Similarly to the annual premium, any other mode of payment may be determined; say, for instance, one single premium for life. At age 90 the present value of all future death-claims is $779.10, and there are 847 persons to provide for the same; therefore, each one must contribute 779.10847, or $0·91987 in advance, that being the one single premium for life.
The limits of a magazine article do not permit more extended illustrations, but the reader can readily reason out for himself how premiums, insuring for life in a limited number of payments, and various other adaptations in vogue, all based upon the same principles, may be arrived at.
Let us now apply the annual premium of $0·49432, as above ascertained, to the insurance fund, and follow its working to the end, computing interest at 412 per cent.:
| Age 90—Living | 847 X ·49432 = | $418 69 | X 1·045 = | $437 53 |
| Death-claims at the end of the year, | 385 00 | |||
| Balance, | 52 53 | |||
| Age 91" | 462 X ·49432 = | $228 37 | ||
| Balance on hand, | 52 53 | |||
| $280.90 | X 1·045 = | $293 55 | ||
| Death-claims at the end of the year, | 246 00 | |||
| Balance, | $47 55 | |||
| Age 92" | 216 X ·49432 = | $106 77 | ||
| Balance on hand, | 47 55 | |||
| $154 32 | X 1-045 = | $161 27 | ||
| Death-claims at the end of the year, | 137 00 | |||
| Balance, | $24 27 | |||
| Age 93" | 79 X ·49432 = | $39 05 | ||
| Balance on hand, | 24 27 | |||
| $63 32 | X 1·045 = | $66 18 | ||
| Death-claims at the end of the year, | 58 00 | |||
| Balance, | $8 18 | |||
| Age 94" | 21 X ·49432 = | $10 38 | ||
| Balance on hand, | 8 18 | |||
| $18 56 | X 1·045 = | $19 39 | ||
| Death-claims at the end of the year, | 18 00 | |||
| Balance, | $1 39 | |||
| Age 95" | 3 X ·49432 = | $1 43 | ||
| Balance on hand, | 1 39 | |||
| $2 87 | X 1·045 = | $3 00 | ||
| Death-claims at the end of the year, | 3 00 | |||
