The expectation of life is not the probable after-lifetime or the period of probable life which fixes the date at which it will be equally probable, according to the table, that a life, setting out from a certain age, will have died or will have survived. This may be found from the mortality table by observing at what moment of age the number, setting out from a certain age, is reduced just one-half. This period is also not of use in computing net single premiums or present values of annuities.
"The most probable after-lifetime" is yet another ex pression, signifying the period extending from the origi nal age to the age when the number of deaths is greatest in the group.
The test of all net single premiums and present values is this : Will they work out by paying all claims as they fall due? To test this, take a large number and carry their net premiums, less disbursements for claims, for ward with interest at the assumed rate, on the basis that deaths will be according to the mortality table, to the termination of the policy when nothing should be left if it is insurance or annuity that is dealt with, and if it is endowment insurance, a sum sufficient to give each his endowment, with nothing over.
88 Component Parts of Premiums: Another unfortunate misconception was created some years ago by the publica tion in a popular little book on life insurance of a division of premiums into their "elements" or component parts. The division showed the loading and the net premiums and also separated the latter into what were termed "mor tality" and "reserve" elements. The partition of the pre miums showed how much money was required, the first year of insurance only, to pay the current cost, at a net one-year term premium, of the actual insurance for that year that is, of the whole insurance, less the reserve or "self-insurance" at the end of that year and also showed how much of the net premium remained after this was deducted, which was called "reserve" element. If the net premium is properly computed, it is, of course, precisely adequate; and in such case, what is left after providing for the current cost the first year, will, when accumulated at interest for one year, be just sufficient to make good the reserve at the end of the first year.
In like manner for the second year, if the net premium is precisely adequate, the remainder, after deducting the one-year term premium at the attained age for the actual insurance for that year, will also be just sufficient, when added to the reserve at the end of the previous year, the sum being improved at the assumed rate of interest, to produce the reserve at the end of the second year; and so on.
But the "net one-year term premium at the attained age for the actual insurance for that year" is not the same each year. It varies each year; and, as the "deposit for reserve" is the remainder after the "cost of insurance" or so-called "mortality element" is deducted, it must also vary from year to year. Indeed, these are what mathe maticians call "complementary variables," ti. e., they vary inversely, their sum always remaining the 89 same, viz.: the level net premium. And in whole life insurances and term insurances, there comes a time when the "cost of insurance" exceeds the whole net premium and absorbs part of the interest earned upon the already accumulated reserve or even absorbs part of the reserve, besides all of the interest; and, in the last year of a term insurance the "cost of insurance" ab sorbs the entire reserve, the current premium and the in terest. When death occurs, the reserve of the policy goes toward paying the death-claim thereunder, and only the remainder of the claim is paid out of the "costs of insur ance," contributed for that purpose by the premiums of that policy and of other policies.
The following illustration of the varying proportions of the component parts or elements of a premium is taken from "Savings Bank Life Insurance," by Elizur Wright, who first called especial attention to the subject.
90 1 At the end of the 68th year, according to the table, the insured must certainly have died; and the reserve therefore amounts to the face of the policy and is ready to be paid over.