Office Premiums   79 The usual formula for whole life policies is

Px =Px(1 +k) +c = (Px+c') (1 +k)

where k, c and c' are constants.

2. Assuming that the expenses of a limited payment or increasing premium policy for a whole life assurance are about the same as for an ordinary whole life policy we have for a limited payment policy

,,Px•ax=Px.ax

and for a policy under which the premium is to be r7rx for n years followed by 7rx for the balance of life

r7rx•ax+rx(ax—ax =Px•ax•

3. If the expenses of a twenty pay life policy are as follows:

(1) an initial commission of 60% of the first premium

(2) initial expenses amounting to $10 per $1,000 assured

(3) annual expenses amounting to

(a) 71%e of the office premium during the premium paying period, and

2. 4 of 1% of the office premium thereafter

(4) settlement expenses amounting to $7.50 per $1,000 assured.

The value of the receipts by the office is 2oPx. ax is where 20Px is the office premium.

The value of the payments to be made by the office is Ax(1.0075)+.6X2oP.t+.01+.075X2oPx•ax2

+.0075 X2oPx(ax —ax)

.01+(1.0075)A,

therefore   2oPx =

.9325Xax —.0075Xax—.6

The office premiums for Endowment policies or for long term temporary assurances may be similarly calculated but the office premiums for short term policies are affected by other than mathematical considerations.