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  "     |  9.8086  |    .0344  | 9.8430 |  9.8430 |
------------+----------+-----------+--------+---------+
>
The present value of the ten yearly expense items
given in the “total” column above is $46.6812,
which is equal to a ten-year annuity of $5.534. 
The several premiums stand now as follows: 
    ENDOWMENT:  $1,000, AGE
30, PAYABLE AT DEATH OR 40
Net Prem.[2] Margin. 
   Total.
At single premium.   $687.228   $71.6394   $758.8674

At five premiums.     150.615    12.9769    163.5939

At annual premiums.    84.172     5.5340     89.7060
[Footnote 2:  Thirty American offices.  Discount
from middle of year, Vx-1/2 or (M x 1.01961) / Dx.]
By the actuaries’ rate we have, with the customary
loading for expense: 
  Single premium:  $721.66 (loaded,
$34.36).  Five premiums, $188.70

  (loaded $37.78).  Annual premium,
$105.65 (loaded $21.11).
Admitting the correctness of the new method, we must
conclude that the present single premium is not sufficiently
loaded to cover its own expenses, while the annual
payment policy pays more than its just share. 
A prominent and thoroughly informed life insurance
president says in this connection:  “Many
of the policies, particularly the short term endowments,
are charged with too high a percentage of expenses
to prove a good investment at maturity or profitable
to the insured in case of surrender.”  This
is not to be wondered at when the applicant for a
10-year endowment policy sees at a glance that he must
pay, in the gross, more than is returned unless he
should die in the interim, in which case a plain “life”
or “term” policy would have answered the
purpose.  Under the new system of assessing expenses
one form is as desirable as another, from the standpoint
of the insured or the company.