values which are subject to forfeiture, thus adhering to the distinctive principles of the plan. Gains or offsets because of surplus, forfeited by death, in like manner appear, according to the principles of the contribution plan, to be properly apportionable in propor- tion to the "costs of insurance," which are the measures of each policy's contribution to pay the death claims of others. Mr. Homans furnished a further formula for distribut- ing profits by the "contribution plan," which may be put as follows: Margin from loading: compute the salvage of actual expenses and contingencies as a percentage of the aggregate loading, and apply the same to loading on the individual premium. Salvage on cost of insurance: compute the salvage of actual net death losses — gross death losses, less the reserve — as a percentage of the ag- gregate net costs of insurance for the same period, and apply it to the cost of insurance under the individual pol- icy. Gain from excess interest: compute the excess of investment gains over the interest required to make good the reserves as a percentage of the aggregate reserves and apply this percentage to the reserve of the individual insurance. To this may be added: Accretions from forfeitures by lapse and surrender: compute the aggre- gate forfeitures as a percentage of the aggregate values liable to forfeiture, and apply to the value of the indi- vidual policy liable to such forfeiture. Salvages and gains from forfeiture of surplus at death: compute the aggregate forfeitures as a percentage of the aggregate tabular costs of amounts of insurance equal to the sur- 109 plus thus subject to forfeiture, and apply to tabular cost of insurance of an amount equal to the surplus, thus subject to forfeiture, in case of the individual policy. Elizur Wright invented a system of determining the surplus earnings of a policy according to the principles of the contribution plan, which is illustrated in his book "Savings Bank Life Insurance," by means of an indi- vidual account of the following character : Age 25. Death or 50. Annual premium: gross, $32.91 ; net, $28.68. NINTH YEAR. Dr. Cr. To Loading $4.23 By Reserve 8th terminal $207.49 " Mortality, as per table 6.53 " Premium 32.9X " Reserve 9th terminal 238.83 " Interest @ 4 per cent 9.19 "Dividend 5.39 " Surplus interest (actual rate 5 per cent) 2.30 " Salvage on mortality 20 percent 1.31 " Salvage on loading 1.78 $254.98 $254.98 It will be observed that this account really duplicates entries, there being charged the full costs of insurance and the full loading, and there being credited the inter- est required to make good the reserve, and then addi- tional entries are made, rebating the margins of costs of insurance and of loading, and also crediting the ex- cess interest. The account could be kept, of course, but it would look decidedly queer if one or more of these additional entries were minus instead of plus. This would surely be the case as to loading for the first year if a correct account were kept and the loading were on the level premium basis. A simpler and more direct system of accounting, and therefore less puzzling to the insured, is as follows : no Age 25. Death or 50. Annual premium: gross, $32.91 ; net, $28.68. NINTH YEAR. Dr. Cr. To Net Mortuary Cost $5.22 By Reserve 8th terminal $207.49 " " Expense Cost 2.45 " Premium 32.91 '* Reserve 9th terminal 238.83 " Interest on net balance at "Dividend 5.39 5 per cent 11.49 $251.89 $251.89 It will not escape notice that under this system only the actual expense and mortality costs are charged and the actual rate of interest earned is credited, thus avoid- ing duplication. The charge for expense is determined by the loading, especially if the same is on the so-called scientific basis, being such percentage of it as the aggre- gate expenses bear to the aggregate loading; the charge for cost of insurance is determined by the tabular cost, being such percentage of it as the aggregate net losses bear to the aggregate tabular costs of insurance; and the credit of interest upon the mean balance is at the rate realized on the mean assets. In neither of these accounts are entries made for gains from forfeitures, but such entries offer no difficulties. If divided in proportion to reserves exposed to the risk of forfeiture, they can be converted into an increase in the rate of excess interest — a simple device and approxi- mately correct. Very few companies keep such individual accounts; nearly all apportion surplus by formula. But when there is strict adherence to the contribution plan, the re- sult will be the same. In order to prevent disturbing fluctuations in the dividends, however, almost all com- panies employ average percentages instead of following the current experience accurately. The bonuses of the Equitable of London, already re- ferred to, were for a long time apportioned every seven III years, but now every five years, which is more common in Great Britain than either a shorter or a longer period. Annual bonuses are not unknown there, howeVer. In the United States, the earliest apportionments were at the end of five-year periods, and in "script dividends," redeemable later and bearing interest until redeemed in cash. Annual apportionment soon became the rule, how- ever; and, precisely as later in regard to deferred divi- dends, absurdly excessive estimates of the annual divi- dends to be expected were indulged in, which, after a few years; made the plan unpopular. About the year 1870 there was a reaction, both against annual dividends and surrender values, which brought into vogue forfeitable policies, with apportionment de- ferred for ten, fifteen or twenty years, and with tontine provisions. So much had been said about the enormous gains from forfeitures during the agitation in favor of surrender values that it was easy to believe that the gains would be large. The lapsing of policies because of dis- appointment as to annual dividends had been very great and was soon made much more widespread by reason of the panic of 1873 and the ensuing hard times. This con- firmed the notion that enormous gains would be realized from forfeitures; but many of the forfeited policies had no reserves to be forfeited, as they were burdened with premium loans, nearly or quite equal to the full reserves. Moreover, the period was one of failing companies and of failing confidence in them, so extraordinary that in about seven years the volume of life insurance in force in the regular companies dropped fully one-third. Only three companies of importance, however, made any use of the full tontine plan, involving the forfeiture of the entire values. It was modified later so as to for- feit the surplus only, which really made it merely a de- ferred dividend plan of the ordinary type. In this form 112 it has been employed by nearly all the companies, only a very few resolutely clinging to annual dividends. Owing to the system of loading most frequently adopted, viz. : on a net level premium basis, as to most policies there is not really accumulated out of the pre- miums, after meeting the expenses incurred on account of them, as well as the mortality cost, enough to pro- vide their reserves before the end of the third year at least. The application of the contribution formula, how- ever, may show a surplus at the end of one year, because the policy may for dividend purposes be charged only with such percentage of its loading for expenses — level each year — as the aggregate expenses to the aggregate loading. The advantages claimed for long dividend periods are : until required for distribution, this surplus is of the na- ture of general surplus and acts as a safety fund; it is payable, as a reward for vitality and for persistency, only to persons who survive the period and have continued their insurance ; and it has the effect to convert life poli- cies into accumulating investments. Its disadvantages are : it tempts to extravagance and to larger commissions for new business, causes men to view life insurance as a speculation, and is invariably disappointing as to invest- ment results. The report of the New York Legislative Investigating Committee in 1906 exposed all these evils of the opera- tion of the tontine or deferred dividend system ; and, in addition to laws limiting expense of new business and general expenses, recommended the enactment of laws prohibiting the issuance of participating policies with dividend periods of more than one year. Such laws were enacted, and there has been similar legislation, requiring dividends to be declared and paid annually, in several other States. 113 It was at first expected that this would materially dimin- ish the attractiveness of life insurance policies and that the volume of new insurance would be much diminished. The great diminution of new insurances during 1907 and 1908 is now ascribed to other causes, however, and it is admitted that there is a much larger production per agent and a complete recovery of former popularity, though dividends are annual. The frequency of accounting, involved in annual dis- tribution, has also resulted in the suppression of many extravagances and leaks which formerly passed un- noticed, but now are seen to affect unfavorably the divi- dend rate, which competition causes every company to bend every energy to maintain and even to increase. 114 SURPLUS— HOW APPLIED. The method of deahng with the surplus earnings of participating policies which the founders of the Equitable of London had in view, was, as we have seen, to divide the same among the policyholders in cash at frequent in- tervals. The method actually adopted by the company, as we have also seen, was to grant "reversionary bonuses," pay- able with the principal sum upon the death of the in- sured, and to make apportionment of the surplus every seven years only. The application of surplus earnings to the purchase of reversionary bonuses, known in this country as "paid-up additions," "reversionary additions" or merely "dividend additions," was also introduced in the United States at an early date. One of the oldest and largest companies still declares its dividends in this form, permitting the cash value of the additions to be taken, however, if the policyholder prefers. Dividends in the form of interest-bearing script came into use in the United States at quite as early a period. At first, the fact that reversionary bonuses were not fairly apportioned, if the same percentage of the sums insured were added without regard to the attained ages of the insured, was not generally understood; though, of course, it was known by those in charge that the aggre- gate net single premiums for these paid-up insurances, so declared as paid-up additions, must not exceed the total surplus earnings. To bring out an even percentage IIS of additions, which would absorb the surplus earnings very nearly, often required very nice calculations. This system of percentage bonus additions, thus in- troduced by the Equitable of London in advance of all other methods, became and yet remains very popular in Great Britain. There are two varieties of it at least. One adds a percentage of the original sum insured and is known as the "simple reversionary bonus" system. The other adds a percentage of the sum insured, includ- ing all bonuses, and is called the "compound reversionary bonus" system. In the United States the practice of most of the life insurance companies is to declare and pay dividends in cash. A single exception has already been mentioned, a great company which declares its dividends as rever- sionary additions, but permits their cash value to be taken, if desired. On the other hand, companies which declare dividends in cash permit the same to be applied at the option of the insured to purchase paid-up additions. Proof of good health is sometimes but not usually required as a condi- tion precedent ; when required, if it is once given and a request for that form of application made, the surplus is so applied thereafter without demanding evidence of con- tinued good health. Cash surplus has also been applied to purchase in- creases of the insurance for a single year, known as tem- porary dividend additions. This, however, was never common, and no new policies of this character have been issued for many years. Especially in connection with deferred dividend plans the option has also been given to apply the cash surplus to purchase a life annuity or a temporary life annuity in reduction of subsequent premiums or otherwise. Another application of the surplus has been to cause the ii6 policy to mature as an endowment, or to accelerate its maturity, if it is already an endowment. This is clearly, in effect, only to permit the surplus to accumulate undis- turbed, the same not to be paid in event of death, but not subject to forfeiture upon lapse or surrender because it is taken into account in fixing the surrender value. Yet another form is to apply the surplus to purchase pure endowments payable at the end of a given period. This is, in effect, a deferred dividend plan, but the surplus vests definitely each year, though payable only at the end of the period, provided the insured survives. Under such a system, the surplus so apportioned is forfeited in event of death, lapse or surrender. "7 SURRENDER VALUES. Even after level premium life insurance was introduced it was the general view that when one failed to pay the premium his insurance lapsed, precisely like any other in- surance policy which expires and is not renewed. To the extent that this view obtained, men came to believe that the large accumulations of life insurance companies were unnecessary. An explanation of the nature of reserves and of the necessity for them made it clear that the holder of a level premium policy has paid more than the value of the insurance enjoyed, thus partially prepaying future costs. When this was understood, the demand for sur- render values, unless held in check by the expectation of great gains from forfeitures, is sure to be well-nigh irre- sistible. The practice of making some allowance on surrender is very old. Provisions for it were contained in the rules of the Equitable Society as long ago as 1795, and there are repeated references to it in these rules at later dates ; but the whole matter was one of discretion. In a few companies in Great Britain and elsewhere this discretion has been exercised in a manner so equitable and even liberal and beneficial to withdrawing policyholders that no hard and fast agreements have ever been demanded of these companies. The contrary course, however, has been so common on the part of most of the companies in this country that the public has demanded either the pro- tection of legislation or definite guarantees of surrender values in the policies themselves. 118 The first general recognition in the United States of the equitable right of the policyholder to a surrender value resulted from the system of reversionary bonuses or divi- dend additions. These bonuses being fully paid for and vested, the position could not well be taken that there was occasion for forfeiting them on the ground of non-pay- ment of the regular premium. Others were much quicker to recognize this, however, than the managers of some of the companies; they were generally very reluctant to grant surrender values. In the United States, the first agitation in favor of sur- render values for life insurance policies was carried on by Elizur Wright in Massachusetts during the "fifties." Mr. Wright was made a commissioner of insurance for that State in 1858, and, from the vantage ground of his position, waged a campaign in favor, first, of compulsory net valuation by the Actuaries' Table and 4 per cent, in- terest, as a test of solvency, and, second, in favor of grant- ing surrender values — both ultimately successful. His idea of the proper form of surrender values was that the terminal reserve by the Actuaries' Table and 4 per cent, interest, less a surrender charge, be applied as a net sin- gle premium for temporary insurance to keep the insur- ance in force for the original amount as long as possible. This was devoting the money to the general purpose for which it had originally been accumulated, viz. : to meet future costs of insurance. Mr. Wright's campaign was brought to a successful close on May 10, 1861, when a law was enacted requiring Massachusetts life insurance companies to grant extended insurance in this manner, which extensions attached auto- matically as soon as the premium failed to be paid when due. The campaign was a hard one, but it was attended and followed by relieving and even humorous features, among them the following : 119 An objection urged to the plan was that the labor of de- termining the term of extension was well-nigh intermin- able and altogether intolerable. When the commis- sioners' report for 1862 appeared, it was found to contain a complete table of net single premiums for temporary in- surances at all ages and for all terms of an even number of years, according to the Actuaries' Table and 4 per cent, interest ; so that the term of the extension could be ascer- tained by inspection. The dismay of the objectors may be imagined, and their defeat was a foregone conclusion. Long before the enactment of the Massachusetts non- forfeiture law, however, as long ago as 1792, a life an- nuity company in Philadelphia, now known as the Presby- terian Ministers' Fund, organized in 1759 and restricting its membership to ministers of that faith, had allowed surrender values in paid-up annuities under particular cir- cumstances ; and in 1852 it began also to allow surrender values in paid-up insurance. By reason of the limited clientele of this company, this had no influence upon the general practice. In i860, while the agitation about surrender values was in progress, and before the Massachusetts non-forfeiture law was enacted, the New York Life Insurance Company introduced a whole life policy paid-up in ten years — the first of that form in this country — and inserted the condi- tion that it could be surrendered, after being in force for at least two years, for paid-up whole life insurance for as many tenths of the original amount as full year's pre- miums had been paid. The credit for this initiative has been variously assigned ; it was publicly claimed by Pliny Freeman, formerly actuary of the company, after he left its service and while he was president of another com- pany, and the claim was not challenged. This was the first guarantee of surrender value priv- ileges by any American life insurance company doing a general business. Even after the Massachusetts non- for- feiture bill had passed, the Massachusetts life insurance companies were so far from being reconciled to that law that for a time they put a waiver of the same into the ap- plications. Later, however, they made a virtue of neces- sity, and urged the beneficial nature of the law as a means of influencing business. Two other companies, the Mutual Benefit Life Insurance Company of New