CHAPTER X
OFFICE PREMIUMS

1. So far we have been dealing with the pure theory of the value of payments contingent upon the survival or failure of human life. Such payments are however generally made under contracts issued by companies which deal in assurances and annuities. These companies cannot be operated without expense, and so the premiums paid must be "loaded" to cover at least all necessary expenses.

Generally the "net premium" for assurances is calculated at a rate of interest lower than the rate which the company may reasonably expect to earn, also at rates of mortality higher than those which the policy holders will exhibit. The net premium so calculated is then further loaded for expenses with a margin for safety. Periodically return payments or credits are made to policy holders out of the excess interest earned, the saving due to favourable mortality, and any unexpended portion of the additional loading after expenses have been met. These returns are called "Profits" or "Surplus" or "Dividends". The loading for policies which will participate in profits is usually in the form of a percentage addition to the net premium plus a constant addition per $1,000. of assurance; for example, if the net premium was $20.16 per $1,000, and the loading formula was 20% plus $3.00 per $1,000, the office premium for a $5,000 policy would be $100.80 X 1.20+$15.00 = $135.96.

An old English form of loading on the annual net premium for a whole life policy provided for

(1) An initial commission of 1% on the sum assured spread over the life.

2. An annual constant of s of 1% on the sum assured.

(3) An annual charge equivalent to 72% of the net premium plus the loadings (1) and (2).

The office premium would be   \ Px =1.075 I Px+ 01 +.00125

ax

=Px (1.086) +a constant depending on the rate of interest.