Question

An insurance company sells a two-year term life insurance policy to an 80-year-old woman. The woman pays a premium of $1,000 per year. If she dies within one of the insured years, the insurance company will pay $20,000 to her beneficiary. According to the US Centers for Disease Control and Prevention, the probability that an 80-year-old woman will be alive one year later is 0.9516 and the probability that an 80-year-old woman will be alive two years later is 0.9512 Find the expected value for the insurance company for that two year term policy.

Answer 1

if the women dies the first year company will pay (20000-1000) to the women, this happens with probability (1-0.9516)

if the women survive the first year, the company will get $1000, this happens with probability 0.9516

if the women dies the second year company will pay (20000-2000) to the women, this happens with probability (1-0.9512)

if the women survive the first year, the company will get $2000, this happens with probability 0.9512

the expected value for the insurance company for that two year term policy is

=$1056