Questions: Life Insurance A 38-year-old woman purchases a 200,000 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. The expected value of the policy for the insurance company is S.

Solution Steps

The probability that the policyholder will die within the year is calculated as \(1 - S\), where \(S\) is the survival probability. Given \(S = 0.999\), the probability of death is \(1 - 0.999 = 0.000949\).

The expected payout is the payout amount (\(P\)) multiplied by the probability of death. Given \(P = 200000\) and the probability of death calculated in Step 1, the expected payout is \(P \times (1 - S) = 200000 \times 0.000949 = 189.8\).

The expected income from the annual premium (\(A\)) is a fixed amount paid by the policyholder. Given \(A = 490\), the expected income is \(A = 490\).

The expected value (\(EV\)) of the policy to the insurance company is the difference between the expected income and the expected payout: \(EV = A - (P \times (1 - S)) = 490 - (200000 \times 0.000949) = 300.2\).

Final Answer: The expected value of the policy to the insurance company, rounded to 2 decimal places, is 300.2.