Jersey and the National Life Insurance Company of Vermont — the latter, under the advice of Elizur Wright as its con- sulting actuary — soon afterward adopted the policy of allowing liberal surrender privileges and have adhered to it to this day. The Mutual Benefit later earned for itself a reputation for especial liberality by voluntarily guaranteeing automatic extension of the insurance for a definite term, upon failure to pay premiums. From time to time other companies conceded surrender values in one form or another — mainly in paid-up insur- ance of the same kind as the original insurance, but for a reduced amount. The movement toward more liberal surrender privileges was in full swing when the tontine insurance reaction set in. It was but partially and tem- porarily checked by that; but the non-forfeiture law of New York, modeled somewhat on the non- forfeiture law of Massachusetts, except that it permitted either paid-up or extended insurance as might be provided in the policy and also required that it be applied for within six months, was amended so as to legalize waivers of its provisions. The allowance of cash surrender values was longer de- layed. Though in 1880 no longer insurance commissioner of Massachusetts, Elizur Wright yet had such influence that he prevailed upon the legislature to repeal the old non-forfeiture law and enact one which required that cash surrender values be allowed with other alternative surrender values. The determination of the amount of the cash surrender value was directed by this statute to be made upon a pe- cuHar basis, invented by Mr. Wright. Starting with the individual terminal reserve, the reasoning was as follows : If all who were not going to die within one year were to withdraw, each receiving the individual reserve of his policy, the remaining reserve, with the new premiums paid, would not be enough to meet the death claims. In like manner, though not to the same degree, if those who withdrew are better lives than those who remain, the re- serves on the remaining insurances may not be sufficient, together with future premiums, to pay out. It is gen- erally considered that, on the average, those who sur- render or discontinue are better lives than those who re- main ; and also that cash values would be an incentive to withdraw, causing many more withdrawals of the best lives than would otherwise take place. This lowering of the average quality of the lives insured is called "adverse selection," and the danger of "adverse selection" was in those days given as the most conclusive argument against cash values. This argument caused Elizur Wright to investigate : How would adverse selection affect the conditions and what could be done to offset the deterioration occasioned by it? The manner in which adverse selection affects the com- pany is by enhancing the actual "costs of insurance," and the way in which it may be oflfset is to increase the reserve by an amount equivalent to the present value of this in- creased risk of death. The way in which it enhances the "costs of insurance" for the remaining lives is by remov- ing lives which would, as a class, have contributed more in their contributions to pay future "costs of insurance" than the actual costs under their policies only would have been ; and the conclusion was arrived at that the measure 122 of this financial damage to the company was a percentage on all future tabular "costs of insurance" which would be realized from the policies surrendered. To the present value of all future "costs of insurance" of a policy — that is, of all future contributions to pay the excess of death claims over the reserves — Mr. Wright gave the name "in- surance value," and he fixed upon a "surrender charge" — that is, a sum to be deducted from the terminal reserve in determining the cash value — equal to 8 per cent, of this "insurance value." This rule was embodied in the statutes of Massachusetts and remained the law until 1900, when a simpler but more arbitrary rule was sub- stituted. If the reader has found it a little difficult to follow the foregoing analysis, he may from that fact form some con- ception of the respect and authority which Elizur Wright's great services had earned for him in Massachusetts, and which enabled him to obtain the favorable attention of legislators for these arg^iments. No one else has ever equaled Elizur Wright in perspicuous and convincing statement of the complex subjects of actuarial science. As the reactionary tontine wave gradually subsided, the demand for more liberal cash surrender privileges became more insistent. The extremely liberal values allowed upon the termination of the tontine period, no surrender charge being deducted from the reserve, had something to do with it ; but much more effective was the conviction that the gains from forfeitures, in fact realized, were a poor return for the risks taken. The following facts also had their influence: The companies which allowed lib- eral surrender values, even when in cash, did not exhibit materially heavier discontinuances than others nor the alarming consequences of adverse selection which had been anticipated; and to offset any relative loss of earn- ings by paying such values they were able to procure in- 123 surances for commissions materially lower than most companies which were illiberal in this regard found it necessary to pay. The publication of the mortality expe- rience of the company paying the most liberal cash sur- render values in the world, the Australian Mutual Prov- ident Society, also influenced men's views : for that com- pany exhibited the lowest mortality among insured lives yet observed, and also very remarkable persistency of policyholders. The opinions of many, including, it is proper to say, the author of this book, were by these con- siderations modified as regards the influence of cash sur- renders upon adverse selection, in effect as follows : So long as a company is in good repute, the privilege of a cash value on surrender at any time does not materially, if at all, increase the number of withdrawals, especially if loan privileges are also granted, and therefore does not cause more adverse selection than do other forms of sur- render values. On the other hand, the analysis of expe- rience as to the effects of such privileges, if offered but once or only at long intervals, invariably reveals marked adverse selection. These considerations greatly weakened the resistance of all companies to the demand for more liberal cash sur- render privileges ; but competitive necessity was, perhaps, the more potent factor, and the action of the New York Life Insurance Company, upon the accession of President McCall in 1892, was the beginning of the end in that re- gard. That company introduced into its policies loan privileges, rather than cash surrender values, but by mere failure to repay the money borrowed, such became in effect cash values, though the company has successfully resisted such utilization of it, when advised of this pur- pose in advance. Several other companies, including all the Massachusetts companies, the National of Vermont and the Mutual Benefit, were already granting cash values 124 or loans, or both ; but the New York Life was so much more active in the field and had so opposed the practice of guaranteeing the allowance of cash loans that its de- parture had great weight with the others, especially as it proved to be a valuable competitive advantage. In 1896, the Equitable's guaranteed cash value policy made its appearance, offering values equal to the Ameri- can Experience 3 per cent, reserves, the Northwestern cash value policy in 1897, and the Mutual Life's in 1898. The last-named offered, indeed, cash values at the end of distribution periods of fifteen and twenty years much in excess of the ordinary reserves, the excess having been accumulated out of the premiums to provide against ad- verse selection, it having been found that the average of health is lower among those who continue their insurance instead of taking cash. In recent years, according to the general view, the pendulum has swung in some cases too far in the direc- tion of liberal values in the earlier years of insurances. Thus some companies allow cash values equal to the full reserves at the end of the third policy year under policies with premiums loaded on the net level premium basis. Values so large cannot, of course, be accumulated from the premiums actually received, after deducting the pol- icy's share of mortuary losses and expenses, if its share of the cost of the procurement of new business is to be made good out of its premiums. In arguing for his cash surrender charge, Elizur Wright gave, as an alter- native measure of the surrender charge, this : "A sum sufficient to procure another freshly-examined life to take the place of the life retiring ;" and, whether on that ground or otherwise, it seems clear that the value allowed upon surrender ought not to exceed what has been ac- cumulated from the premiums paid, after meeting all expense and mortuary contributions properly charge- able thereto, 125 Surrender values, then, generally take three forms, available at the option of the policyholder, viz. : Cash, paid-up fractional insurance of the same kind as the orig- inal, paid-up temporary or extended insurance for the original amount. Commonly, the others are made pre- cisely equivalent to the cash value by some standard ; but this is not always the case. The privilege of surrender- ing for a life annuity or for a temporary life annuity, or even for a temporary annuity certain, may also be given. Usually one of these values — more commonly the ex- tended insurance — attaches at once upon failure to pay premiums when due; while to take advantage of the others requires action on the part of the insured. A special form of extended insurance is the grace of one month for the payment of premiums, which most com- panies now give. 126 LOANS ON POLICIES. Before the introduction of surrender values in the United States, in cash or otherwise, at least one form of loan upon the security of a life insurance policy was known. It was the "loan-note" or "premium-note" plan, very much in vogue in the early history of mutual or participating life insurance in this country. This plan consisted in taking the note of the insured for a part of each premium — ^usually 40 per cent, in the early days, but sometimes as little as 33^ per cent, and sometimes as high as 50 per cent. The notes bore inter- est, payable with the cash portion of the premium ; divi- dends were applied usually upon the principal of the in- debtedness, but frequently first to pay the interest and the remainder to reduce the indebtedness and occasionally, especially in later years, to pay interest and to reduce the cash part of the premium. Although the notes were often in such form as to be personal obligations, seldom was an attempt made to collect upon one; and, in practice, the mutual obligations were deemed to be canceled when, by failure to pay a premium, the insurance became void. Thus the notes became in effect advances against the poli- cies and were Secured solely by the values or reserves of the insurances. This practice was criticised very severely by Elizur Wright in his reports as commissioner of insurance; be- cause, while the same companies were declaring that it was dangerous and preposterous to allow surrender values in any form, under this "loan-note" plan they were per- 127 mitting surrender values which were frequently equal to the entire reserves. The inconsistency is apparent, and, as has already been mentioned in connection with the dis- cussion of surrender values, to grant loans is tantamount to giving cash surrender values; for if the insured de- sires a cash surrender value, he has only to borrow to the limit of the loan value and then to cease paying premiums whereupon the insurance lapses, he remaining in posses- sion of the proceeds of the loan. The borrower does not usually sign a note which ren- ders him liable personally; and, as stated, an attempt is not often made to enforce payment, except from proceeds of the policy, i. e., as an offset to its forfeited reserve. Notwithstanding which, there was in those days, and there yet remains, this important distinction between cash loans and cash surrender values : loans are utilized in many cases as a means of continuing the insurance, and not as a means of surrendering it in order to obtain the cash value. This is plainly seen, both in the large propor- tion of renewals of policies against which loans are made, and also in the large number of loans negotiated when the cash values were also available and by surrendering the policies might have been taken. It was also illus- trated by the original "loan note plan" ; for under it the loan was made an inducement to come in, instead of to go out. In times of financial stress, the privilege of borrowing is very often availed of for the purpose of maintaining the insurance, and policies containing this privilege prove veritable "friends in need." At such times cash surren- der privileges, unaccompanied by loan privileges, result in increased discontinuances — an injury to the company, and to the insured as well. An experience of this sort in 1893 caused a prominent company, which granted cash values on surrender but refused loans, to change its policy and to 128 grant loan privileges also. That, except as a result of straitened finances, men are ordinarily tempted by the mere fact that cash values are available to surrender poli- cies which can at any time be surrendered for cash, is not now credited ; and it is well known that the privilege of a loan often enables the insured to keep up insurance which otherwise in hard times he would be compelled forthwith to abandon. Therefore, though loans may be made a means of securing cash values if they are not otherwise obtainable, this is not done in most cases. Nevertheless, except in the operation of the "loan-note" plan (which was generally discarded after the 70's be- cause it had been sold on the representation that the divi- dends would take care of the notes, and this they failed to do, with the result that decreasing insurance, the notes being deducted at death, was furnished at an increasing rate, interest on the indebtedness being added to the cash part of the premium), American life insurance companies did not until after 1890 favor granting loans. Especially was this true of all companies that opposed cash surrender values, with a single exception; while all the companies that allowed cash surrender values, also with a single ex- ception, granted loans also. After the crisis of 1873, a leading company, which did not give cash values, sagely proceeded to save as much of its insurance in force as pos- sible by giving credit, and by this means largely it suc- ceeded in actually increasing its volume of insurance in force each year during a period within which the aggre- gate insurance in force in all the regular companies of the United States fell off one third. Singularly enough, an- other leading company was during the same period in- fluenced to adopt a most illiberal course as to loans through fear that they would be availed of as cash sur- render values, and upon the representation of one of its principal agents that policyholders were realizing on their 129 policies in that company in order to keep up their insur- ance in other companies that were less liberal. There was a very strong disinclination on the part of many companies to grant loans. It was argued that to do so was to encourage the policyholder to put in jeopardy the provision which he had made for his beneficiary ; and much almost tearful solicitude was expressed in that re- gard. It was ignored that the policyholder had shown a proper sense of responsibility as regards the beneficiary, by taking the insurance, and was obviously the best judge as to his duties in this respect; and also that in many cases the ability to borrow may save the family from pinching distress and from the loss of the protection of the policy as well. In attempting to avoid such loans, at least one company was once so inconsistent as to create means by which others could lend upon its policies at higher rates than could be obtained upon other loans with se- curity so unquestionable. An objection at one time oflfered to making any policy loans whatsoever was the disrepute into which the "loan- note" plan eventually came, by reason of bitter disappoint- ment regarding the dividends received. The distinction between the results of the representation that these notes would be covered by dividends and never need be paid and the results of merely lending upon policies was not at first clearly apprehended, or, in some cases, may have been obscured purposely. An attempt was made by more than one company to confine policy loans to advances for the purpose of pay- ing premiums. This did not work well, however; for when the policyholder was forced to realize on his policy, he had, in such cases, to address himself to a professional lender, with the usual result. The insured was thus wronged and the company not benefited. AH the companies have now been brought, by legisla- 130 tion or by their own determination of what is wisest and best, to recognize that the only question which the com- pany can properly take cognizance of is : "How large a loan may safely be granted against the security repre- sented by the policy?" This question has been answered in various ways, as follows : Some companies have been known to confine the aggre- gate amount available as a loan to a small percentage of the terminal reserve, say 50 per cent. Others have per- mitted advances up to the full terminal reserve, less the interest payable in advance. Others have fixed upon other percentages. Yet others lend an amount equal to the full terminal reserve at the end of the next year of in- surance, deducting interest in advance and all premiums to fall due before the end of the next policy year. The cash value, if less than the reserve, is usually the meas- ure of the loan which may be granted, and the loan is limited to the entire cash value or to a certain percentage of it. A special form of loan privilege has been as follows : After the point has been reached in the course of the dividend period of a deferred dividend policy, when the premiums payable thereafter to the end of the period do not in the aggregate exceed the cash value guaranteed at the end of the period, it is provided that any or all premiums will be advanced, if requested. The "loan-note" plan was revived a few years ago in a particularly objectionable form, i. e., to advance a portion of each premium during the dividend period of a deferred dividend policy, the remainder being paid in cash. Such plans usually involve, also, allowing the interest to accu- mulate, and a return-premium provision is also frequently a feature, yielding sufficient, so that the indebtedness is released at death in addition to