SCIENTIFIC LIFE INSURANCE § I. Reserve life insurance. § 2. The mortality table. § 3. The single premium for any term. § 4. Level annual term premiums and reserves. § 5. Term policies end straight life. * 9. Limited premium payments. § 7. The endowment feature. § 8. The choice of a policy. § 9. Insurance assets and investments as savings. I 10. Future of insurance.
The premium must always be fixed in advance. The cal culations for determining the premiums on different kinds of insurance policies are many and complex, but all con form to a few general nrinciples. The three factors assumed are an average mortality table, a rate of interest (or yield on investments), and an expense rate in proportion to the premiums on outstanding insurance. Insurance on the re serve plan is often called scientific insurance because, upon the basis of these assumptions resulting from experience, it makes exact mathematical calculations of the premiums and reserves needed for insurance of any particular kind in re spect to age of insured, number of payments, method of pay ing the beneficiary, and any other conditions. The premium thus fixed is, however, only a maximum, and usually is re duced as the result of conditions more favorable than those assumed.
§ 2. The mortality table. When large numbers of men are taken as a group, a certain proportion of those at each age may be expected to die. A mortality table starts with a group of persons, as 100,000, at a given age, as 10 years, and shows the number who die and the number who survive at each year of age until all are dead. The tables generally used in the United States are the "Actuaries" which assumes the limit of life to be 100 years, and the American Experi ence Table of Mortality, constructed by Sheppard Homans in which assumes the limit of life to be 96. Some figures from the latter table, at specified years, are given below: The actual deaths in any group of insured are not exactly the number in the mortality tables. But this is not an es sential difficulty as long as the deaths are fewer than the figures of the tables, at least in the earlier years of the policy. Any excess of premiums thus collected but increases the safety of the insurance or reduces the need of later pay ments. In fact, the mortality in all well conducted companies in the United States is below the figures of these tables., partly because the tables were conservatively calculated. partly because of the favorable influence of medical selec tion, especially among the recently insured, and partly be cause of the improvement in longevity since the tables were constructed.
The premiums given as illustrations in the following dis cussions are "net premiums," or natural premiums, esti mated as just sufficient to meet the actual payments required by the contracts in the policies. To provide for the ex penses of management, an addition is made to the net premium, called the "loading." The entire premium is Fig. 1, Chapter 13, shows the rise of mortality rates between the ages 35 and 65, which calls for more and more rapidly increasing pay ments under the simple assessment plan.
called the "gross premium." The loading, a large part of which goes for agents' commissions and the costs of manage ment, is a very considerable addition to the net premiums, adding in the case of the standard companies nearly 25 per cent to the premiums for an endowment policy, nearly 30 per cent on a limited payment, and more than 40 per cent on a straight life. A part of this, however, may be re funded to the insured in the form of "dividends." § 3. The single premium for any term. It is apparent that the natural assessment premium (ignoring the factor of interest) for $1000 of insurance is expressed by the death rate for that year, e. g., at age 20 the payment of $749 by each of the 100,000 living at the beginning of the year will provide the $749,000 needed to pay the losses. If premiums are collected at the beginning of the year and losses are paid at the end of the year, and if interest can be earned meantime at the rate of 3% per cent, the premium in advance for a one-year term policy is the natural premium dis counted, e. g., $8.64 is the present worth of $8.95, which is the natural premium at age 35 due a year later, interest being per cent. In these calculations there is no allow ance for expenses, the necessary "loading." In the same manner may be determined the natural assess ment premium for each year of insurance. It is a simple matter to determine the amount of a single premium, at any age, that is adequate to pay for insurance covering any selected number of years (term insurance) up to the entire period of each insured person's life (full life). It is neces sary only to apply the formula of present worth and that of compound interest on investments.i Thus the losses of any future year, according to the table of mortality, discounted by the rate of yield on investments, are the present worth of insuring the entire group for that year. The single premium for each of the insured for any term of years is the sum of the present worth of insurance for all the years of the term, divided by the number living at the beginning of the period? The payment in advance of the single premium for any 1 See Vol. I, p. 279.
