PRACTICAL BUSINESS OF LIFE INSURANCE. 737 



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 8944.97, and, with the annual pre- 

 mium of 111.97, due at the beginning of year 95, amounts to $956.94, 

 which, invested at 4-|- per cent, interest, will by the end of the year 

 produce the sum of 81,000. Theoretically, then, there is no loss from 

 a person dying according to the last year of the mortality table, be- 

 cause 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 re- 

 duces 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 88.75, while the death-rate would amount 

 to 811.16 per 81,000. The fact that the reserve has reached 8215.94, 

 and the amount at risk is only 8784.06, reduces the cost from 811.16 

 to 88.75. For the year 94 the death-rate would amount to 8857.14 

 per 81,000, while the cost of insurance is only 847.17, since the reserve 

 has accumulated to 8944.97, leaving but 855.03 at risk. 



As a final illustration of the whole method take the reserve at the 

 end of year 44, 8203.05, add the annual premium of 811.97, being 

 together 8215.02, invest at 4|^ per cent, interest, and it will amount to 

 8224.69 ; deduct the cost of insurance, 88.75 (being the amount at risk 

 8784.06 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 con- 

 fusion, 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 distinc- 

 tively 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 valua- 

 tion, 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 

 VOL. XIX. 47 



