This is Actuarial Mathematics. A is the actuarial present value.

sub_10L is the value of the future loss at time 10 on a fully discrete whole life insurance of 1 issued to age 45, given survival to time 10 (based on net premium).

You are given:

(i) p54 = 0.9

(ii) A45 = 0.28

(iii) A54 = 0.4

(iv) ^2A54 = 0.25

(v) i = 1/9

Calculate Var(sub_10L)

The answer is 0.165