Sec. 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.

Sec. 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