3. A car with a replacement value of $20,000 can be insured against a total loss with an insurance policy sold for a premium of $1200. The insurance company selling the policy and the consumer purchasing the policy agree that there is a 5% probability that the car will be destroyed.

a. What is the actuarial (fair or expected) value of the policy?

b. If the insurance maintains a large, well-diversified portfolio of such policies, what is its expected profit from the sale of this policy?

c. What is the expected profit (or gain or loss) to the consumer from the purchase of this policy?

d. Under what circumstances is the sale of this policy a rational transaction for the insurance company?

e. Under what circumstances is the purchase of this policy a rational transaction for the consumer?