the face of the policy being paid. The "same old lie" about accumulated surplus 131 being certain to pay ofif all loans was furbished up anew and made to do service. Often the victim, since he did not pay interest, did not know there was a large indebtedness accumulating against his policy. A special form of premium advances is an automatic non-forfeiture premium loan provision, first introduced in Australia, to the effect that upon failure of the insured to pay a premium when due, it shall be paid for him and be charged against his policy as a loan, provided the loan value, in excess of existing indebtedness, will enable this advance to be made. Under this provision the insurance is continued in full force, without the loss of dividend or other rights, except that one or two companies require proof of good health as a condition to resuming payment. Such advances are continued, if premium payment is not resumed, until the entire loan value of the policy has been absorbed by the advances and interest upon them — the loan value at the end of the policy year when the last premium could be advanced. As originally employed by one company at least, the insurance was continued only until the amount of the loan value at the time the first of such advances was made, had been so absorbed. This was manifestly unfair, because each premium, charged as a loan, set forward the reserve and loan values by one policy year precisely as if it had been paid in cash. i3« INSURANCE OF IMPAIRED LIVES. In the United States the insurance of impaired Hves was first essayed by the Universal Life Insurance Com- pany, chartered in New York in 1865. Of it Elizur Wright says in his report for 1865, as Commissioner of Insurance: "A part of the business they propose is that of insuring at advanced rates such portion of the Hves rejected by other offices as they may consider properly insurable in that way. This has been practiced with ap- parent safety to the company and benefit to the public by several companies in England, and that it is desirable here no one who has any faith in life insurance or ac- quaintance with the business can doubt." The career of the Universal was meteoric in more ways than one. Mismanagement, bad investments and the sudden determination of insurance departments to dis- allow loans on renewal commissions as assets, caused its collapse. It may be that the insurance of impaired lives had something to do with it, though that is by no means certain. Carelessness in that regard would, of course, be fatal. In any event, the system was considered to have been discredited. The failure, too, of the American Pop- ular, which also undertook the business, confirmed this impression. For many years no further effort was made to deal with this matter in any broad way. All the companies gradually came to discriminate between the lives offered which were acceptable. In most cases the mode of deal- ing with those which were not deemed strictly first class, was to offer an endowment insurance policy, preferably 133 for a short term, such as ten or fifteen years. Such a policy contributes no more "cost of insurance" or pro- vision for current mortality in proportion to the actual insurance than does any other; but the actual insurance diminishes more rapidly, and after a term of years is extinguished without the privilege of renewal, except upon new application and examination. Extra premiums were also occasionally charged, but usually only for sex or occupation. In 1892, under the guidance of Mr. L. G. Fouse as consulting actuary, a plan was formulated for insuring "under-average" or "sub-standard" lives, as they now came to be called. This plan was adopted for the use of a com- pany organized to transact that business solely. It con- sisted in charging an increasing lien against the insur- ance, equal at all times to the single premium at the cur- rent attained age, and collecting a cash premium equal to the regular premium for a policy on the plan desired. Part of this premium was applied to pay for natural pre- mium insurance for the diminishing actual insurance, and the remainder to furnish an increasing "self-insurance" fund in abatement of the lien. The company came to grief through gross mismanagement; but before that time others had taken up the idea. A variation of this original lien plan was adopted by competing companies. The variation most common and acceptable in practice, which is also still employed, is to charge a single premium lien which neither increases nor bears interest, diminished every year by the amount of the premiums actually paid upon the policy. This lien plan was not new ; it had long been used in other coun- tries. But its use, as a hard-and-fast system applicable to all cases, was new ; it had elsewhere been utilized as a part of a plan for taking care of each case when offered, according to its idiosyncrasies. 134 The inflexibility of the Hen system had to be consider- ably relaxed, as the insurance of impaired lives became more extended ; because it was soon discovered that there were many grades of impairment which offered a fair prospect of being dealt with successfully in this manner. The least that could be done was to make three or four classes, the amount of lien originally charged being ac- cording to the degree of impairment. At least one of the companies which actively engaged in this business used also the system of "rating-up" the life, by which is meant accepting the applicant on the precise plan and for the precise amount applied for, but at the premium for a higher age. Another sometimes accepts an extra premium as an equivalent of the lien. Another method in use when the impairment is not believed to be great is to issue the policy at participating rates, exactly as applied for, but in a special dividend class. Since the prohibition of deferred dividend plans in most States, the plan of "rating-up" to the premium for a higher age has been more frequently employed — some- times with the surrender values based on the actual age, thus really making the excess premium over that for the actual age a mere extra one-year term premium — but most frequently with the surrender values for a policy issued at the age assumed or "rated up." The four plans mentioned above had all been used in other countries, the company usually determining what it would offer after the application and examination were received and considered. If the impairment is believed to add a constant amount to the hazard, regardless of the age, an extra premium is deemed the suitable equivalent of it. If the impairment is believed to be an increasing one — as, for instance, one that really impairs the vital force — the plan selected is that of "rating-up," which not 135 merely gives a higher "cost of insurance" the first year but one which is at all times greater than the tabular cost at the actual attained age and greater in an increasing ratio. If the impairment is one that tends to improve, if not soon fatal, the diminishing lien plan is employed, which gives a maximum percentage of increase over the tabular "cost of insurance" the first year, gradually subsiding. In other countries, it has usually been the opinion that impairments are more frequently of the second class and call for "rating-up." This view seems now to be gaining ground in the United States. It is undeniable, however, that here a considerable pro- portion of the lives accepted as "first class," especially prior to the introduction of plans for insuring under- average lives, were such as, in some other countries, where impaired lives have long been accepted, would have been penalized by a lien, extra premium or rating-up. Doubtless the principal reason why the lien plan long held precedence here, aside from the fortuitous circum- stance that it was the first introduced, is to be found in the requirements of our agency system. The applicant, being much solicited, is unwilling to make his choice until he knows what is offered ; consequently agents find it im- practicable to submit cases to the company for special rating. This is in part the result of the agent's training, or want of it; but a proposal to "rate up," it being un- known in advance whether it will be two years or twenty, is neither so concrete nor so attractive as a proposal to lien, especially if diminishing. In Australia the leading company overcomes this difficulty by sending the medical examiner about with the agent. There is no certainty that, because the lien plan pro- vides sufficient in the first years to cover the actual cost of the insurance, it will show a margin in later years. That, unless a special reserve to cover extra hazard is 136 maintained, must depend upon whether the lives really do tend to improve, which can be certainly determined only by the experience of many years. This does not apply to Actuary Fouse's original lien plan with an in- creasing lien, offset only by an actual "self-insurance" accumulation. The success of "rating-up," if carefully and intelli- gently done, may be regarded as established by the suc- cessful use of it by many excellent companies. These experiences, however, do not indicate that the perma- nently increased "cost of insurance," which the plan pro- vides, is unnecessary ; for the ratio of actual to expected losses at the attained ages on the rated-up basis is at best fully as great as the ratio of actual to expected losses at their actual ages on lives which were accepted as first class. 137 DEPARTMENTAL VALUATIONS. The form in which life insurance companies' state- ments were originally cast was as follows : RESOURCES. Present assets $192,397.69 Present value premiums receivable 918,597.92 Total $1,110,995.61 LIABILITIES. Sums due and payable $25,250.00 Sums payable, but not due 42,115.25 Present value, future death claims 980,396.81 Surplus 63,233.55 $1,110,995.61 In making up this balance-sheet the present values of premiums receivable were found by computing the pres- ent value of each premium as a life annuity due, either for life or a limited term; then, by the same mortality table and rate of interest, the net single premiums for the insurances in force were computed, these being entered as the "present value, future death-claims." Until within a century, actuaries made up these bal- ance-sheets by putting in the present value of the "gross" or "office" premiums, i. e., the premiums actually charged, as a resource, while they did not charge any- thing on the other side of the account, as the present value of future expenses and contingencies. This is called a "gross valuation" or a "gross premium valuation," and 138 the meaning of the term is that the "gross premiums" have been valued as a resource. Other actuaries entered as a liability to offset the pres- ent value of the gross premiums, a sum, more or less arbitrarily determined, as the present value of expenses payable in future. Such a valuation is known as a "modified gross (or gross premium) valuation." When valuation was introduced in the United States by Elizur Wright, then Commissioner of Insurance of Massachusetts, he caused the account to be made up, in effect, as follows: The "present value, premiums receiv- able," was the present value of the net premiums for the ages at which the respective policies were issued, com- puted by the same mortality table and rate of interest as were used in the valuation. This amounted to the same thing as allowing the present value of the gross premiums and then charging, as a liability, the present value of all the loadings ; and the rationale of it was that the assump- tions upon which the loading was originally computed to provide for expenses and contingencies were deemed to have held in the past and to be certain to hold in future. The mode of valuing by offsetting the value of net pre- miums only in computing reserves is called "net valuation" or "net premium valuation." In introducing net valuation as a test of solvency — it was not at first called a test of solvency but merely a measure to determine sufficiency of resources by that standard, and companies were per- mitted to continue which, when tested by such, could not qualify as solvent — Elizur Wright also simplified the form of the statement by taking out the item of "present value, premiums receivable," from the resources and put- ting in as a liability only the excess of the "present value, future death claims," over the "present value, net pre- miums receivable." This excess was the total "net re- serve" or "net premium reserve" — and was also, of 139 course, the aggregate of the individual net reserves. It was called "net reserve" because it was that sum which must be held in reserve to enable the company to meet its engagements to pay mortuary losses on the basis that it will receive in future the net premiums as they become due, mortality and interest being precisely as assumed. Department valuations are usually made as of Decem- ber 31. On that date the insurances are at all stages in their respective insurance years, from being issued on December 31, and so with a full year's premium paid, to having been issued on January i, and so with a new pre- mium due the next day. In order to get a precisely cor- rect aggregate of the reserves, it would be necessary to compute the reserve for each policy at midnight Decem- ber 31, accurately, and add them together. This was at first actually attempted by some actuaries, and for greater exactitude the results carried to thousandths of a dollar. An approximation sufficiently close for all practical purposes, however, is obtained by grouping the issues of each month together and valuing the policies of that group as if all were issued on the 15th of the month. This gives what is known as mean monthly reserves. Another approximation, which also answers all practical purposes, consists in valuing all the policies as if they had all been issued on June 30, and were, therefore, exactly six months into the current policy year in each case. This gives what is called mean reserves or mid-year reserves. The reserves of individual policies are also frequently taken to the nearest dollar, which does not materially af- fect the totals. If at any stage a policy promises a surrender value or other benefit, of a value in excess of the ordinary reserve at that time, a special reserve is charged so as to provide for accumulating such excess guaranty. If the gross pre- 140 miums are less than the net, the present value of the de- ficiency is charged as an extra or "deficiency" reserve. Policies with impairment liens are sometimes valued as if there were no such liens; this in effect assumes that the actual cost of insurance for the reduced amount is, and will continue to be at all times, fully equal to the tab- ular cost of insurance for the full amount as was antici- pated when fixing the amount of lien. Some companies, however, have caused these policies to be valued as in- creasing insurances and have used a sub-standard mor- tality table. Policies that are issued at "rated-up" ages, are also valued on the same basis as policies actually issued at those ages, and by the usual standard tables of mortality. Net premiums due and in course of collection and net deferred premiums, are allowed as resources to offset the full reserve, which is always computed on an annual pre- mium basis except as regards weekly premium policies or sometimes monthly premium policies. At the present time, all departments but one, value policies which are issued with a preliminary one-year term provision, on the basis that the net premium for the first year is the one-year term net premium, and the net premium thereafter is the net level premium called for by the conditions of the contract, applying thereafter. The one department which remains an exception values in that manner certain policies issued by companies that come under a special statute, even though the policies contain no such preliminary term provision, but holds that all policies of companies not coming within the pro- visions of the special statute must be valued on the basis that the net premiums are level each year, no matter what the terms of the policy, if only the gross premiums are level or practically so. In this construction of the term "net valuation" or "net premium valuation," the depart- 141 ment in question is upheld by the opinions of some actu- aries that a gross level premium necessarily implies a net level premium. Other actuaries, however, hold the con- trary opinion. The issue seems also to involve legal questions, as to the construction of statutes or of policy contracts, or both ; which legal questions were determined by the Supreme Court of Vermont in Comrs. vs. Bankers Life Insurance Co., in favor of preliminary-term valua- tion. By all departments, with the same exception, industrial or weekly premium policies are valued as if they were issued on December 31 of the year in which they are written, and at an age one year higher. The effect of this is to charge a terminal reserve, one year deferred and at an age one year higher, against each policy, and also to get rid of counting deferred premiums as resources. The practice is defended on the grounds, first, that industrial policies do not at once come into full benefit, and, second, that initial expenses absorb the earlier weeks' collections. The one dissenting department values these policies like any other, but modifies the total by certain very conserva- tive assumptions concerning discontinuances during the first and second years. The question whether, in the interest of a further sim- plification of the balance-sheets, all loans to policyholders should not be deducted from the reserves — and all net un- collected and deferred premiums, also, for that matter — may be well worth discussing, since the resources in the statements of some companies that have written much of their insurance upon "dated back with lien" plans, are in- flated by the liens, and their liabilities are inflated by the corresponding reserves. It seems reasonable that the net reserves should be entered as a liability, with these liens and loans and the net uncollected and deferred premiums and the "present value, premiums receivable," all deducted 143 therefrom — in short, with everything deducted that really is an offset. Elizur Wright refused, however, to eliminate the item of liens created by the "loan-note" plan — these did not represent money actually once paid and then borrowed back — in his report for 1863, as follows: "It has been objected to our synopsis by some of the companies re- ceiving only cash premiums that it is unfair to them in treating premium notes among the assets, the same as cash. They do not pretend that such notes, when the amount given by each policyholder is kept within the net value of his policy, are not as good as cash against any claim which can arise under the policy. Nor do they allege that a company which rigidly limits its premium notes by this rule, and receives as much interest on them as on any of its