[Footnote 1:  The expense allowance on a plain life policy for $1,000, taken at age 33, would be about $5.29; net premium (com. ex. 4 per cent.), $18.04; total office premium, $23.33; present rate $24.10.]

Taking the case of the single premium endowment policy for $1,000, we find that the following sums are required, each year to provide for the care of the reserve and to pay the government fees (1 per cent. of reserve): 

1st year $6.9982 | 6th year $8.4136 2d " 7.2560 | 7th " 8.7381 3d " 7.5258 | 8th " 9.0781 4th " 7.8082 | 9th " 9.4346 5th " 8.1039 | 10th " 9.8086

The insurance expenses should be covered by the 20 per cent. allowance given below: 

1st year $ .4422 | 6th year $ .2566 2d " .4100 | 7th " .2076 3d " .3762 | 8th " .1556 4th " .3402 | 9th " .0988 5th " .2996 | 10th " .0344

Consequently the total contribution required from this policy each year is: 

1st year $7.4404 | 6th year $8.6702 2d " 7.6660 | 7th " 8.9457 3d " 7.9020 | 8th " 9.2337 4th " 8.1484 | 9th " 9.5334 5th " 8.4034 | 10th " 9.8430

The present value of all these contributions is found to be, at 4 per cent. interest, $71.6394; in other words, this sum paid at the outset, provides a fund from which we may deduct the current expenses of each year in advance, and by accumulating the balance at the assumed rate of interest from year to year, we shall have enough to pay the anticipated expenses, leaving nothing over.

In the above case the sums in hand at the beginning of the year are as follows: 

1st year $71.3694 | 6th year $42.6981 2d " 66.7669 | 7th " 35.3890 3d " 61.4650 | 8th " 27.5009 4th " 55.7055 | 9th " 18.9979 5th " 49.4594 | 10th " 9.8430

We find a somewhat different condition existing during the first years of a 5-year endowment policy.  As there is more insurance and less banking, the requirements are as follows: 

------------+----------+-----------+--------+---------+

| 1 P. Ct. | 20 P. Ct. |        |         |
|   on     |    on     | Total. | Initial |
| Reserve. |   Cost.   |        |  Fund.  |
------------+----------+-----------+--------+---------+
1st year    | $1.5038  |  $1.2572  |$2.7610 |$12.9769 |
2d   "      |  3.0406  |   1.0216  | 4.0622 | 23.6015 |
3d   "      |  4.6503  |    .7852  | 5.4355 | 33.2979 |
4th  "      |  6.3367  |    .5378  | 6.8745 | 41.9538 |
5th  "      |  8.1039  |    .2996  | 8.4035 | 49.4594 |
6th  "      |  8.4136  |    .2566  | 8.6702 | 42.6981 |
7th  "      |  8.7381  |    .2076  | 8.9257 | 35.3890 |
8th  "      |  9.0781  |    .1556  | 9.2337 | 27.5009 |
9th  "      |  9.4346  |    .0988  | 9.5334 | 18.9979 |
10th "      |  9.8086  |    .0344  | 9.8430 |  9.8430 |
------------+----------+-----------+--------+---------+

As the premium payments extend over only five years, the expense contributions must all be paid during that time and are most conveniently made by a uniform addition to the net premium.