2 Let P he the present worth of all the policies for a group of the same age, p the present worth of one policy, X the total insured at the beginning of the period. f the natural assessment premium this year, or the natural premium required for any year. Then 2 P (1 r) (1 (1 (14-r)n definite term provides a reserve fund sufficient, on the as sumptions made, to carry all the insurance without further payments. Each year there is added to the fund the income earned on investments, and there is subtracted the amount of the losses for the year, until the death of the last member of the insured group. If the deaths in the earlier years are fewer than were expected in the mortality table, this will be offset eventually by more deaths at the advanced years: but in the meantime a reserve larger than was expected is yield ing income, thus providing a larger sum than is needed to pay all the policies at maturity. This surplus might be dis tributed as so-called "dividends" from time to time to those surviving, or be added pro-rata, at intervals, to the amount of the policies as accumulated dividends.
§ 4. Level annual term premiums and reserves. It is a matter of no very abstruse mathematics (in principle) to find the equivalent of this single premium in any one of many other forms of premium payment. The processes are but variations of present worth and compound interest calcula tions. Such calculations, however, lead into many complexi ties of practical detail difficult to explain in brief compass, and are the special task of the actuary (the mathematical expert dealing with such problems in the insurance business). The most• useful actuarial equivalent of the single premium is the level annual premium for any period (term or life). Almost all policies now written have the level annual premium as a feature. The amount of the level annual premiums at first is greater than the losses: this causes for a time the steady accumulation of a reserve that yields income. Then. as the losses grow, they overtake and finally surpass the amount of the annual premiums. Therefore, the total re serve for any group of insured, within the definite term fdr which insured, increases year by year to a maximum and then declines until it reaches zero with the payment of the last claim. The individual reserve for each policy not yet matured increases steadily the longer it is in force, what ever be the term. The total reserve is essential to the sol vency of the company and the payment of all the policies as they fall due.
The companies that issue policies on the level premium plan or reserve plan are known as ."old line" companies, or as "legal reserve" companies, because the state laws require every company of this type to maintain the reserves cal culated on the basis of a certain rate of yield. The growth of the legal reserve companies in recent times constitutes one of the financial marvels of the age. They had in 1919 more than 58,000,000 policies in force, for a total of nearly $36,000,000,000 of indemnity (insurance in force) ; their total income was nearly $1,600,000,000 (about one fortieth being from investments, the remainder from premiums), and their total assets $6,700,000,000. These figures grow so rapidly that any statistics are soon out of date. The up ward curve may be seen in the following data: Number of Amount of Total Total policies in force insurance in force income of year assets Reserve insurance is carried on by both mutual and stock companies; of late some large stock companies, such as the Equitable and the Prudential, have been transformed into mutual companies. The mutual company legally belongs to the policyholders, though its control is actually in the hands of a self-perpetuating group of trustees and officers, more or less supervised by state officials. The gross premiums in reserve insurance are, for the purpose of safety, fixed at a figure larger than the expected cost of the insurance, and normally the earnings from interest are higher, the mortality is lower, and expenses are less than those on which the cal culation of rates is based. From the excess of income result ing, the company sets aside a surplus and then divides the rest among the policyholders. These returns, virtually but the refund of excess premiums, are called "dividends" (a somewhat misleading term, not to be confused with dividends on corporate stock). The policies that receive dividends are called "participating" and are said to participate in the earnings. Formerly the majority of policies paid "deferred" dividends after five, ten, or twenty years, according to vari ous tontine and semi-tontine plans, the survivors to these periods receiving their dividends plus those of the other pol icyholders who had died or had withdrawn from the com pany. This form of policy was objectionable in that it in volved a lottery element, the survivors winning the "divi dends" that should have been paid to the deceased; it was made illegal in New York and other states, and in most cases dividends are now paid annually. The stock company, or ganized for profit, frequently charges lower premiums for "non-participating" policies, and then retains such profits as may result from keeping expenses below receipts.