cash investments, can be less prepared to meet any and all demands upon it than if it received only cash." This is really the whole argument on that side of the case; but it does not appear that diminishing the net re- serve liability by these liens and thus causing them to be omitted from the resources traverses these truths in any way. Most companies, in placing liens for the reserves on dated-back policies, take obligations either for the last terminal reserve, the present mean reserve or the next terminal reserve. Either of the last two methods sets all, or nearly all, the cash premiums, received at the time, free to be used to cover the current year's mortuary and ex- pense costs. As a mere proposition of law, a company may be held to have the right to charge any lien it pleases ; but it seems reasonable that, when a lien is exacted in ex- cess of the correct amount of the reserve, the excess should be treated as a lien for impairment, and that the company should not be permitted to realize upon it by 143 putting up no other reserve out of the premiums on the poHcy until the reserve charged against it catches up with the amount of the lien. All the State departments, with the same exception as in other regards, accept the valuation of a company's policies, by the department of its home State. Elizur Wright, in his report for 1862, as Commissioner of In- surance of Massachusetts, thus states the arguments in favor of an exchange of valuations or, more accurately, in favor of "a single annual valuation of each company" which "may be made to suffice for all the States," as fol- lows: "In regard to the life insurance companies of New York, we are happy to be able to say that Mr. Barnes, the faithful and efficient superintendent of the Insurance De- partment of that State, has taken measures to add to his elaborate annual investigation of their assets and securi- ties a valuation of their policies on a plan similar to our own. Should this design be carried out, it will be very desirable that some arrangement may be made between the States by which the companies may be saved the labor and expense of furnishing the data of their policies to more than one State, and a single valuation of each com- pany may be made to suffice for all the States, as this is obviously a work which, if well done in any one State, need not be repeated the same year in other States." Unfortunately, New York adopted first Farr's English Life Table No. 3 and 5 per cent., and afterward the American Experience Table and 4^ per cent, as its stand- ard, whereas Massachusetts had already chosen the Actuaries' Table and 4 per cent. Therefore the differ- ence in standard kept up the practice of a duplication of valuations. In the general methods of valuation, used by all de- 144 partments, but one change of great importance has been made since net valuation was introduced by Elizur Wright. Until in the seventies, companies were permit- ted to report loans against renewal commissions as re- sources, when within their commuted value, and in some cases so to report also the commuted values of renewal commissions payable in future which had been purchased for cash in cases when the renewal commissions were within the loading. This was tantamount to permitting a company to count as a part of its resources, the present value of part of the loading and was thus a departure from net premium valuation. Had this been permitted as to non-participating policies, with gross premium not ex- ceeding the net premiums, the present value of a part of the net premiums would have been credited twice; for part would thus be given as a resource and all would be deducted in arriving at the net reserve. This continued to be allowed by departments until the privilege was scandalously abused. Then a sudden ruling the other way completed the ruin of a number of com- panies and made it impossible for weak companies to sur- vive, because they could not pay, out of the loading on first year's premiums, a sufficient commission to procure the volume of insurance requisite to maintain themselves. Being no longer permitted to borrow against future pre- miums to eke out this insufficient loading, they were un- able to continue in the race. The only changes relative to standards for depart- ment valuations have been as follows: Several States followed the lead of Massachusetts and adopted the Actuaries' Table and 4 per cent, interest as the standard of valuation. Others followed New York and made the American Experience Table and 4^ per cent, the stand- ard. From about 1891 to 1901 the Actuaries' Table and 14s 4 per cent, was also the standard employed by the New York department. As to policies issued since December 31, 1900, the standard in both Massachusetts and New York is the American Experience Table and 3^ per cent. This has now been followed in several States. 146 THE POLICY CONTRACT. The Application : The application — or, as it is called in Great Britain, the proposal — contains the representations, warranties, promises, consents and agreements of the applicant for the policy. The statements to the company's medical examiner, signed by the applicant, are also made a part of his application by reference. These statements and promises are usually made a consideration for and a part of the policy. Sometimes copies are also attached to the policies, and in some States copies must be fur- nished the insured in order that the statements may have the efifect of warranties instead of the effect of repre- sentations merely. The distinction between warranties and representations may be illustrated as follows: If a company desires to contest a claim on the ground of misrepresentation, it must prove that the misrepresentation was fraudulent. To ptove this, it must establish these things : The repre- sentation was untrue. The maker knew it to be untrue when made, or should have known it. It was material. It was fraudulently made, i. e., with intent to deceive, and did, in fact, deceive and was relied upon. These are all matters of fact to be determined by the jury. If the other three are established, fraud is inferred. If the statements have been warranted, however, the case stands thus : No proof is required as to knowledge of the facts, as to intent to deceive or actual deception, or as to ma- teriality. It is now only requisite to prove that the state- 147 ment was made and was untrue, in order to defeat the claim and render the poHcy utterly void. As to promises, the only distinction is that when per- formance is warranted and this promise is accepted as part of the consideration, it must be carried out to the letter ; while if a mere promise not so warranted and not a part of the consideration, it might be necessary for a company to prove its materiality. Thus, if the insured warrants that he will not engage in naval or military service, to do so will avoid the insurance, although his death be in no way occasioned by such service; but it might perhaps be otherwise if it were a mere promise. It is rare nowadays that promises are warranted, and in virtually all such cases the purpose is to conceal re- strictions and conditions. Breaches of warranty were at one time much relied upon as defenses against death claims, and it was not so uncommon as it should have been, for payment to be refused on that ground though the breach were unim- portant. The idea was that the company ought not to pay unless the contract firmly held it to do so. Even at this time, the statements of the applicant usually have the effect of warranties when made. Thus, reference to them, making them a part of the policy or a part of the consideration for the policy, gives them this effect. In most cases, however, this is waived after one, two or three years by an "incontestable" provision ; and in some States the statutes require a copy of all statements that are made warranties to be attached to the policy, and failure to do so destroys their warranty character. Wherever statements have the effect of warranties, if a dispute about a death claim reach the courts, the com- pany's attorneys are pretty nearly certain to defend on the ground of breach of warranty, even when fraud could be proved; because it is easier to show that some state- 148 ment is not strictly true or that some engagement has not been strictly performed than to convince a jury that fraud has been practiced. The Promise to Pay : A life insurance policy is usually what is known as a unilateral contract ; that is, a contract calling for performance on one side only, viz., by the company. It may be objected that to keep it in force requires the payment of premiums on the part of the in- sured. But the insured does not engage to pay the pre- miums ; he may do so or not, as he pleases, and he is not bound to do so. If he does pay them, the company has engaged that it will insure him. Payment, therefore, is a condition subsequent ; and a life insurance policy is a uni- lateral contract, of the form of a promise to pay, condi- tioned upon a certain consideration being paid. Whether the words "promise to pay" or the word "insure" is em- ployed, the meaning is the same. Place of Payment: It is frequently provided in the policy that both premiums and proceeds of the insurance are payable at the home office of the company. But there is also generally a provision that premiums are payable elsewhere to an authorized agent in exchange for a re- ceipt signed by certain officers of the company, and coun- tersigned by the agent. Proceeds of the insurance are usually actually paid by draft on the company, or on some depository of the company, which is delivered to the claimant at any convenient place. Annual or More Frequent Premiums : The privilege is usually given to pay premiums annually, semi-annually or quarterly, and to change from one to the other form of payment upon request. In the United States, however, semi-annual or quarterly premiums are merely instal- ments of the annual premium. Prepayment of Premiums: Most policies contain no provision for prepayment of premiums, but companies 149 will permit such prepayment in one of two ways, viz. : by depositing the discounted sum required to prepay the same, the unused amount of the deposit with interest thereon being payable with the sum insured, if the life fails before the premiums, thus prepaid, are due; or by actually prepaying the premiums at their present values, treated as pure endowments, in which case .nothing addi- tional is allowed, in event of death on account of the pre- payment. Time of Payment of Premiums : Premiums are usually payable on definite days, but are practically always re- ceivable before the due dates. Unless the policy provides otherwise, or a contrary custom amounting to a waiver can be clearly proved, a company will not be required to accept premiums when they are overdue. Grace in Payment of Premiums : A grace of thirty days in some cases and of one month in others is often granted by the provisions of policies for the payment of all pre- miums after the first or after the first year's premiums as the case may be. The insurance remains in force during the grace, subject usually to deduction of the forborne premium. Interest is charged on the overdue premium in most cases. Time of Payment of Sum Insured: The value of a policy at the completion of an endowment or deferred dividend period is usually payable at once. Death claims are nearly always payable at once upon approval of proof of loss. To Whom Payable : In event of the survival of an en- dowment or deferred dividend period the cash proceeds of a policy are usually payable to the insured; in event of death, either to a designated beneficiary or benefi- ciaries, or to the executors, administrators or assigns of the insured. If taken out by a designated beneficiary upon the life of another, there must be an insurable inter- 150 est to support the insurance. Any insurable interest, though for a less amount than the sum insured, is in some States held to be sufficient to sustain it, payable to the beneficiary; in other States the excess is required to be paid to the personal representatives of the insured. If taken out by the insured, it is usually held that, since he had an insurable interest in his own life, he may name the beneficiary. Nowadays most policies grant the in- sured the privilege of changing the beneficiary, which, being equivalent to a "general power of appointment," leaves the policy his property until his death. The courts have held that a policy which gives to the insured the power to realize upon it, or to dispose of it at a certain time, has a value as a part of his personal estate and is liable for his personal debts even though payable to a given beneficiary in event of death. The proceeds, in event of death, however, are not so liable, except that in several States the amount of insurance which may be carried in favor of a wife, the same being paid for by the husband, is limited directly or indirectly by limiting the amount of premiums thus payable. Conditions of Payment : The payment at the comple- tion of an endowment or deferred dividend period is usually conditioned only upon the premiums having been paid as stipulated. The payment of death claims, how- ever, is usually subject to certain conditions, as, for in- stance : That the statements in the application and to the medical examiner are true and the promises there made, if any, fulfilled; that the insured has not engaged in cer- tain prohibited occupations or done certain specified acts ; that he has not traveled or resided beyond certain limits ; and that death has not been by suicide or the result of duelling, or of other violations of the law. These condi- tions are usually removed after one, two or three years by an "incontestable" provision. Some companies impose iSi no condition from the outset. Such companies, of course, aim to make a very thorough investigation before issuing the poUcy. Correction for Mistake in Age : An understatement of the age obviously calls for an adjustment of the amount payable under the policy to the amount of insurance which the premium actually. paid would have purchased at the rate of premium at the true age. Most policies have a provision for this mode of adjustment and some policies provide for adjustment for misstatement of age, i. e., for increasing the amount payable if the age is over- stated, as well as diminishing it if the age is under-stated. Incontestable Provisions : On June 27, 1879, the Equit- able Life Assurance Society of New York made all its policies, old and new, incontestable for any cause, except non-payment of premiums, after they were kept in force three years. The term has since been reduced, first, to two years, and, afterward, to one year. President Hyde said concerning it: "The Equitable is in business to pay losses. It was not organized to engage in litigation with widows and fatherless children, or to make money by receiving interest on what may be due them, or by dis- counting policies that should be paid immediately and in full." The policies of nearly all companies are now incon- testable after a limited period. Such policies had, before their introduction here, been occasionally issued in Great Britain, an extra premium being charged. The experiment has also been made of issuing all poli- cies "incontestable" from date of issue ; but this has been abandoned after a thorough test. Whether policies containing such a provision are really incontestable in case of fraud is not settled. Public policy is involved and the courts disagree, some holding that a company may thus waive its right to defend, even in IS2 event of fraud, and others that it is inconsistent with pub- lic policy to permit fraud to be successfully practiced. Seldom, however, has any company actually contested the payment of a claim when this provision was in force. Assignments: Policies are usually assignable unless payable to minor children or, generally, to children, which may create an interest in favor of children yet unborn. Unless payable to the insured's estate, or the right to change the beneficiary has been reserved, the beneficiaries must join in the assignment to make it valid and binding upon them. The policy usually provides that assignments must be in duplicate, that both copies must be sent to the company, one to be returned with the company's endorse- ment and one to be retained by the company; and also, that the company will not be liable for the validity of any assignment. In practice, the company, before paying over the proceeds of an assigned policy, requires the sig- natures of all persons who appear to have or may have any interest. When these are not forthcoming, it awaits an action, pays the money into the court and leaves the parties to fight it out. Instalment Benefits and Commutation: Some policies promise to pay in instalments, either during a fixed term or for a fixed term and as much longer as the beneficiary may survive. In event of the death of the beneficiary during the lifetime of the insured an arrangement may usually be made for commuting these instalments into an equivalent lump sum payable at maturity ; or, in event of the death of the beneficiary after the insured but during the fixed term, then a commutation of the instalments re- maining unpaid into a lump sum, payable at once. The privilege is also granted in many policies which are writ- ten for a lump sum, of converting the same into payable in instalments equivalent in value to the sum insured. This privilege may usually in such case be availed of by the IS3 insured during his lifetime, or by the beneficiary upon making claim. In most policies, likewise, a similar privi- lege is given of converting the lump sum into payable by contimtous instalments for a fixed period, and as much longer as the beneficiary may survive. Dividends of Surplus : The usual language of a partici- pating policy on the subject of surplus merely stipulates that the holder shall participate in the surplus by receiv- ing the dividends apportioned to him by the company. Some companies require each applicant to bind himself and all who may have any interest in the policy to abide by the company's apportionment. This is sometimes in the policy, sometimes in the application. Application of Surplus : Where dividends are payable annually they are usually available in cash. Until 1907, when the Armstrong laws went into effect in New York, they were usually payable only in case the next year's premium was paid; or, in other words, if taken in cash, they were only available as reductions of the next year's premium, and if applied, only in case the next year's pre- mium was paid. Now in all companies doing business in New York, dividends are payable without regard to whether the next year's premiums are paid or not. The privilege is usually given to convert cash dividends into paid-up reversions or additions to the sum insured. To make this available, a certificate of good health is sometimes required when the insured elects first to make this application, which, however, continues to be made thereafter without requiring further certificates. The practice of requiring such proof of good health has now been generally abandoned. When dividends are deferred for periods of five, ten, fifteen or twenty years, the option is usually given to withdraw the surplus in cash or to apply it to increase the form of surrender value selected, or, if the insurance is i.';4 continued in force, then to purchase paid-up additions to the sum insured or an annuity to be applied in reduction of subsequent premiums. But if the sum insured is in- creased, it is customary to require proof of good health. Dividends declared after the deferred dividend period has elapsed are usually apportioned annually in cash ; but sometimes the policy calls for apportionment every five years or at the expiration of longer periods. Under deferred dividend policies, no part of the sur- plus already accumulated is paid in event of withdrawal or of death during the dividend period. A few com- panies, however, have issued accumulative surplus poli- cies, under which the surplus may either be withdrawn or be permitted to accumulate and under which, there- fore, in event of death or withdrawal, the surplus already accumulated is paid over. Conversion to Other Forms : It is a common provision in renewable-term policies that the insured may, without proof of good health, change to other forms of insurance, usually at the rate of the attained age, less the application of the value of the term policy, if any, but sometimes at the premium at the original age by paying the difference with interest. Such policies are called "convertible." Upon proof of good health, a change may be made on the former basis from one plan to another in almost any com- pany, even though at a lower premium; a change on either basis to a higher premium policy will also usually be permitted without proof of good health. A few com- panies insert in their life policies the option to pay up at any time by a single premium or to begin paying up by limited premiums, giving the rates, and in their limited payment policies, the option to change to a life policy at the premium at age at entry, applying the excess of re- serve to reduce the subsequent life premiums. Preliminary Term Conditions : Various modes of mak- iSS ing the first year's premium a preliminary one-year term premium have been employed. Massachusetts companies, operating under the Dewey law, in their policies issued before January i, 1903, made no mention that the pre- mium was term, but relied solely on the provisions of the law," which provided that these policies be so valued. Though "preliminary term" is now provided for in the laws of several States, usually the requirement is that the policy so specify. Several other companies write their policies precisely as if they were not term the first year, and insert, after the acknowledgment of the receipt of the first year's premium, language of the following purport : "Being the premium for preliminary term insur- ance only." Others have made the contract a complete one-year term policy, followed by a separate policy, taking effect upon payment of the second year's premium, both policies, however, being on the one sheet of paper. Others have written the policy as if not term the first year, inserting a stipulation that it should be valued as term insurance for the first year and thereafter on the basis of a level premium insurance beginning one year later and at an age one year higher. Other companies have made the first year's premium pay for insurance against death "within one year from the date hereof," with the privilege of renewing at the end of the year as an insurance of another sort "from that date," thus clearly separating the two contracts. Some of the com- panies last mentioned have made only such part of the first year's premium, as equals the whole life premium at the next age, a preliminary term premium. These, where there is an excess premium the first year, account for it by making it a consideration for the privilege of renewal and put up a pure endowment reserve because of it, i. e., value on the straight modified preliminary term plan. Income or Guaranteed Interest Provisions : In all cases 156 where, instead of a lump sum at death or at the comple- tion of the endowment period, an income is to be given for a term of years or for Hfe, and then the principal sum is to be paid, if the income is more than 3 per cent., 3^ per cent, or 4 per cent, (whichever rate is employed by the company in computing its premiums) on the principal sum, a premium is really charged for an insurance for the principal sum plus an amount equivalent in value to the income guaranteed in excess of the rate counted upon. Surrender Provisions: In most policies nowadays sur- render privileges are available after three years, in some after two years and in a few after one year. The insured is usually allowed the option of a cash value, a paid-up insurance value or an insurance for the full amount for a limited term. Sometimes a value in a paid-up life an- nuity is also offered. The extended insurance is always non-participating; the paid-up insurance granted is also nearly always non-participating. According to the terms of some policies, and under the laws of some States, sur- render must be within a limited time after failure to pay a premium; but under the laws of most States and the provisions of most policies nowadays either the extended insurance or the paid-up insurance — usually the former — takes effect automatically upon failure to pay a premium, and if either of the other values is preferred, it must be applied for within a short period of time. Non- forfeiture : When the privilege of surrender for paid-up insurance was first put into policies and for a long time afterward, it was called a "non- forfeiture" pro- vision, though it might not be available unless the policy was surrendered within six months after failure to pay a premium. In like manner, inaccurately, though with more reason, a provision that on failure to pay a premium the extended insurance surrender value shall at once at- tach, is called "automatic non-forfeiture." But under IS7 such a provision the benefits of the original policy lapse and it is converted into paid-up, non-participating term insurance. The original rights can usually be restored only upon proof of good health and the payment of over- due premiums with interest. An interesting form of real "non-forfeiture" has come into use with the last two decades, having been introduced by the author of this book in 1894. It was copied from the practice of the Australian Mutual Provident Society and consists in charging the premium up as a loan at once upon a default in payment, provided the value of the policy, in excess of existing indebtedness and interest, will cover the loan and in continuing this process until these advances exhaust the value. The policy remains of the same nature as if the premiums were all paid in cash. One or two companies which employ this plan have required proof of good health as a condition to re- sumption of payment ; but this is not consistent with the fact that the premium has been advanced against the in- sured's own funds. There have also been other abuses of the plan, abuses now happily discontinued. The usual practice is to permit resumption of payment at any time before the value is exhausted, the overdue premiums and interest thereon being either paid in cash or permitted to stand as a loan. Loans : Loans to the full amount of the cash values at the end of the year, interest being paid in advance, are generally allowed under all policies issued nowadays. Some companies, however, limit the loans to a part only of the cash value. A special form of loan provision prom- ises to lend a given amount, according to the policy year, provided the premiums are paid up to the end of the next policy year. The loan values in such a case are usu- ally equal to the full reserve — or, if there are cash values, to the' full cash values — at the end of the next year ; but is8 J^H 21 1021 u^t be paid, fir^t, dis^ unt to the end of out of the lo^ the next poliS^^^^^^-emtiweKSca^jjne premium or pre- miums to the eiw'''wU™i^^^*J!i-J1iese deductions should be made in calculating what will be the net avails of any such loan. ISP DEFINITIONS OF LIFE INSURANCE TERMS. Abnormal Death-Rate. — As used in assessment life insurance, an unusually high death-rate, though due to normal causes, such as insufficient numbers to assure reliable yearly average or an undue proportion of old men. More correctly, an un- usually high death-rate, due to abnormal causes, such as poor initial selection by medical examination or adverse selection by withdrawal of good lives. — See p. 42. AccELERATivE. — An expression for a method of applying dividends to hasten a policy's becoming paid-up or its maturity as an endowment. — See pp. 116, 117. AccELERATiVE ENDOWMENT. — An endowment insurance, with a provision for accelerative application of dividends. — See p. 117. Accumulation Plan. — A deferred dividend plan, differing from all forms of "tontine,"' in that no promise is made of accre- tions from surplus forfeited by other policies. In actual prac- tice, such returns were made, however, under the policies, to which this name was originally given. Acid Test. — A mode of testing the urine, in a medical examina- tion, to determine whether sugar is present, i. e., whether there may be diabetes. Active. — Those lives, out of certain number setting out, all "ac- tive," who have not died, withdrawn, retired or become dis- abled. Actual Insurance. — The excess of the sum insured over the ter- minal reserve, which latter is thus considered as a "self- insurance fund," having been accumulated from premiums previously paid. The idea is that the "actual insurance" would be the company's net loss, were the policyholder to die within the year. — See pp. 44, 89. Actual Mortality. — The deaths actually taking place during the period, usually as distinguished from the "expected mortality" according to a given table. Also, less accurately, employed to signify the actual amount of death-claims as distinguished from the expected amount. 161 Actuary. — i. A technical expert in the mathematics, theory, law and practice of life and other personal, i. e., annuity, health and accident, insurance. 2. The mathematical officer of a life insurance company and, elsewhere than in the United States, usually also its manager. Actuaries' Table of Mortality. — A table of mortality, deduced from the combined experience of 17 British offices — therefore, in most countries known as the 17 Offices Table — both male and female lives. Introduced in this country in 1859 by Elizur Wright, Commissioner of Massachusetts, as the standard for valuing life policies. Widely used for that purpose in this country. Also known as the Combined Experience Table. It is an aggregate table. — See pp. 28, 31, 32, 144, 145. Additions. — A brief expression for "paid-up additions" to the sum insured, purchased by the application of dividends. Also called "reversionary additions." — See pp. 115, 116. Admission Fee. — A fee charged a member of an assessment or fraternal society, upon admission. An initiation or entrance fee. Advances. — Policy loans, t. e., loans upon life policies, are usually merely "advances," both because thus a portion of the amount payable at maturity is advanced, and also because repayment is not required except out of the proceeds of the policy, there being no personal obligation. — See pp. 127, et seq. Advances to Agents. — Sums advanced to agents against commis- sions, usually against renewal commissions. At one time these were admitted as assets of companies. This is no longer permitted, unless the repayment of the same is se- cured. Such advances are included in the four items of cost of new business which are limited by Section 97 of the in- surance laws of New York. — See p. 145. Adverse Selection. — The withdrawal of a larger proportion of healthy lives than obtains in the aggregate lives insured, re- sulting in lower average health among those who remain. — See pp. 43, 44, 122, 123, 124. Advisory Board. — A board, consisting usually of persons who are induced to insure on the basis that a percentage of the pre- miums received in a given territory is to be divided among those of them who survive and maintain their own insurance in force. The duties are nearly always nominal and the repre- sentations of probable returns fraudulently extravagant. Proscribed by the laws of many States. 162 Age. — The age in ordinary life insurance is usually computed as at the nearest birthday. In industrial insurance, as at the next birthday, which is also the custom as to all life insur- ances in Great Britain and some other countries. Age upon Admission, i The age when the policy is issued or the Age at Entry. j insured admitted to membership. Agent. — In life insurance, a solicitor for applications or a col- lector of premiums. Aggregate Table. — A mortality (or a sickness) table, deduced from the experience among lives at each given age, without regard to the duration of their policies. Albuminuria. — The presence of albumen in the urine. If per- sistent, may indicate Bright's disease. Allocation. — See "Apportionment." Allowances. — Sums allowed an agent for various expenses, as postage, rent, office expenses, etc. American Experience Table. — A mortality table, ultimate in form, deduced by Sheppard Homans from the early experi- ence of the Mutual Life Insurance Company of New York, omitting all exposures during the first five calendar years after admission. Somewhat arbitrarily graduated. Adopted as the standard of valuation in many States. — See pp. 28, 31, 32, 144, 14s, 146. Amount at Risk. — The total insurance in force. Sometimes em- ployed as a synonym for the "actual insurance." Annual Dividend. — Entitled to participate in the earnings and to receive a dividend annually, either in case the next annual premium is paid — as was previously the rule — or without that condition, as required under the laws of New York since 1906. The term is applied alike to policies yielding a dividend at the end of the first year and to those yielding no dividend until the end of two or even three years, if payable annually thereafter. — See pp. 112, 113, 114, 154. Annual Income Policy. — A policy, the proceeds of which are payable in annual instalments. Annual Premium. — A premium payable once each year in ad- vance. — See p. 149. Annuitant. — The person in receipt of an annuity. In the case of a contingent (i. e., survivorship) annuity, the person to whom the annuity will be payable, in case he survive the in- sured, i. e., the nominator. 163 Annuity. — A sum of money payable one or more times each year, whether during a fixed term in which case it is an annuity certain ; during life, in which case it is a life annuity ; during joint lives, in which case it is a joint life annuity; during the life of the last survivor, in which case it is a last survivor annuity; or after the failure of another life, in which case it is a contingent or survivorship annuity. It may also be "immediate," i. e., with the first payment at the end of the first interval ; "due," i. e., with the first payment in advance ; or "deferred," i. e., with the first payment at the close of a given period. And it may be "temporary," i. e., subject to termination at the end of a fixed period or at prior death. — See pp. 46, 47, 65, 75- Applicant. — The person applying for insurance. Originally the application was made in the name of the beneficiary, but now always — or nearly so — by the person whose life is to be in- sured. Application. — The printed and written document, applying for the insurance and containing various statements, representa- tions and warranties made to secure the insurance. The pro- posal. — See p. 147. Apportionment. — The allotting, whether tentatively or definitely, of shares of the surplus to the various policies which are to participate. An allocation. See pp. 106, et seq. Armstrong Laws. — The life insurance laws of New York en- acted in 1906 after the investigation by the New York Legis- lative Investigating Committee and on its recommendation. Named for the chairman of the committee. The term usually refers to the limitations and restrictions contained in these laws.