Question

A 33-year-old woman purchases a $100,000 term life insurance policy for an annual payment of $490. Based on a period life table for the U.S. government, the probability that she will survive the year is 0.999051. Find the expected value of the policy for the insurance company. Round to two decimal places for currency problems.

Answer 1

Given that, P(woman survive the year) = 0.999051 and

P(woman died in the year) = 1 - 0.999051 = 0.000949

If woman survive company will get, $490 and if she died then company have to pay (100000 - 490) = $99510

Therefore, the expected value of the policy for the insurance company is,

= (490 * 0.999051) + (-99510 * 0.000949)

= (490 * 0.999051) - (99510 * 0.000949)

= 489.53499 - 94.43499

= 395.10

=> Expected value = $395.10

Answer : $395.10