§ 5. Term policies and straight life. A person purchas ing life insurance, taking out a policy, finds himself facing a choice among a confusing variety of policy forms. Apart, however, from some comparatively minor features such as those mist described, as to distribution of dividends, the various forms of policies result from combining in various ways three features. The first of these is the term within which the level premium is calculated. This may be one year, or any number of years, most frequently five or some multiple. Whatever be the term, the rate of premium is calculated with respect to the expected mortality at the ages included, and at the renewal of the insurance for a new term the premium rate "steps up" to that required to meet the expected losses at the higher ages. Evidently, the shorter the term for which a policy is written, the lower the rate of premium, for the early years, because the smaller the reserve needed to keep down payments in the later years of the term. For example, on a twenty-year term policy taken at age 35 the natural premium would be $10.80 a year. Break this term up into two terms of ten years each, and the annual premium for the first ten year would be $9.36 ; but when the policy is renewed for the second term of ten years (at age 45) the rate would be nearly $15.00. The policy known as "straight life" or "level life" is simply term in surance for the term limit (or highest age) of the mortality table (in the American Experience table that is 96). The net premium for straight life at age 35 is $19.91, and this permits (at the rate of earnings assumed) the accumulation of a reserve of $310.75 at the end of twenty years, whereas the reserve on the twenty-year term ending then is zero. The income of this reserve, added to the annual premium, is enough to meet the expected losses in the later years as they gradually rise. (These amounts are on the assumption of the American mortality and 3% per cent interest.) § 6. Limited premium payments. A second feature in
which policies differ is in regard to the number of premium payments to be made according to the calculation. If the number of payments is any less than the number of years of the term the policy is one of "limited payment." The most limited payment is the single premium already described, which may be used in connection with any term from one year to life. The single premium is simply the reserve required to meet the cost of the insurance, without further payments, to the end of the term. The net single premium, or reserve, for a straight life policy, at age 96 is $1000, the face of the policy. The most common limited payment policy is the twenty-payment life. The annual premium for this at age 35 is $27.40, which is more than twice as much each year as the premium on a twenty-year term ($10.80) although it provides no more indemnity. But whereas the reserve on the term policy at age 55 is zero, the reserve on the twenty-payment life is $566.15, this being just the amount of a single-pay ment life policy if taken at age 55.
By just as much as the experience of any company (or separate group of insured) is more favorable than the figures assumed as to rate of yield on investment, mortality, or ex penses, there will be excess premiums to refund ("divi dends"), which may be used by the insured to reduce his annual premiums or to purchase additional insurance or to add to the reserve. In the more successful companies an ordinary life policy eventually accumulates a reserve suffi cient to carry the policy to the limit of age without further payments, and thus becomes in fact a limited payment policy.
§ 7. The endowment feature. A third feature in respect to which life insurance policies differ is as to the extent to which they include the feature of saving with that of in surance. We have seen that, just to the extent that any reserve whatever is accumulated to keep the premium level, to prevent its "stepping up" as the mortality rate advances with age, there is an act of saving distinct from the payment of a premium for insurance in that year. This is brought out clearly in the case of many insurance policies which pro vide for a "surrender value" annually equal to the accumu lated reserve. So, in our example, the reserve of the straight life policy was $310.75, and that of the twenty-payment life was $566.15. If the insured survives he may, according to the terms of many policies draw for his own benefit these amounts, the "surrender value." This privilege in many cases unfortunately defeats the purpose of insurance for the families, and tempts men to use the proceeds of their policies for enjoyment or for investment in business.
A further step is taken in the savings process in endow ment policies. In these the level premium for a definite term is made high enough to accumulate a reserve more than sufficient for a single-payment life policy beginning at the end of the limited payment period. The premium on endow ment policies is so calculated that the reserve equals the face of the policy at the end of the payment period. For example, on a twenty-year endowment the net annual pre mium is $38.35, the terminal reserve is $1000, which is the surrender value. Many persons are attracted to endowment insurance by the oft expressed thought that "You don't have to die to beat it." But this is a mistake. The endowment policy is merely a convenient but somewhat costly plan of saving, hitched on to an insurance policy, with which "actu arially" it has no essential connection. In "scientific" in surance the insured pays its full actuarial cost for each feature of the policy that he buys: so much for the insurance, so much additional for the accumulation of the endowment. The premium for endowment insurance is much higher than that for term life insurance alone during the same period. If insurance is the thing one needs, one is purchasing only a fraction as much for the same annual outlay.
It will be observed that only the survivors to the end of the term get the endowment, and those dying earlier receive no more than if they carried the cheapest term insurance. This gives to the endowment policy a strong "tontine" or lottery character, the survivors profiting at the cost of those who die within the term. This often deceives the uninformed applicant for insurance into the belief that, despite the costs of management, an endowment policy yields a much higher return than other conservative investments at compound in terest. The excess of the net endowment premium over the net term premium in our example is annually $26.65, which, compounded at 4 per cent, would be about $825 at the end of the period; but this is sufficient to give the survivors $1000 each, or approximately 6 per cent compound interest. The survivors are lucky not only in living but in getting a monetary prize (paid for by those who have died) for their success. All those who have died, however, would have been better off if they had taken out some cheaper form of policy (term, or straight life, or limited premium) and had deposited in the savings bank each year the difference in the premiums.
