When it is said that the reserve is that sum which, to gether with future premiums, will enable the company to fulfill its promises, mortality and interest being as as sumed, it can only be meant that the reserve is the aggre gate sum which enables the company to fulfill its aggre gate promises. When the aggregate reserve is apportioned to individual insurances, this statement is not true, as to each of them taken separately. An individual who is about to die will require much more than the premiums he will pay which may be none at all plus his portion of the aggregate reserve, in order to meet the claim under his insurance; and, of course, others which of them it would be inconvenient or even impossible to determine will require corresponding less. The minimum may be taken as the reserve on the basis that, paying net pre miums as per the original computations, the insured is really to be taken as a first-class life, ti. e., equal to one who passes a fresh examination for life insurance. The so-called individual reserve, then, is merely an average, 98 found by partitioning the aggregate reserve; and the sufficiency of reserves is really determined by the aggre gates. At the same time, the aggregate, of course, may at any time be reconstituted by merely adding up these individual portions. That is the usual course.
Two general statements of the prospective view of the reserve are very useful, viz.: First, it is the difference between the net single pre miums for the insurance yet to be furnished and the pres ent values of the net premiums yet to be received.
Second, it is the present value of the excess of the ag gregate net premiums that would be charged for the in surance yet to be furnished, if beginning now, over the aggregate net premiums, which are actually payable and which are fixed according to the ages at the time the in surances were originally taken.
If the gross premiums are assumed in these computa tions to be receivable for the purpose of paying future claims, this is called "a gross premium valuation"; and unless the gross premiums are smaller than the net, the reserve will be smaller than if the net premiums were em ployed in the computations. When net premiums are
employed, it is called "net valuation" or "net premium valuation." A net premium valuation is required in all or nearly all the States of this country as a standard of solvency; it assumes that all the loadings realized upon renewal premiums will be needed to cover future expenses and contingencies. This assumption is, of course, not ac curate; and, as we have seen, it is wholly invalidated if the loadings have been so computed that the margin on renewal premiums is not only to take care of future ex penses and contingencies, but also to make good a defi ciency due to the loading on the first year's premiums being a less amount than the policy's share of the actual expenses of the first year of insurance. But it is the effect of requiring net valuation unless a method of loading, calling for a lower net premium the first year with higher net premiums thereafter, though with gross premiums the same each year, is recognized as admissible.
The usual implication, when gross premiums are level, is that net premiums are also level; and by some actuaries of very high standing it is held that this implication is neces sary and subject to no exception, i e., that it applies in all cases, no matter what the conditions of the policy, even though calling for preliminary term insurance or in some other manner attempting to set up varying net premiums, but with the gross premiums the same each year. It is not denied that valuation on the preliminary term basis that is, with a lower net premium the first year and larger net premiums thereafter will assure solvency; but these actuaries declare that it is in no proper sense "net valua tion" if made by employing such "net premiums" when the gross premiums are in fact level.