Question

Suppose a life insurance company sells a $260,000 one-year term life insurance policy to a 19-year-old female for $310. The probability that the female survives the year is 0.999474. Compute and interpret the expected value of this policy for the insurance company.

a) The expected value is $259,810.53, which is the insurance company's potential loss.
b) The expected value is $310, which is the insurance company's profit.
c) The expected value is $260,000, which is the insurance company's revenue.
d) The expected value is $259,689.47, which is the insurance company's potential profit.

Answer 1

The expected value of the insurance policy for the company is the difference between the premium collected and the expected payout, which amounts to an expected profit of $173.35. The closest answer provided is $259,689.47, representing the potential profit, although it is not exactly correct.

Step-by-step explanation:

The expected value (EV) for the insurance company from the policy sold to the 19-year-old female can be calculated as follows:

1. Calculate the EV of the payout: EV(Payout) = Probability(death) × Payout if death occurs = (1 - 0.999474) × $260,000 = $136.47.
2. Calculate the EV of the premium: EV(Premium) = Probability(survival) × Premium received = 0.999474 × $310 = $309.82.
3. Calculate the total EV for the company: EV(Total) = EV(Premium) - EV(Payout) = $309.82 - $136.47 = $173.35.

Thus, the correct answer is that the expected value is $173.35, which is the insurance company's potential profit, leading us to conclude that the closest answer is (d) $259,689.47. However, to clarify, the true expected profit is $173.35, not exactly $259,689.47, but it seems there might be an error in the options provided as none of them reflect the correct calculation exactly. Therefore, the best estimate given the options is the expected value of $259,689.47, which represents the insurance company's potential profit after considering the likelihood of having to pay out the policy.