§ 8. The choice of a policy. The choice of a policy by an applicant for insurance presents much difficulty in view of the manifold differences in the details of the various con tracts, the contingent nature of so many features on which the ultimate cost will depend, and further because of the various circumstances of the insuring individuals, making different policies suitable to their different needs. Moreover, the advice of the agent is too often of little assistance, when it is given in view of the amount of his commission, and with the desire to make an immediate sale, rather than with regard to the true interest of the insured. The first condition of a wise choice is to get into a sound company, of which there are now many, for mere size does not necessarily in dicate either superior soundness or superior economy in a reserve company. The various policies written by any hon estly conducted reserve company are all actuarily equivalent on the basis of the assumptions made, and all provide re serves adequate to meet their outstanding contracts. There are certain questions on which the applicant must be clear and which he alone can answer.
(1) What is it he most needs—is it the protection of incur• ance, or is it an opportunity to deposit savings regularly? The insurance method differs from the method of depositing savings by its contingent nature, the resulting income of any individual being possibly much greater than the amounts actually saved (e. g., when the insured dies or is injured soon after taking insurance), and possibly less or nothing at all.
(2) What is the period within which insurance is most needed? (3) How much can he devote to insurance or to saving respectively, and how will this amount probably change in the course of years, increasing or decreasing? The premium in personal insurance (life, accident, sickness, invalidity, old age pensions) is in almost all cases paid out of some current income. The premium paid is just so much subtracted from the amount available for present direct use and applied to the purchase of future incomes for one's self or family.
(4) What would be the most suitable mode and distribu tion of indemnity payments? The payment usually takes the form of a lump sum payment at death or at the maturity of the endowment. In recent times there has been a growing use of original forms of payment which give to the bene ficiary annual or monthly instalments for a definite number of years or for life.
In the light of the foregoing discussion, it is apparent that the more immediate and greater the need of insurance, and the more limited the present income of the insured, the briefer the term for which insurance should be taken for the greater the amount of indemnity that can be bought with a given outlay. A young man in his twenties or thirties, with a limited salary or with his capital invested in business, needs particularly to protect his wife and his children until they are of age. The difficulty with term policies, especially for shorter terms, is the stepping up of premiums, which later makes the cost prohibitive. However, life insurance is essentially needed by one having dependents (wife, young children, sisters, parents, etc.), and is far less often impor tant to the older man than it is to the man between twenty and fifty years of age. A good golden mean for many men is a twenty-payment life policy, its surrender value at age fifty-five being an endowment for nearly two thirds the face of the policy. The best general purpose policy for the active business man who can use and invest his funds safely and well is the "straight life." A very desirable kind of in surance (as yet little developed) for salaried men is that terminating at some chosen retirement age, (say sixty-five years) combined with an old-age pension for life thereafter.
§ 10. Future of insurance. It is striking evidence of the importance of the marginal principle' that insurance should still be desired by men when the cost is so high and so large a part of the total premiums is absorbed in expenses. In surance of all kinds grows apace, but its use would be wider and its benefits greater if the "tare and tret" of doing the business could be reduced. It seems a reasonable hope, now that the experimental stages are passed, that this may be done. It is true that some portion of the expenses of in surance companies give to the insured valuable services, such as inspection of houses for fire prevention, medical examina tion, and home nursing to reduce illness and conserve life and these services might be further extended. In the case of all kinds of insurance as yet a large expense for agents has been necessary to educate men to see the value of insur ance and to purchase it, as well as for many other competi tive expenses. It has been found that much of this expense can be saved by insurance in groups (for all employees in an establishment), by compulsory insurance (as of all work ingmen), and by central state administration serving to reg ularlize and unify the organizations. An important problem to be solved in the future is to find methods of insurance equal to or exceeding in their efficiency those now in use, but at much more moderate cost. It is not improbable that uni versal cooperative state insurance, both of life and property, will be worked out. This important question will be further considered in connection with "social insurance" as a mea sure to benefit the working classes.
8 See ch. 12 I 8. REFERENCES.
Dawson, M. M., The business of life insurance. New York. A. S. Barnes & Co. 1905.
Gephart, W. F., Principles of insurance, vol. I, Life. New York. Macmillan. 1917.