the actual cost of insurance, but a time arrives when it does not suffice, and then a part of the interest on the reserve must contribute the difference. It will be noticed that the reserve grows constantly, so that by the end of the year 94 it is $944.97, and, with the annual premium of $11.97, due at the beginning of year 95, amounts to $956.94, which, invested at 412 per cent, interest, will by the end of the year produce the sum of $1,000. Theoretically, then, there is no loss from a person dying according to the last year of the mortality table, because the whole amount of the sum insured has already accumulated under the reserve.
This reserve, too, may in a certain sense be said to have a twofold function: it not only provides for the future, but also annually reduces the amount at risk, whereby the cost of insurance becomes less than it would otherwise be. Thus, by the above table for the year 45, the cost of insurance is only $8.75, while the death-rate would amount to $11.16 per $1,000. The fact that the reserve has reached $215.94, and the amount at risk is only $784.06, reduces the cost from $11.16 to $8.75. For the year 94 the death-rate would amount to $857.14 per $1,000, while the cost of insurance is only $47.17, since the reserve has accumulated to $944.97, leaving but $55.03 at risk.
As a final illustration of the whole method take the reserve at the end of year 44, $203.05, add the annual premium of $11.97, being together $215.02, invest at 412 per cent, interest, and it will amount to $224.69; deduct the cost of insurance, $8.75 (being the amount at risk $784.06 X 1·116 per cent., the death-rate), and the balance remaining, 8215.94, is the reserve at the end of year 45.
But, however instructive these details, it may be well, to avoid confusion, to sum up the whole process in the statement that the annual premium is a device to collect a larger amount than the death-rate in the earlier years of insurance, and to use these over-payments, improved at compound interest, to meet the deficiencies which arise in later years. The premium and reserve are so nicely adjusted that they are strictly equitable for the living as well as the dying at every year of life.
The view of the reserve or net valuation here presented is distinctively American. It has been embodied in State legislation, and has an important bearing upon the question of surrender values, presently to be considered. There are other methods for determine: the valuation, which take into account all future payments due, and all losses and expenses to be incurred to the end of the table; but these are questions beyond the scope of this article.
To the net premium of which we have treated, a certain percentage is added to defray expenses and to provide for contingencies; it is called loading, and together with the net premium constitutes what is known as gross or office premium. In mutual companies, the only ones that will be here considered, the loading is made higher than any
