For a block of fully discrete whole life insurance of 1,000 on N lives age 60, you are given:

The future lifetimes are independent.

A₆₀= 0.29 and ²A₆₀= 0.11

i= 4%

P is the annual premium for each policyholder.

(a) If N= 500, use normal approximation to calculate the annual premium P such that the probability of a positive total loss is 2.5%.

(b) If P= 15, use normal approximation to calculate the minimum number of policies N the insurer must issue so that the probability of a positive total loss is less than or equal to 2.5%.