Question

A 55-year-old woman purchases a $100,000 term life insurance policy for an annual payment of $456. Based on a life table from the U.S. government, the probability that she will survive the year is 0.9962. Find the expected value of the policy for the insurance company for one year.

Answer 1

P(survive) = 0.9962

P(died) = 1 - 0.9962 = 0.0038

Profit in case of survive = $456

Loss in case of died = 456 - 100000 = -99544

So, E(x) = 0.9962*456 - 99544*0.0038 = $76

Hence, expected value of the policy for the insuracne company for one year is $76.

Please comment if any doubt. Thank you.