— See pp. 82, 113, 154. Assessments. — Originally, a premium demanded after the claim, toward the payment of which it was to be applied, had arisen. Nowadays, a premium, the amount of which is not fixed definitely in advance, or any extra premium, over and above the regular premium, the amount of which was not agreed upon. Assessment Plan. — Any plan of insurance in which either the amount payable upon the maturity of the policy or the pre- mium payable is not definitely determined and fixed, in ad- vance. ■ %\ Assets. — Present resources, excluding premiums that are receiv- able in future, except that in the United States "deferred 164 premiums" are allowed, the policies being valued as if the full annual premiums had been paid. — See p. 138, et seq. Assignee. — The person to whom a policy is assigned. Assignment. — The instrument assigning the policy. In the United States this must be duly executed and the company notified or a copy filed with it, as its policy provisions specify. Some companies require that their consent be obtained in writing. In Great Britain there may be "equitable assign- ment" by merely depositing the policy with another. — See p. 153. Assumption of Risks. — A form of reinsurance by which the company directly assumes the payment of the policies rein- sured. Upon the acceptance of this either expressly or by paying premiums to the company a policyholder makes a novation with it and releases the reinsured company. Assurance. Insurance. — In Great Britain "assurance" is al- ways used in life insurance literature and "insurance" applied only to other forms. Assured. — Not used commonly in the United States, where the person whose life is insured is called the insured. In Great Britain the beneficiary is called the "assured." Attained Age. — The present age or the age at the time the life is observed, as distinguished from the age at entry. Automatic Extended Insurance. — The insurance automatically continued in force for a definite period of time as a non- participating term policy. — See pp. 119, 120, 126. Automatic Extension. — The term for which such an insurance is continued in force. Automatic Non-Forfeiture. — ^A general expression for the idea that some value, i. e., paid-up insurance, extended insurance or advance of the premium automatically attaches upon fail- ure to pay a premium. Most accurately applicable to auto- matic premium loans. — See pp. 157, 158. Automatic Premium Loan. — A loan of the amount required to pay a premium which has not been paid when due, made auto- matically upon the non-payment of the premium and applied to pay the same. The effect is that, so long as such loans can be made, the policy remains in full force, without change of form or forfeiture of any rights. Originated with the Aus- tralian Mutual Provident Society. — See pp. 132, 158. Automatic Paid-Up Insurance. — A paid-up insurance for a part of the sum insured by the policy, automatically taking effect upon the failure to pay a premium when due. — See pp. 121, 126. i6s Beneficiary. — The person to whom the sum insured is to be paid, in event of the death of the insured. — See pp. 150, 151. Benefit. — The sum payable upon the occurrence of the event insured against. Binding Receipt. — A receipt, given in exchange for a premium paid in advance, usually when the application is taken, pro- viding that in case the applicant is accepted for the plan and amount applied for, the insurance shall date from the day the receipt is given. Bond. — The security given by an agent, signed by individual sureties or a surety company, that he will faithfully account for and pay over all collections. Also a name, sometimes given to some forms of life insurance policies. Bonus. — The word used in Great Britain instead of "dividend" ; it usually means a "dividend addition" to the sum insured. Also an extra commission to an agent, payable upon a contin- gency, as for securing a certain amount of business. — See pp. 107, 108, 119. Branch Office. — In the United States, usually an agency under a salaried superintendent, and especially in a city where sev- eral offices are maintained. In other countries, a branch office is the principal office in a State or nation, not the domi- cile of the company, which office has power to issue policies. Breach of Warranty. — Failure to perform any act or otherwise to keep any promise which the insured has warranted that he would do; also falsity of statements warranted to be true. — See pp. 147, 148. Brokerage. — In the United States, usually a commission upon the first premium only, no renewal commissions to be paid. Original meaning, a commission paid to a broker, as distin- guished from an agent. The other meaning arose from the fact that brokers usually demanded such a commission. Call. — Synonymous with assessment. Cancellation. — The avoidance of a policy by the company by returning or tendering the premium or a portion thereof and taking up the policy or declaring that it will not be liable thereunder. Usually no right to do this is reserved in life insurance policies; but, if there is fraud in the inception, it may be done, at least before the policy becomes incontestable by its terms. Carlisle Table. — A mortality table, long standard in Great Britain and still frequently used in the courts of this coun- try to value life interests, reversions, remainders and other 166 estates dependent upon the continuance or cessation of human life. — See pp. 27, 28. Cash Value. — The surrender value of a life insurance policy when payable in cash. — See pp. 121, et seq. Certificate. — A printed and written document, evidencing mem- bership in an assessment or fraternal beneficiary society. It is usually equivalent to a policy of insurance. Change of Beneficiaries. — The right to change the beneficiary is now usually reserved to the insured; if not limited by excluding the insured and his estate, the effect is that the policy is the property of the insured. — See p. 151. Combined Experience Table. — Another name for the Actuaries' or 17 Offices' Table. Commission. — The remuneration of a life insurance agent, when contingent upon the volume of premiums or, more rarely in the United States, of insurances. Usually payable out of the premiums as collected. Consideration. — The inducement to issue the policy and to con- tinue to be bound by it. Therefore, of course, the payment of premiums, when due. If so provided, also the statements and promises in the application and to the medical examiner, which in such case are warranties. — See p. 149. CoNSOL. — A bond, issued by the Government of Great Britain, promising a perpetual income. Also, in the United States, a life insurance policy, promising to pay after the death of the insured, an income for the life of the beneficiary and a fixed sum upon her death. — See pp. 70 and 71. Contingent Annuity. — See Annuity. Continuous Instalment. — The proceeds of a life insurance pol- icy, payable in instalments for a certain term of years and during the after-life of the beneficiary. — See pp. 67, 68, 69. Contribution Plan. — A method of distributing earnings among participating policyholders, invented and first introduced by Sheppard Romans and David Parks Fackler. It apportions the surplus as follows : Excess interest, upon the reserve ; mortality savings, upon the cost of insurance ; and savings in loading, upon the loading. — See pp. 106, 107, 108, log. Contract. — A legal reserve life insurance policy is a unilateral contract, i. e., the policyholder is not bound; the contract, therefore, is defeated by failure to pay premiums, but no right of action accrues. Since it is drawn up by the company, it is construed most strictly against it and favorably for the policyholder. — See pp. 147, et seq. 167 Cost of Insurance. — The net one-year term premium for the amount of "actual insurance," I i., the sum insured less the terminal reserve. — See pp. 44 and 89, et seq. Creditors. Exempt From. — See "Exempt." Dated Back. — Issued as if upon a day already past and at the age of the insured upon that day. Sometimes done merely to "save the age," i. e., avoid an increase of the age by one year; sometimes done by charging the reserve as a loan, cleverly manipulating surrender values and estimated returns, so as to make it appear to be a great bargain, whereas it is none. — See pp. 142, 143. Death Claim. — A claim under a life insurance policy by reason of the death of the insured. Death Loss. — A loss incurred by reason of the death of the in- sured. Death Rate. — The rate at which deaths take place. When a death rate of so much "per 1,000," wholly misleading as a basis for comparison, because distribution at the various ages different in each such group. Declined. — Rejected, or declined, for insurance. Decreasing Insurance Policy. — A policy which decreases in amount. Three such plans have been employed in this coun- try: (i) a "natural premium" policy with an unchanging pre- mium, applied to purchase its quantum of one-year term in- surance ; (2) an insurance at current cost for the amounts of the "actual insurance'' under a whole life policy; and (3) a policy at a level premium in force for a fixed amount to age 60, diminishing each year for 10 years and then level at the reduced amount throughout life. Decreasing Premium Policy. — Also called Diminishing and Re- ducing Premium. A self-explanatory term. Four forms have been known here: (i) The premium reducing each year by 3 per cent, upon all premiums paid; (2) reducing by a fixed amount each year; (3) reduced after the second year by a fixed amount; (4) reducing by a varying amount each year. Under the first two, when the reducing factor exceeds the premium, the excess is paid as an annuity. The third is usually a device to get the whole excess as an additional "loading" the first year; and the last is often used by full preliminary term companies as a cloak for taking a very large premium for term insurance for one year only. See "Pre- 168 mium Reduction,'' "Reducing Premium" and "Guaranteed Dividend." Default. — Failure to pay premium or interest on a policy loan, when due. It may result in forfeiture and will, unless policy provides for "grace" or some form of automatic extension or non-forfeiture. — See pp. 149, et seq. Deferred Annuity. — An annuity, entering upon the receipt of which is deferred longer than until the end of the first inter- val, i. e., beyond one year if annual, etc. Deferred Dividend Plan. — A plan under which the declaration of a dividend is postponed for a term of years — usually ten, fifteen or twenty. — See pp. 112, 113. Deferred Insurance. — An insurance which does not go immedi- ately into force. Deferred Premiums. — The monthly, quarterly or semi-annual instalments of the annual premium, remaining to be paid. — See pp. 141, 142. Degree of Impairment. — The rating of an impaired life, especially when rated by a percentage of the expected "normal" mor- tality, as 120 per cent., 200 per cent., etc. — See pp. 133, et seq. Delivery. — The physical transmission of a policy to its purchaser. Deposit in the mails is delivery and cannot be recalled. Merely to leave a policy for examination is not delivery. Unless a premium has been accepted or there is a special agreement, a policy is not in force until delivered. Deposit for Reserve. — What remains of the net premium after the "cost of insurance" is deducted, which sum with its in- terest goes to increase the terminal reerve. — See pp. 89, et seq. Diseased Lives. — Lives, the health of which is much impaired. DrsTRiBUTiON. — The actual disbursement or crediting of dividends of surplus; division of surplus. Differs from apportionment or allocation, in that, unless provisional, it is final and vests the title to the surplus. Distribution Period. — A term at the end of which the surplus earned during such period is distributed. — See pp. 106, et seq. Dividend — The share of the surplus allotted to a particular pol- icy in a distribution. A cash bonus. Dividend Additions. — Paid-up additions to the sum insured, by way of dividend. A reversionary bonus. — See p. 115. 169 Dividend Endowment. — A life or limited payment life policy which becomes an endowment by reason of the application of dividends to increase its reserve and so to cause it to ma- ture and become payable during the lifetime of the insured. — See pp. n6, 117. Double Endowment. — A policy promising the payment of a cer- tain sum in event of death within a given period and of twice that sum upon survival of the period. The "actual insurance" is nil during the later years of the period, the reserve exceed- ing the sum payable at death. This fact tends to equalize the effect of impairment of the life ; and, the rate being virtually the same without regard to impairment, if the life is insur- able at all, the policy is often issued to impaired lives. — See p. S8. Dues. — The periodical payments to assessment or fraternal so- cieties, for expense purposes only. "Elements" of a Life Insurance Premium. — Every life insur- ance premium may be resolved into two portions, the "net premium'' and the "loading," each of which will be "level," if the gross premium is "level" and if the method of valuation is "net level premium." The net premium may also be re- solved into two portions, "cost of insurance" and "deposit for rserve" which, however, vary in amount from year to year — i. e., vary "complimentarily," because together they are always equal to the net premium. — ^See pp. 89, et seq. Endorsement. — A special provision or additional promise, writ- ten upon a policy. Also used, less accurately, for such a provision or promise attached to the policy. Endowment. — A sum of money payable at the expiration of a given term, contingently upon the survival of a given person or persons. Also called a "pure endowment." The word is often used as an abbreviated expression for "endowment in- surance." — See pp. 45, 56. Endowment in Advance. — The name given to a special form of loan, to be repaid, principal and interest, by equal periodical instalments to cease at the expiration of a given term or earlier if a given life should fail. The endowment is paid in advance, upon the promise to pay the periodical premiums until the expiration of the term or prior death, which prom- ise is secured by a mortgage upon real estate. The premium is usually equal to the premium for an endowment insurance 170 payable at the expiration of the period or at prior death, plus interest at a certain rate upon the sum insured. Such policies really yield a higher rate of interest, however, than this nom- inal rate, because the endowment insurance, which is a sink- ing fund to pay off the mortgage, is computed at a lower rate of interest. Endowment Insurance. — A sum of money payable at the expira- tion of a fixed term or upon the prior death of the insured. — See pp. s6, et seq. Endowment Policy. — A policy of endowment insurance. More accurately, a pure endowment policy. Entrance Fee. — An admission fee. Estimate. — A calculation of probable or possible financial result, based upon assumptions which are not certain to be realized. Examination. — The questioning and physical investigation of an applicant for life insurance, made by a physician upon the request of the company. — See p. 147. Examiner's Fee. — The fee of the medical examiner. In frater- nal insurance societies, usually required to be paid by the applicant; in regular life insurance companies, usually paid by the company. Exempt. — In most States the proceeds of a policy which is made payable to a wife are exempt from seizure to pay the debts of the husband ; but, if the right to change the beneficiary is reserved, this may not be true, and certainly such a policy may be applied toward the payment of the husband's debts while he is yet living. The statutes usually exempt certificates of fraternal societies from seizure to pay debts of the member or beneficiary. — See p. 151. Expectation of Life. — The term which persons, who at the out- set are of a given age, will live, on the average, mortality being as per a given table. Sometimes called the "Expec- tancy." Not the same as "Probable Life.'' Not used in computing premiums or the values of life annuities. — See pp. 86, 87, 88. Expected Deaths. — The number of deaths which, mortality being as per a given mortality table, would take place among a given group of lives, in a given period, usually one year. Expected Losses. — The aggregate amount of death claims which, mortality being as per a given mortality table, would be in- curred among a given group of lives insured for specified amounts, in a given period, usually one year. 171 Expected Mortality. — Literally the same as "Expected Deaths," but usually employed in the technical sense of the aggregate net tabular "costs of insurance'' under the policies in force upon a given group of lives, in a given period, usually one year. That is, the total "Expected Losses" less the reserves that would be released because of the deaths. — See p. 102. Extended Insurance. — Continuance of the insurance by applying the reserve of the policy or a part of it to pay the single premium for a temporary insurance for as long a term as possible, limited, however, in the case of an endowment policy to the endowment term, the remainder of the reserve being applied as a single premium to provide as large an endow- ment as possible, at the end of that term. Sometimes er- roneously called "Extended Insurance Value." — See pp. 119, et seq. Extra Hazard. — Risk of death beyond the ordinary. Not applied usually to impairment of health, but to risks of occupation, travel, residence, etc., and covered by an extra premium. — See p. 135. Extra Premium. — A premium, in addition to the ordinary pre- mium, required because of some extra hazard. — See p. 135. Face of Policy. — The sum insured exclusive of dividend addi- tions, return premiums or other such increments. Failure to Pay Premiums. — See "Default." Farr's English Life Tables. — Certain mortality tables, deduced from the birth and death registrations and repeated censuses of Great Britain, by Dr. William Farr. Farr's Table, No. 3, with interest at S per cent, was the first standard used for valuation of policies by the Insurance Department of the State of New York. — See pp. 29, 144. First- Year Term. — See "Preliminary Term." Forfeiture. — The loss of part or all of the reserve or of the surplus earnings of a policy or both, usually incurred by fail- ure to pay a premium when due. — See p. 149. Fraternal Insurance. — Insurance in a fraternal beneficiary so- ciety, usually on the assessment plan. Fraud. — Fraud vitiates all contracts, i. e., renders them voidable at the instance of the injured party. Consequently, and also on grounds of public policy, some courts refuse to enforce a policy, secured by fraud, even when incontestable by its own terms. — See pp. 152, 153. 172 Fraudulent Misrepresentation. — To prove fraudulent misrep- resentation it is necessary to show that it is material, that it was relied on, that it is untrue, that the maker knew it to be untrue, and that he made it with intent to defraud. See "Warranty." — See pp. 147, 148. Free Tontine. — The same as "Semi-Tontine," except that these policies were "free" from restrictions after a certain period, from which they acquired the name. — See pp. 112, 113. Friendly Societies. — The British term for "fraternal beneficiary societies.'' The British societies, however, give much more attention to sickness insurance than do the American fra- ternal societies. Friend's Certificate. — A certificate of character, as well as of health and habits, formerly secured from one or more of the friends to whom the applicant for life insurance referred. Gain and Loss Exhibit. — An analyzed profit and loss statement of a life insurance company. General Agent. — This expression, as used by the courts and in text-books on agency, means an agent who is clothed with all the powers of his principal, ». e., with power to represent the principal generally. In life insurance it means merely a solic- iting agent in charge of a given field and with other soliciting sub-agents under him, or even only that he has such sub- agents, though not exclusively in charge of a given field. Gold Bond. — The name which has sometimes been given to a life insurance policy which promises payment in gold coin of a given standard of weight and fineness. Government Annuity Life Tables. — Mortality tables — of which there have been three sets, each distinguishing male and female lives — deduced from the experience of the British Government annuitants. — See pp. 29, 30. Grace. — A special condition that a premium will be received, if tendered within a certain period after the due date. This may signify : (a) That the insurance lapses but will re-attach upon the payment of the premium during the days of grace unless death has already occurred ; or (b) That, if the premium shall be paid during the days of grace, the insurance will thereby be rendered effectual with- out interruption, although the insured be dead before payment is made ; or 173 (c) That the uisurance continues in full force during the grace, whether longer continued in force by premium or not. The last mentioned is now the form usually, indeed almost invariably, used in the United States. The usual period of grace is one month. Grace in payment of premiums was provided for in the original Deed of Settlement of the "Old Equitable" of Lon- don, in 1762. — See pp. 126, 150. Gross Premium. — The premium actually charged. The office premium or entire premium. — See pp. 76, 79, 100. Gross, or Gross Premium, Valuation. — A method of computing reserves by offsetting against the present value of policy ob- ligations payable in future, the present value of the gross premiums payable in future, instead of the net premiums. In effect it assumes that the whole of the future premiums can be applied to the payment of claims and that nothing will be needed to provide for future expenses or contingencies. — See pp. 99, 138, et seq. Guaranteed Dividend Policy. — A "Premium Reduction" policy in which the amount of the reduction of the premium is in- correctly called a "dividend." Frequently merely a trick to get a larger expense margin the first year while deluding the purchaser into thinking that he is securing a better bargain. High Pressure. — An expression for agency methods which offer a large cash "bonus" or other reward for securing a given "quota" of new business (the same being usually beyond the usual capacity of the agent) within a given time. Health Certificate. — ^A certificate, warranting that one is — sometimes also that one has continuously been, since the pol- icy was taken — in good health, given to secure reinstatement after lapse for non-payment of premium. — See p. 157, also pp. 116, 154. HM Mortality Table. — A mortality table, deduced from the ex- perience of 20 British life insurance companies. Sometimes called the "Twenty Offices' Table." The initials "HM" stand for "Healthy Male," but this table is not called the "Healthy Male" table ; that name is applied to one of Dr. Farr's tables. There are also HF (meaning Healthy Female), HM<5> (meaning Healthy Male "ultimate") and DM (meaning Dis- eased, i. e., Impaired, Male) Tables deduced from the ex- perience of the 20 Offices ; and, appearing some years later, the Hf'^] (J. e., select Healthy Male) table, constructed by 174 Dr. Thotias Bc)|i^^prAelie 4|Bwialyziiig the experience for the first fWe years of insurance^nd jmning the same to the Impaired Lives.