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 191 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 i 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.