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# Scientific Life Insurance

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.

## § 1. Reserve life insurance.

The plan of reserve insur ance provides a remedy for the difficulties just indicated. The essential purpose of the reserve plan is to collect during the earlier years of the insurance policy, when the mortality is less, a sum larger than is needed to meet the current losses. This sum, the reserve, is kept invested and accumulating an income sufficient to offset the increase in losses as years ad vance. In reserve insurance, therefore, the premium never increases from year to year, although it may be so arranged as to diminish or to cease entirely some time within the term for which the insurance continues.

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.

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.

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.

## § 9. Insurance assets and investments as savings.

Of all savings institutions insurance probably is destined to be the most important. It is probable that abstinence will more and more express itself not in accumulating large capital sums to provide for one's old age or for survivors, but in providing insurance for dependent survivors, and invalidity and old-age pensions for the insured and others, payable as terminable annuities. In any case, the results to be ex pected in the changing forms and magnitude of private fortunes are certain to be great. The assets of life insurance companies in the United States have already attained the enormous sum of nearly \$7,000,000,000, a sum equal to the reported savings bank deposits. In the last thirty years life insurance assets have more than doubled in each decade, and are now increasing by more than a quarter of a billion dol lars annually. These great funds, which in equity nearly all belong to the policyholders, form already approximately one thirtieth of all the private capital of the country. They are invested in many ways, in real estate, in loans secured by mortgages on real estate, in bonds, municipal, railroad, and industrial. This is one of the ways in which the equit able ownership of the wealth of the nation is being practi cally and effectively socialized. The problem of wise legis lation for these organizations, of their competent and honest management, and of their relation to the social, business, and political life of the nation, is certain to be of ever increas ing importance. We are hardly more than emerging from the experimental stage of insurance, hardly more than at the beginning of its development.

§ 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.

## Huebner, S. S.,

Life insurance. N. Y. Appleton. 1915.