— i^i^/5^lr^j^^\3Si2^1I«^n but not on the same terms as "firsT-etessi" hves. Also called "sub-standard" or "under-average" and, in Great Britain, "diseased." — See PP. 133. et seq. Impairment Lien. — A lien upon, or diminution of, the sum, nominally insured, as a means of providing against an im- pairment of the life. The lien usually diminishes each year by the amount of the premiums received, until it is thus extinguished and the policy is in force for the full amount. See pp. 134, et seq., also 141. Incontestable Provision. — A provision in a life insurance policy that after the policy has been in force a certain time, usually for from one year to three years, payment at death or ma- turity will not be disputed except for non-payment of pre- miums. — See p. 152. Increasing Insurance Policy. — A policy with level premiums but with the sum insured increasing — See p. 61. Increasing Premium Policy. — A policy, usually for a fixed sum insured, the premiums of which increase ; usually applied to a policy the premiums of which increase regularly, as dis- tinguished from a "natural premium" or "renewable term" policy with premiums corresponding to the increasing hazard- Indisputable Provision. — See "Incontestable Provision." Industrial Insurance. — Life or disability insurance with weekly — or perhaps also with monthly — premiums. Inspection of Risks. — In "ordinary" insurance a secret investi- gation of the conduct and habits of an applicant. In "indus- trial" insurance a physical examination by a physician, not so exhaustive as for "ordinary." Instalment Insurance Policy. — A life insurance policy, the pro- ceeds of which at death or maturity are to be paid in in- stalments. — See pp. 64, et seq., also p. 153. Insurable Interest. — The financial interest of a beneficiary in the life of the insured. The interest of a wife, husband, children or even of other relatives, if dependent upon the insured, is usually recognized for an indefinite amount in all cases if the beneficiary takes out the insurance and pays the premiums, but in some States only to a limited amount if the insured pays the premiums. In most States, 175 if the insured pays the premiums, he may designate to whom the insurance shall be payable without regard to insurable interest, provided the policy is so written. In fraternal societies different statutes apply. — See pp. 150, 151. Insurance Value.— The present value of the future "tabular costs of insurance" of a policy. Used as a basis for the "surrender charge'' permitted by the former statutes of Massachusetts. — See pp. 122, 123.' Insured Loans. — Loans upon real estate with endowment life insurance policies for a like amount held as collateral, under an agreement that interest and premiums are to be paid until the policy becomes payable by reason of death or maturity when the proceeds are to be applied to repay the loan. Interest Standard. — The rate of interest specified by the statute to be used to valuing policies. Four per cent, was selected for Massachusetts in 1859; 5 per cent by New York a few years later; 4^ per cent, later became the standard in New York for many years. In 1901 3^ per cent, became the stand- ard in New York, Massachusetts and several other States, and companies were permitted to use 3 per cent, of which many companies have taken advantage. — See pp. 14S, et seq. Intermediate Insurance Policies. — Policies for a sum not to exceed $500 each, with premiums payable quarterly or more frequently. So called because deemed intermediate between ■'ordinary" and "industrial." Joint Life Annuity. — An annuity payable so long as both of two persons or all of three or more persons survive. It may, however, be for a limited term only or until prior failure of the joint lives by the first death occurring, in which case it is called a "Temporary Joint Life Annuity." — See p. 75. Joint Life Insurance. — An insurance which is payable upon the failure of the "joint lives"; i. e., upon the death of the first of them to die. It may, however, be for a limited term, in which case it is a "Temporary Joint Life" policy, or may provide for an endowment at the end of the term, in which case it is known as a "Joint Life Endowment Insurance'' policy — Se;2 pp. 73, et seq. Joint and Survivorship Insurance. — An insurance payable upon the death of the first of two lives to die, but also continuable for the full sum insured or a smaller sum (such as half) payable upon the death of the survivor. 176 Lapse or Lapsation. — The determination of an insurance through failure to maintain the same in force by the payment of premiums. Lapse Profits. — The accretions to the surplus earnings of per- sistent surviving policyholders by reason of forfeitures by the lapse of other policies. — See pp. 103, 109, 112, 123. Lapsed Policy. — A policy which has ceased to be in force by reason of non-payment of premiums. Last Survivor Annuity. — An annuity payable until the last sur- vivor of a group of two or more lives shall die. Legal Reserve. — The mathematically adequate reserve required by law. — See pp. 138, et seq. Legal Reserve Companies. — Companies which operate under legal reserve laws. Level Premium Policies. — Policies, the premiums upon which are of the same amount each year during the premium-paying period. Level Premium Companies. — Inaccurately used for "Legal Re- serve Companies." Lien Plan. — The plan of insuring impaired lives by issuing life, limited payment or endowment policies at the usual rates, but subject to a "lien" or reduction of the sum insured. Also sometimes applied to the plan of issuing a policy on the "dated back" basis ; i. e., issued at the rate for a younger age, with an interest-bearing lien imposed to cover the reserve. — See pp. 134, et seq. Life Annuity. — An annuity which terminates upon the failure of a given life. It may be limited to a given term, in which case it is called a "Temporary Life Annuity." — See pp. 45, et seq. Life Policy. — A policy payable upon the death of the insured. Often inaccurately used as interchangeable with "Ordinary Life" or "Whole Life"; i. e., such a policy with premiums payable throughout life; but really applicable whether pre- miums be so payable or within a limited term or in one sum in advance. Limited Payment or Limited Premium Life Policy. — A life policy with the payment of premiums limited to a certain term of years or until the prior death of the insured. — See p. 54- 177 Limited Payment or Limited Premium Endowment Insure ANCE Policy. — An endowment insurance policy, with the pay- ment of premiums limited to a term of years, shorter than the endowment term, or until the prior death of the insured. Limited Tontine. — See "Semi-Tontine." Loading. — The excess of the gross or office premium over the net premium, which is added to the net premium to provide for expenses and contingencies and, if the policy is partici- pating, for dividends. — See pp. 76, et seq., also loi, 102. Loan Note Plan. — A plan prior to about 187s very popular in the United States, which permitted a certain part of each life insurance premium on the life, limited payment life or en- dowment plan to be represented by a note, annual dividends being applied to pay the interest and any excess to reduce the principal of the indebtedness. — See pp. 127, et seq., also p. 142. Lost Policy. — Some companies refuse to issue a duplicate for a lost policy; but all companies will pay claims under lost policies to the last-recorded beneficiaries, provided satisfac- tory indemnity bonds are given. Maturity. — The falling due of an endowment or of an endow- ment insurance by reason of the completion of the term while the insurance is in force and the insured survives. Mean Assets. — The assets of the beginning of the year plus the assets at the end of the year, the sum being divided by two. Mean Reserve. — The reserve on the assumption that policies average to be in force just six months after their anni- versaries — approximated by adding the last terminal reserve, the next terminal reserve and the net annual premium, the sum being divided by two. Same as "Midyear Reserve." — See p. 140. Mean Valuation. — The process of computing the aggregate of the mean reserves. Medical Certificate. — A "Health Certificate" given by a physician as a result of a medical examination. Meech's Table. — A table of mortality constructed from the com- bined experience of thirty American companies. Little used and nowhere standard. — See p. 29. Midyear Reserve. — See "Mean Reserve." 178 Misrepresentation. — A false representation. Such, unless war- ranted, do not render the insurance void unless material, re- lied upon, known to be false when made and made with fraudulent intent. — See pp. 147, 148. Misstatement of Age. — A representation that the age is less or greater than it really is. Formerly adjustment of the sum insured for an error as regards age was permitted only when the age had been understated, but now the practice is also to permit such adjustment when the age has been overstated. — See p. 152. Mixed Company. — A stock life insurance company which issues participating policies. Monthly Income Policy. — A policy promising payments to the beneficiary monthly for a fixed term of years or for life. — See p. 64. Mortality Gain. — The excess of the net mortality claims to have been expected, according to the mortality table, over the net actual death claims; "'net" in each case signifying "after the reserve or 'self-insurance' has been applied." — See pp. 31, 32, loi, 102. Mortality Table. — A table, showing from age to age, the num- ber dying and surviving out of a certain number, setting forth from a given age, called "the initial age." See pp. 24, et seq. Mortuary Dividend. — See "Return Premium." Mutual Company. — A company, without capital stock or with "guaranty capital" only, which is or may be controlled only by its policyholders. Mutual Policy. — A "Participating Policy." Natural Premium Policy. — A renewable one-year terra policy; that is, a policy renewable indefinitely upon the payment of one-year term premiums, covering the risk of the single year only. — See pp. 38, et seq. Net Premium. — The premium which, according to a given mor- tality table and rate of interest, will precisely provide the benefits guaranteed by the policy without providing anything for expenses and contingencies. — See p. 76. Net Reserve or Net Premium Reserve. — The reserve computed on the basis that the net premiums only will be available toward providing the benefits guaranteed by the policy. Also called "Net Value." — See pp. 139, 140. 179 Net Valuation or Net Premium Valuation. — The process of computing the aggregate net premium reserves. Often, in- exactly, used for "net level premium valuation" as dis- tinguished from "select and ultimate" or "preliminary term" valuation. — See pp. 99, 139. Net Value. — The same as "net reserve." Nominator. — The life insured under a survivorship annuity. The other life is called the "annuitant." Nominee. — The beneficiary of a policy, which reserves to the insured the right to change the beneficiary. Non-Forfeiting or Non-Forfeitable. — Not subject to be for- feited by failure to pay premiums. Sometimes used to mean, guaranteeing automatic extended insurance or even automatic paid-up insurance. — See pp. 157, 158. Non-Participating Policies.— Policies which are not entitled to participate in the earnings. Sometimes called "stock poli- cies." Northampton Table. — A mortality table constructed by Dr. Richard Price from the death registers of two parishes of Northampton, England, in 1769. Long the standard for life insurance computations in Great Britain, though exhibiting death rates much higher than the actual. Yet employed sometimes in the courts. — See pp. 27, 28. Notice. — The laws of several States require the mailing of notice of the falling due of premiums, failure to comply with which prevents lapsation of the policy for non-payment. Nylic. — A plan introduced by the New York Life Insurance Company for deferring a part of the remuneration for writ- ing new insurance and paying the same only to successful and persistent agents. Occupation Hazard. — An extra premium is sometimes charged to cover the risks of a particular occupation. "Old Line Insurance." — Level premium life insurance on the legal reserve plan. OM Table. — A male mortality table, deduced from the experience of all the British offices up to 1893, under ordinary life poli- cies. OCM], a select male table from the same experience; OM(IO), the ultimate section of this select table; OM(5), a male table deduced from the same experience after excluding the first five policy years ; OF. a female table from this ex- perience; 0[AM] and OfAF], select male and female annuitant mortality tables from the experience of the same companies —See p. 30. 180 Options. — Privilege of exercising choice among several modes of settlement at the close of a "tontine" or other dividend period or of an endowment term. — See pp. 154, 155. Ordinary Business. — As distinguished from industrial and "in- termediate,"' policies for $500 or more, with premiums pay- able not more frequently than quarterly. Ordinary Life Policy. — A policy, payable at death, with level premiums payable throughout life. — See p. 52, et seq. Overstatement of Age. — See "Misstatement of Age." Paid-up Policy. — A policy which continues in force for life or until matured as an endowment without further payment of premiums. Paid-up Value. — The amount of paid-up life or endowment life insurance claimable upon surrender. — See pp. 120, 121, 126. Participating Policy. — A policy which participates in the earn- ings of the company. Partnership Insurance. — Joint life or joint life and survivor- ship insurance upon the lives of the members of a partner- ship, payable to the firm or in redemption of the interest of the deceased partner. — See p. 73. Paying into Court. — In an interpleader by a life insurance company, when two or more are contesting over the title to the proceeds of a policy, it frees itself from liability for costs by paying the amount into court to abide the event. — See P. 153- Permit. — A written waiver of some restriction of a life insur- ance policy. Perpetuity. — An annuity payable perpetually. The best-known example is the British "consols." Policy. — The printed or written contract of insurance. Policy Loans. — Loans upon the security of a life insurance policy. — See pp. 127, et seq. Postponed. — Deferment of the acceptance of a life. Preuminary Term Policy. — A whole life, limited payment life or endowment insurance policy, providing that the premium for the first year or, more rarely, the premiums for the first two or more years are for term insurance only. — See pp. 13s. 156- Preliminary Term Reserve. — The reserve of a whole life, limited payment life or endowment insurance policy, computed on the basis that the insurance for the first year or the first two or more years is term insurance. "Full preliminary term" 181 means that the entire first year's premium, whatever the form of policy, is a term premium; "modified preliminary term," that on certain limited payment life and endowment insur- ance forms, a portion of it is not term; and "straight modi- fied preliminary term" that of all limited payment life and endowment insurance first premiums the excess over the corresponding whole life rate is not term. — See pp. 79, et seq. Premium. — The consideration paid for insurance. Premium Note. — A note given for a premium or a portion of it. — See p. 127. Premium Reduction Policy. — A policy with premiums subse- quent to the first, lower than it by a specified amount. Usu- ally a cover for a larger expense margin the first year. Probable Life. — The period at the expiration of which precisely half the number, setting out a given age, will have died. — See p. 88. Proof of Good Health. — The proof, required for reinstatement, that one has been and is in good health, furnished by a "Health Certificate" or a "Medical Certificate." See p. 157, also pp. 116, 154. Proofs of Loss or of Claim. — Attested evidence of the fact, cause, time and place of the death of the insured and of the right of the beneficiary. Proposal. — The British word for "Application." — See p. 147. Prospective Method. — The method of computing the reserve by deducting from the net present value of all policy obligations, the present value of all net premiums receivable in future. — See pp. 93, et seq. Provisions. — The conditions, restrictions and privileges contained in a policy. Quarterly Premium. — A premium payable quarterly. — See pp. 84, 8s. Rate. — The amount of premium per $1,000 (or other unit) of insurance at a given age on a certain plan. Rating Up. — Issuing a policy upon an impaired life, charging the rate for an age older than the actual age. — See pp. 135, et seq. Ratios. — Percentages, frequently of one thing to another which is in no way related, purporting to compare the advantages of one company with those of another. Usually misleading. Rebate. — The discount allowed the policyholder off his premium or premiums, not by way of dividend, but as a special con- cession not called for by the policy. 