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.

The present value of the amounts in column 3 is $60.0819, and the
equivalent annuity for five years is $12.9769. This amount, received
for five consecutive years, will put the company in funds to pay
current expenses and leave a reserve of $42.6981 at the beginning of
the sixth year, which, as we have seen in the analysis of the
single-premium policy, is the sum required for future expenses on the
paid up basis.

In like manner we find that the 10-year annuity equivalent to the
present value of the annual contributions in the case of an
annual-payment policy is $5.534, thus:

------------+----------+-----------+--------+---------+
| 1 P. Ct. | 20 P. Ct. | | |
| on | on | Total. | Initial |
| Reserve. | Cost. | | Fund. |
------------+----------+-----------+--------+---------+
1st year | $.8234 | $1.3514 |$2.1748 |$ 5.5340 |
2d " | 1.6473 | 1.2478 | 2.8951 | 9.0275 |
3d " | 2.5096 | 1.1388 | 3.6484 | 11.9116 |
4th " | 3.4124 | 1.0210 | 4.4334 | 14.1277 |
5th " | 4.3572 | .8916 | 5.2488 | 15.6161 |
6th " | 5.3479 | .7534 | 6.1013 | 16.3160 |
7th " | 6.3853 | .5966 | 6.9819 | 16.1572 |
8th " | 7.4726 | .4270 | 7.8996 | 15.0763 |
9th " | 8.6127 | .2418 | 8.8545 | 12.9977 |
10th " | 9.