You are given the following information about a policy issued at age 50. The gross premium payable at age 65 is 2000, and a death benefit of 100 000 is payable at age 66 for death occurring between age 65 and 56. A cash value of 20 000 is paid at age 66 for policyholders surrendering at that time. Moreover 15V = 20 300, and 16V = 22 500.
The insurer's best estimate for mortality, withdrawal and interest is given by
q(d)65 = 0.005, q(w)65 = 0.008, i = 0.04.
Anticipated expenses at the beginning of the year are 5% of the gross premium, plus 100. In addition, the expected settlement expenses are 200 for a death claim and 100 for withdrawal.
Now here is the actual experience. Out of 1000 policies at the beginning of the 16th policy year, there were 4 deaths and 10 withdrawals. The actual interest rate earned was 0.048. The actual expenses incurred were 230 per policy at the beginning of the year, including both percentage of premium and fixed expenses, 150 to settle each death claim, and 120 for each withdrawal.
For the year running from time 15 to time 16, calculate the actual profit less the expected profit, and classify this difference by source. For the latter, assume that all expense gains are calculated after the gains from the other sources.