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Rate-Making Term and Whole Life and Limited Payment

RATE-MAKING TERM AND WHOLE LIFE AND LIMITED PAYMENT. The very earliest form in which is found what is now known as regular life insurance, that is, life insurance of a fixed amount and for a fixed premium, is that of term insurance or insurance for a limited period. For a long time such policies were always issued without the privi lege of renewal and either for one premium or for annual or other periodical premiums.

How to compute the net premium for an insurance of one year has already been shown. To find the net single premium, payable in advance, for an insurance of \$1,000 for two years from age so, assume that there are 100,000 such insurances; that deaths will be as per the Actuaries' Table; that money will earn interest at 4 per cent. per annum, until disbursed; and that death claims are payable at the end of the year in which death occurs. Then the payments will be \$676,000 at the end of one year and at the end of two years, or \$1,35o,000 in all. If no interest were earned, each would need to pay in his share of this sum, or \$1,35o,000 100,000 = \$13.50. But since the funds are to earn 4 per cent., annually com pounded, the aggregate sum required to be paid in advance to accumulate to sufficient to pay the claims as they fall due, is \$676,000 1.04 and \$674,000 1.o816 that is, these sums discounted for one and two years, respectively.

If, then, each of the xoo,000 entrants deposits his share in advance, he will only need to pay in \$1,273,151 ÷ Poo, 000 = \$12.73 instead of \$13.50; that is, \$12.73 will be the net single premium for an insurance of \$1,000 for two rears from age 1o.

If the net single premium for an insurance for three years is desired, it is only necessary to add the claims pay able at the end of three years, discounted three years (\$672,00o ÷ 1.1249), before dividing by 100,000. And in like manner to get the net single premium for an in surance for four or five or any number of years.

This rule may be stated in a general form, thus : The net single premium for a term insurance of \$1,000 for three years is found by multiplying the probability of dying the first year (676 100,000) by the value of \$1,000, discounted one year (\$1,000 ÷ 1.04); by multi

plying the probability of dying the second year (674 100,000) by the value of \$1,00o discounted two years (\$1,000 -+- 1.0816), and by multiplying the probability of dying the third year (672 100,000) by the value of \$1,000, discounted three years (\$1,000 ÷ 1.1249) and by adding the products together.

And, generally, the net single premium of an insurance of \$1 for a term of years may be found by multiplying the probability of dying the first year by the discounted value of \$1 due in one year; by multiplying the probability of dying the second year by the discounted value of \$x due in two years, and so on for the term; and by adding these products together.

It must be noted that by the probability of dying the second year, that is, at age II; or the third year, that is, at age 12, etc., the probability that one who is II or 12, or as the case may be, will die within one year, is not meant; but, instead, the probability that one who is now Jo will die in his nth year of age, or his 12th year of age, or as the case may be. Thus the probability, by the Actuaries' Table, of one who is II years of age dying within one year is 674 99324; but the probability of one who is now DI dying in his t ith year is 674 ÷- 100,o0o.

If the term is life, these computations must be made for every year up to the highest age in the table, plus 1, less the age at admission; that is, for age 1o, up to 86 (i. e., 96 1o) years by the American Experience Table, and 90 (1. e., 100 io) years by the Actuaries' Table.

It will be observed that this is one year more than in a life annuity. The reason is that of the entire number none survives by one year the extreme age to whom an annuity payment would be made; but, on the other hand, there are deaths in the year of the extreme age, so that on the assumption of all deaths at the, end of the year, in surance payments would be made at the end of that year.

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