182 Reducing Premium Policy. — A policy the premiums for which are guaranteed to diminish. See "Decreasing Premium Policy." Regular Companies. — Legal reserve life insurance companies. Reinstatement. — The process of restoring one's life insurance after the same has lapsed or been forfeited. Renewable Term Policy. — A policy of insurance for a specified term with the privilege of renewing for succeeding terms without proof of good health, but at the rate required for the advanced age. Renewal Commissions. — Commissions payable upon renewal pre- miums; that is, upon premiums falling due after the first year of insurance, payable as the same are collected. — See P- 145- Renewal Contract. — A contract with a soliciting or supervising agent, by the terms of which a part of his remuneration is to be paid in renewal commissions. Renewal Premiums. — The premiums upon an insurance receiv- able after the first policy year. Sometimes also applied to deferred portions of the first annual premium. Renewal Receipt. — A receipt for renewal premiums or for de- ferred first-year premiums, signed by an officer of the com- pany and countersigned by the agent receiving the premium. Reinsurance Reserve. — Literally the reserve required to rein- sure the policies but in life insurance used as a synonym for "legal reserve." — See p. 93. Representations. — The statements made in the application or replies to the medical examiner for the purpose of procuring a life insurance policy if not warranted. — See p. 147. Reserve. — Literally a sum held in reserve. But in life insurance synonymous with the "value" of a policy. It may be con- sidered from the "retrospective" (that is, as an "unearned premium" reserve) or from the "prospective" standpoint (that is, as a "reinsurance" reserve). From the latter standpoint it must be a sum sufficient, together with future net pre- miums, mortality and interest being as assumed, to enable the company to discharge its policy obligations. From the former standpoint it consists of what should remain of the net premiums collected in the past after meeting all policy obligations, interest and mortality being as assumed. This is the American view, based upon the proposition that loadings which have been imposed to provide for expenses and con- 183 tingencies, must be treated as required for that purpose, and consequently that net premiums only can be taken into ac- count in computing reserves. — See pp. 93, et seq. Reserve Liens. — Liens for the amount of the reserve, taken when insurances are issued upon the "Dated Back" basis. — See pp. 142, 143. Retrospective Method. — The method of computing the reserve by accumulating at the assumed rate of interest the excess of the net premiums received over the annual tabular "'costs of insurance." — See pp. 93, et seq. Return Premium Policy. — A life or endowment insurance under which, in addition to paying the principal sum at death, all premiums or a portion of each premium or a certain number of premiums are returned. — See pp. 61, et seq. Reversions. — In Great Britain, promises to pay given sums at death, especially applied to "dividend additions." — See pp. 108, IIS- Reversionary Additions, Dividends or Bonuses. — Paid-up ad- ditions to the sum insured, by way of dividends or bonuses. In Great Britain these are of two forms, viz. : "Simple Re- versionary Bonus," under which a percentage of the original sum insured is added to the policy, and "Compound Re- versionary Bonus," under which a percentage of the total sum insured, including previous additions, is added to the policy. — See pp. 108, 115, 116. Risk. — The probability of loss. The life insured. Safety Clause. — The provision that, in event of impairment of the reserve, the insured shall make the impairment good by scaling his policy, by letting the deficiency stand as a interest- bearing lien thereon, by increasing his subsequent premiums to an amount equivalent in value to the impairment or by paying the same in cash. Salary. — In industrial insurance, "ordinary salary'' means col- lection fees or renewal commissions, and "special salary" means "first-year commissions," or direct compensation for writing new business. Salvage on Loading. — The portion of the aggregate of the load- ings on premiums realized during the year, which remains after providing for all expenses and contingencies deemed properly chargeable thereto. See pp. loi, 102. Select Mortality Table. — A mortality table showing the death rates arranged according both to age and duration of policy. —See p. 31. 184 Select and Ultimate Reserve. — The reserve of a life insurance policy computed upon the basis that the mortality to be ex- perienced in future will be as per a select mortality table, while net premiums receivable will be the net level premiums computed according to the ultimate section of the same mortality table, which is known as the "ultimate table." By this means the special salvages in mortality, due to fresh medical selection, are discounted and applied toward covering the expenses of new business. The standard for limitation of expenses of new business, and also the minimum standard for valuation of policies issued since 1906, under the insur- ance laws of New York. — See pp. 31, 82. Selection. — ^An expression for the process, exercised for or against the company, by reason of the conscious or uncon- scious operation of intelligent selection, such as "medical selection," by means of which the company seeks to accept only good risks, and "adverse selection" by means of which the lives insured select to continue the insurance or to abandon it, according as they are of opinion that they are likely to die soon or to live long. — See pp. 25, 43, 44, 122, 123, 124. Self-Insurance Fund. — An expression signifying the "terminal reserve," introduced by Elizur Wright to express the idea that the insured contributes this amount toward meeting the death claim under the policy. — See p. 21. Semi-Annual Premium. — A premium payable semi-annually. Semi-Endowment Insurance Policies. — Policies promising the payment of a certain sum in event of death during a certain term and of half that sum in event of survival to the end of the term. — See p. 58. Semi-Tontine Policies. — Policies of life insurance which pro- vide that the surplus earnings of a group of policies shall be accumulated for the benefit of the persistent survivors, all who die, lapse or surrender before expiration of the dividend period forfeiting their share of such surplus. — See p. 112. Seventeen Offices' Mortality Table. — The "Actuaries' Table,'' so called because it was deduced from the experience of seventeen British insurance offices. — See p. 28. Single Premium Policy. — A policy of life or of endowment in- surance which is paid for by a single premium in advance. — See p. 52. i8s Special Agent.— In legal phraseology an agent who has only special authority to act in a particular matter as distinguished from general authority. In life insurance, a soliciting agent who has no supervision over other agents. Starred. — Marked with a star. Usually signifies that the life is no longer deemed desirable, and that no unusual concessions concerning time of payment of premium should be granted. This practice was once common but is now seldom met with. State Standard. — ^An expression for the table of mortality and rate of interest adopted by the State for determining the re- serve liabilities of life insurance companies. — See p. 145. Step Rate. — Another name for "natural premium,'' so called be- cause the premiums increase each year, or at the expiration of each period of years — e. g., five years. Stipulated Premium Policies. — Policies of assessment insur- surance upon which the payment of a certain stipulated pre- mium is required periodically, but the privilege to assess is reserved. The companies issuing such policies usually do not maintain the full legal reserves thereon. Stock Company. — A life insurance company with an irredeem- able stock capital, as distinguished from a mutual company, which may have a guaranty capital redeemable out of the surplus. Stock Policy. — A non-participating policy of life or endowment insurance. Sub-Standard. — Below the standard requirements for first-class lives ; the same as "under average," "impaired," "diseased." See pp. 133, et seq. Suicide Provision. — A provision that, in event of suicide, usu- ally whether sane or insane, the policies shall be void or only the premiums shall be returned or the amount of the reserve be paid. These provisions are usually confined to the first year or the first two or three years. Surplus. — The excess of a life insurance company's assets over all liabilities, including capital stock and the legal reserve or such higher reserve as the company has voluntarily set up in accordance with law. — See pp. loi, et seq. Surrender. — A release, for a consideration, of a life insurance policy to the company, usually accompanied by its return to the company. — See p. 118, et seq. 186 Surrender Charge. — A deduction from the reserve of a life in- surance policy in determining the amount of the surrender value thereof. — See pp. 122, 123. Surrender Value. — The consideration in cash, paid-up insurance, extended insurance or an annuity given by the company for the surrender of a policy of life or endowment insurance. — See pp. 118, et seq. Survivorship Annuity. — An annuity payable to one or more per- sons from and after the death of one or more other persons during the after-lifetime of the former. — See pp. 65, et seq. Survivorship Insurance. — A life insurance payable upon the death of a given person to a given beneficiary if then sur- viving. Temporary Additions. — Additions to the sum insured by way of dividends, payable only in event death occurs within a temporary period, usually one year. A method of applying surplus not now in use. — See p. 116. Temporary Annuity. — An annuity payable for a period not longer than a given term of years or than the survival of a given life or lives. "Term Annuity." — See p. 48. Temporary Insurance. — Insurance payable only in case death occurs during a specified term. "Term Insurance." — See p. SO, et seq. Terminal Reserve. — The reserve at the end of the policy year. — See pp. 93, et seq. Term Annuity. — The same as "Temporary Aimuity.'' Term Insurance. — The same as "Temporary Insurance." Term Insuieance, First Year. — The same as "Preliminary Term." Term Policy. — A policy of term insurance. Term Premium. — A premium for term insurance. Thirty American Offices' Mortality Table. — See "Meech's Table." — See pp. 29, 30. Twenty British Offices' Mortality Table. — See "HM Table.'' — See p. 29. Tontine Policies. — Policies of life insurance under the provi- sions of which nothing was to be paid or allowed in event of lapse or surrender during a certain period, and the entire accumulations from all policies of this class were to be ap- portioned among the persistent survivors. — See pp. 112, 113. Ultimate Mortality Table. — A mortality table deduced from an experience from which the durations of insurance affected by fresh medical selection have been excluded. Among such 187 tables are the American Experience Table, the HM(5) Table and the QM'io Table. See pp. 28, et seq. Under-Average Lives. — Lives which are not up to the standard of first-class lives; "sub-standard," "impaired," "diseased."— See pp. 133, et seq. Understatement of Age. — See "Misstatement of Age." Underwriter. — One who becomes responsible as an insurer. Also, less correctly, one who is engaged in the insurance business as officer, manager or agent. Unearned Premium Reserve. — See "Reserve." See pp. 93, et seq. Valuation. — The process of computing the aggregate of the reserves of a life insurance company or of some of its policy obligations. See p. 138, et seq. Value. — Sometimes used as equivalent to "reserve." Void. — Not valid or binding. Waiver. — Consent, express or implied, that a provision or re- striction in the policy for the benefit of the company shall not be enforced. Warranty. — A statement or promise given as a consideration for a policy, the truth of which, or performance of which, is guaranteed. If the warranty be untrue in any respect, or be not strictly performed, the policy is voidable at the option of the company, which is not required to prove that the misstatement or failure of performance is material or that there was fraud. The "incontestable provision" which usually takes effect after from one to three years, cancels the warranty. — See pp. 147, 148. Weekly Premiums. — Premiums payable weekly, which, unlike the usual monthly, quarterly and semi-annual premiums, are not treated as mere instalments of the annual premium, and accordingly the unpaid portion of the annual premium is not deducted in event of death. Whole-Life Policy. — A policy payable at death, with premiums payable throughout life. See "Ordinary Life." 188 ACTUARIES' TABLE OF MORTALITY. Yearly Yearly Probability Probability Number Number of of Age. Living. Dying. Dying. Surviving. lo 100,000 676 .0067600 .9932400 II 99.324 674 .0067859 .9932141 12 ^,650 672 .0068119 .9931881 13 97.978 671 .0068484 .9931516 14 97.307 671 .0068959 -9931041 IS 96,636 671 .0069434 .9930566 16 95,965 672 .0070026 .9929974 17 95,293 ^3 .0070625 .9929375 18 94.620 67s .0071336 .9928664 19 93.945 677 .0072064 -9927936 :o 93.268 eSo .0072909 .9927091 21 92,588 683 .0073768 .9926232 22 91,905 686 .0074641 .9925359 23 91,219 690 .0075643 -9924357 24 90,529 694 .0076659 .9923341 25 89,835 698 .0077700 .9922300 26 89,137 703 .0078866 .9921134 27 ^,434 708 .oc«oo6i .9919939 28 87,726 714 -0081389 .9918611 29 87,012 720 .0082750 .9917250 30 86,292 727 .0084248 -9915752 31 85,565 734 .0085784 .9914216 32 84,831 742 .0087468 -9912532 33 84,(^ 750 .0089191 .9910809 34 83,339 758 .0090955 .9909045 35 82,581 767 .0092877 .9907123 36 81,814 776 .0094849 .9905151 37 81,038 785 .0096867 .9903133 38 80,253 795 .0099064 .9900936 39 79,458 805 .0101311 .9898689 40 78,653 815 .0103619 .9896381 41 77,838 826 .0106118 .9893882 42 77,012 839 .0108943 .9891057 43 76,173 857 .0112509 .9887491 44 75,316 881 .0116973 .9883927 45 74,435 909 .0122120 .9877880 46 73,526 944 .0128389 .9871611 47 72,582 981 .0135157 .9864843 48 71,601 1,021 .0142595 .9857405 49 70,580 1,063 -0150611 .9849389 SO 69,517 1,108 .0159386 .9840614 51 68409 1,156 .0168982 .9831018 52 67,253 1,207 .0179473 -9820527 53 66,046 1,261 .0190927 .9809073 54 64,785 1,316 .0203133 .9796867 189 ACTUARIES' TABLE OF Number Numler Age. Living. Dying. 55 63,469 1,375 56 62,094 1.436 57 60,658 1,497 58..... 59,161 1,561 59 57,600 1,627 60 55,973 1,698 61 54,275 1,770 62 52,505 1,844 63 50,661 1,917 64 48,744 1,990 65 46,754 2,061 66 44,693 2,128 67 42,565 2,191 68 40,374 2,246 69 38,128 2,291 70 35,837 2,327 71 33,510 2,351 72 31,159 2,362 73 28,797 2,358 74 26,439 2,339 75 24,10a 2,303 76 21,797 2,249 77 19,548 2,179 78 17,369 2,092 79 15,277 1,987 80 13,290 1,866 81 11,424 1,730 82 9,694 1,582 83 8,112 1,427 84 6,685 1,268 85 5,417 I, III 86 4,306 958 87 3,348 811 88 2,537 673 89 1,864 545 90 1,319 427 gi 892 322 92 570 231 93 339 155 94 184 95 95 89 52 96 37 24 97 13 9 98 4 3 99 I I 190 MORTALITY. Yearly Yearly Probahility Prohability of of Dying. Surviving. .0216643 .9783357 .0231261 .9768739 .0246793 .9753207 .0263856 .9736144 .0282464 .9717536 .0303362 .9696638 .0326116 .9673884 .0351204 .9648796 .0378398 .9621602 .0408256 .9591744 .0440818 .9559182 .0476138 .9523862 .0514741 .9485259 .0556300 .9443700 .0600872 .9399128 .0649328 .9350672 .0701581 .9298419 .0758049 .9241951 .0818834 .9181166 .0884679 .9115321 .0955602 .9044398 .1031794 .8968206 .1114692 .8885308 .1204444 .8795556 .1300648 .8699352 .1404064 .8595936 .1514357 .8485643 .1631938 .8368062 .1759121 .8240879 .1896785 .8103215 .2050951 .7949049 .2224804 .7775196 .2422340 .7577660 .2652741 .7347259 .2923820 .7076180 .3237300 .6762700 .3609866 .6390134 .4052632 .5947368 .4572271 .5427729 .5163043 .4836957 .5842697 .4157303 .6486486 .3513514 .6923077 .3076923 .7500000 .2500000 1. 0000000 .0000000 AMERICAN EXPERIENCE TABLE OF MORTALITY. Number Age. Living. 10 I0O,CXX) II 99,251 12 5^,505 13 97.762 14 97,022 IS 96,28s 16 95,550 17 94,818 18 94,089 19 93,362 20 92,637 21 91,914 22 91,192 23 90,471 24 89,751 25 89,032 26 88,314 27 87,596 28 86,878 29 86,160 30 85,441 31 84,721 32 84,000 33 83,277 34 82,551 35 81,822 36 81,090 37 80,353 38 79,6x1 39 78,862 40 78,106 41 77,341 42 76,567 43 75,782 44 74,985 45 74,173 46 73,345 47 72,497 48 71,627 49 70,731 SO 69,804 51 68,842 52 67,841 Yearly Yearly ProbaUUty Probability Number of of Dying. Dying. Surviving. 749 .007490 .9925x0 746 .007516 .992484 743 .007543 .992457 740 ■007569 .992421 737 .007596 .992404 73S .007634 .992366 7^2 .007661 ■992339 729 .007688 .992312 727 .007727 .992273 72s .007765 .992235 723 .007805 •99219s 722 .007855 .992145 721 .007906 .992094 720 .007958 .992042 719 .008011 •991989 718 .008065 •991935 718 .008130 .991870 718 .008197 .991803 718 .008264 .991736 719 •008345 .99x655 720 .008427 •99x573 721 .008510 .991490 723 .008607 •991393 726 .008718 .991282 729 .008831 .991169 732 .008946 .99x054 737 .009089 .9909XX 742 .009234 .990766 749 .009408 .990592 7S6 .009586 .9904x4 76s .009794 .990206 774 .010008 .989992 785 .010252 .989748 797 •0x0517 •989483 812 .010829 •989x71 828 .01x163 .988837 848 .011562 .988438 870 .012000 .988000 896 .012509 .987491 927 .013106 .986894 962 .013781 .9862x9 1,001 .014541 .985459 1,044 .015389 .9846x1 191 AMERICAN EXPERIENCE TABLE OF MORTALITY. Number Age. Living- S3 66,797 54 65,706 55 • 64,563 56 63,364 57 62,104 58 60,779 59 59,385 60 57,917 61 56,371 62 54,743 63 53,030 64 51,230 6S 49,341 66 47,361 67 45,291 68 43,133 69 40,890 70 38,569 71 36,178 72 33,730 73 31,243 74 28,738 75 26,237 76 23,761 77 21,330 78 i8,g6i 79 16,670 80 14,474 81 12,383 82 10,419 83 8,603 84 6,955 85 5,485 86 4,193 87 3,079 88 2,146 89 1,402 90 847 91 462 92 216 93 79 94 21 95 3 number Dying. 1,091 1,143 1,199 1,260 1,325 1,394 1,468 1,546 1,628 1,713 i,8ao 1,889 1,980 2.070 2,158 2,243 2,321 2,391 2,448 2,487 2,505 2,501 2,476 2,431 2,369 2,291 2,196 2,091 1,964 1,816 1,648 1,470 1,292 1,114 933 744 555 385 246 137 58 18 3 193 Yearly ProiabiUty of Dying. .016333 .017396 .018571 .019885 .021335 .022936 .024720 .026693 .028880 .031292 ■033943 .036873 .040129 .043707 .047647 .052002 .056762 .061993 .067665 ■0757Z3 .080178 X)87028 •094371 .102311 .111064 .120827 ■131734 .144466 .158605 .174297 .191561 .211359 ■23S';.52 .265681 .303020 .346692 •395863 .454545 .532466 .634259 ■734177 •857143 1. 000000 Yearly Probability of Surviving. ■983667 .982604 .981429 .980115 .978665 .977064 .975280 .973307 .971120 .968708 .966057 .963127 ■959871 •956293 •952353 •947998 •943238 .938007 •932335 .926267 .919822 .912972 .905629 .897689 •879173 .868266 •855534 •841395 .825703 .808439 .764448 ■734319 .696980 ■653308 -604137 545455 •467534 .365741 •265823 .142857 .000000