the same purpose would be accomplished for an equal annual premium of $11.97. The somewhat larger expense in the earlier years of insurance avoids the necessity of enormous charges at the high ages.
The method of arriving at the equal annual premium is based upon very plain reasoning, and can be explained in a simple manner.
Let us assume, with the American Experience Table, that, out of 100,000 persons at age 10, there remain 847 living at age 90, and that they die, according to the table, as follows:
| Age. | Number living. | Number of deaths. |
| 90 | 847 | 385 |
| 91 | 462 | 246 |
| 92 | 216 | 137 |
| 93 | 79 | 58 |
| 94 | 21 | 18 |
| 95 | 3 | 3 |
| 1,628 | 847 |
Were these 847 to form an association, based on the condition that the payments remain equal throughout, and be collected from the survivors at the beginning of each year, and that $1 be paid at the death of each member, there would be 1,628 contributions during the whole period, to provide for 847 death-claims. The requisite annual premium would therefore be 8471628 dollar, or $0.52027 (52 cents). Let us examine the working of this fund:
| Age 90—living, 847 X ·52027 = | contributions | $440 67 | |
| Death-claims | 385 00 | ||
| Balance | $55 67 | ||
| Age 91—living, 462 X ·52027 = | contributions | $240 37 | |
| Balance | 55 67 | ||
| $296 04 | |||
| Death-claims | 246 00 | ||
| Balance | $50 04 | ||
| Age 92—living, 216 X ·52027 = | contributions | $112 38 | |
| Balance | 50 04 | ||
| $162 42 | |||
| Death-claims | 137 00 | ||
| Balance | $25 42 | ||
| Age 93—living, 79 X ·52027 = | contributions | $41 10 | |
| Balance | 25 42 | ||
| $66 52 | |||
| Death-claims | 58 00 | ||
| Balance | $8 52 |
