Term life insurance & death probability

Question

A man wishes to purchase a 5-year term-life insurance policy that will pay the beneficiary $25,000 in the event that the man's death occurs during the next 5 years. Using life insurance tables, he determines that the probability that he will live another 5 years is 0.96. What is the minimum amount that he can expect to pay for his premium? Hint: The minimum premium occurs when the insurance company's expected profit is zero.

Answer 1

If p is the minimum premium then

there is a 0.04 chance that he will die in the next 5 years, and 0.96 chance that he will live

So companies expected profit = 0.96p - 0.04 x 25000 = 0 giving p = 1041.67