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Page:Popular Science Monthly Volume 19.djvu/756

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736
THE POPULAR SCIENCE MONTHLY.

It will be observed that, at the end of every year, with the exception of the last one, an unexpended balance remains; dividing this by the number of survivors, we get the amount that applies to each individual living at that period. This is called the net valuation, or, more commonly, the reserve for each policy.

At the ages we have under consideration, the reserve would be as follows:

End of Year. Living. Balance. Reserve for each.
90 462 $52 53 $0·11370
91 216 47 55 0·22014
92 79 24 27 0·30721
93 21 8 18 0·38952
94 3 1 39 0.46261
95 . . . . . . . . . . .
 

While the reserve, as here given, is strictly correct in amount as well as in principle, other methods of calculation are employed in practice; but, for a simple explanation, the plan here adopted will probably serve better than any other. The difficulty has also been that the very high age of ninety had to be selected for the above illustrations, because every computation has to be carried to the end of the table, which would be very lengthy and tedious for a young age. But, the explanation having been given, a closer inspection of the reserves applying to age twenty will afford a broader insight into the subject:

Age 20—Net Annual Premium $11.97 per $1,000.

End of Year. Death-rate, per cent. Cost of insurance. Reserve.
20 ·780 $7 77 $4 74
21 ·785 7 78 9 67
22 ·790 7 79 14 82
 
30 ·843 7 88 64 92
40 ·979 8 27 155 80
44 1·083 8 63 203 05
45 1·116 8 75 215 94
50 1·378 9 83 286 56
60 2·669 14 65 451 27
70 6·199 23 33 623 60
 
94 85·714 47 17 944 97
95 100·000 00 00 1,000 00
 

From the above table it will be seen that the annual premium may be looked upon as consisting of two parts, one defraying the annual cost of insurance dependent upon the death-rate, the other put aside as a reserve fund. Up to a certain period the premium is larger than