To meet these difficulties in part, various modifications of the flat-rate assessment plan are employed, such as classification by age at entry, so that each member pays a flat-rate according to age at entry; or large initiation fees at entry which form a temporary "reserve" to offset increasing mortality in late years. Finally, the policies may be issued on the natural premium plan, by which the members of each age class pay exactly what the insurance costs for the year. Under this plan the company will remain solvent, but with this and all the other expedients the surviving members are forced to drop the insurance in later years.
Assessment insurance is sold by business companies organized for profit, by fraternal orders, and by various types of mutual organizations. The business companies have had a dismal history of hardship to surviving members and of eventual failure. They are disappearing under the influence of hostile legislation resulting from a better popular knowledge of insurance principles. The fraternal orders combine insurance with other objects of a benevolent and social character. With good management, a favorable death rate, and very low expenses, some of them have provided protection at very low rates for many years. Others have failed with disappointment and disaster to the older members. Still others are struggling with difficulties that presage dissolution. Many now have some form of reserve accumulations, and some have so improved their methods that they closely resemble reserve companies. The assets of all the assessment companies are now $1.37 per $100 of insurance in force, while the legal reserve companies have $22.66. The assessment companies now get 10 per cent of their total incomes from their funded investments, as against 24 per cent for the old-line companies. Even with the favorable conditions under which the fraternal orders conduct their insurance business they are doomed to failure unless they adopt rates and policies based upon adequate reserve accumulations. Many thousands of present members are paying for insurance at rates which will not suffice to meet the future losses. The assessment plan fails to eliminate the one great risk, that of leaving the survivors without insurance in advancing years.
§ 10. # The reserve plan.# The reserve plan, if honestly administered, gives complete protection against 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 advance. In reserve insurance, therefore, the premium never increases from year to year, altho it may be so arranged as to diminish or to cease entirely sometime within the term for which the insurance continues.
The premium must always be fixed in advance. The calculations for determining the premiums on different kinds of insurance policies are many and complex, but all conform to a few general principles. 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 or outstanding insurance. Insurance on the reserve 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 respect to age of insured, number of payments, method of paying the beneficiary, and any other conditions. The premium thus fixed is, however, only a maximum, and usually is reduced as the result of conditions more favorable than those assumed.
§ 11. #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 table most widely used in the United States is the American Experience Table of Mortality, constructed by Sheppard Homans in 1868. The figures of this table, at different years, are given below:
Age Number Living Deaths each year Death rate per 1,000
10 100,000 749 7.49 20 92,637 723 7.80 30 84,441 720 8.43 35 81,822 732 8.95 40 78,106 765 9.79 50 69,804 962 13.78 60 57,917 1,546 26.69 70 38,569 2,391 61.99 80 14,474 2,091 144.47 90 847 385 454.54 95 3 3 1,000.00
The actual number of deaths of any group of insured will not correspond exactly with the figures of any mortality table. But this is not an essential defect of a table so long as the figures of the table are approximately correct and are at least as great in the earlier years as the actual mortality. For any excess of premium thus collected but increases the safety of the insurance and reduces later payments. In fact the mortality in nearly all companies in the United States is much below the figures of the American Experience Table, partly because of the influence of medical selection on the recently insured and partly because of the decided improvement in longevity since the table was constructed.
§ 12. #The single premium for any term.# It is evident that the natural assessment premium payable at the beginning of the year for $1000 of insurance for that year is expressed by the death rate, e.g., at age 35, the payment of $8.95 by each of the 81,822 living at the beginning of the year will provide the $732,000 needed to pay the losses.[5]
In the same manner would be determined the natural assessment premium for each year of insurance. Now, when it is possible to invest the premiums so as to yield a minimum rate of income 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 necessary only to apply the formula of present worth and that of compound interest on investments.[6] Thus the expected losses of any year according to the table of mortality, divided by 1 + rate of yield on investments raised to the power of years distant, equals the present worth of insuring the entire group for that year. The sum of the discounted cost of insurance for all the years of the term divided by the number living at the beginning of the period, gives the single premium for each of the insured. Let P be 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