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.

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.

Transcript text: 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. 5 . 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 $S$ $\square$

Solution

Solution Steps

Step 1: Calculate the Probability of Death within the Year

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 $1 - 0.999 = 0.000949$.

Step 2: Compute the Expected Payout by the Insurance Company

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 $P \times (1 - S) = 200000 \times 0.000949 = 189.8$.

Step 3: Calculate the Expected Income for the Insurance Company

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

Step 4: Calculate the Expected Value of the Policy to the Insurance Company

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