13 64 Modified Preliminary Term Reserves Mean Reserves 2
Comparative Reserve Tables © 1915
< Previous > < Next >
r-
43
MODIFIED PRELIMINARY TERM RESERVES.
Dr A. Zillmer, the eminent German actuary, in 1863 first made
suggestion that policies might be valued by the formula:
Ax+ntx+l Sx+n
i e., by valuing the net premium, Px+i, for an age one year higher,
instead of Px, the net premium for the age at entry.
The purpose was to allow for initial expenses in the procurement
of business, which, then as now, were estimated to absorb, together
with mortuary losses for the first year, pretty much all the first year’s
premiums. Dr. Zillmer had in view only ordinary life policies, how-
ever.
Some years later Dr. T. B. Sprague, the most distinguished
actuary of Great Britain, endorsed this plan warmly, as suitable for
use in Great Britain under the conditions which obtained there; but he
made the reservation that it was true only of the whole life plan and
that from larger premiums some reserve should be made the first year.
Precisely the same guarded endorsement of the principle was given
several years ago by Mr. Emory McClintock, actuary of the Mutual
Life Insurance Company of New York.
The reasoning which supports this view seems to be that while
a whole life policy is a life insurance, a limited payment life policy
is an insurance with an addition to the premium each and every year,
including the first, to prepay the whole life premiums that would fall
due after the limited-premium period, and an endowment policy is an
insurance with an addition to the whole life premium each year, includ-
ing the first, to cause the policy to mature at the expiration of the
endowment period. In consequence, there should be reserved from
this excess premium what was designed for the purpose and is required
for its fulfillment.
The foregoing calls for net premiums and reserves by the follow-
ing formulas:
