An insurer sells a very large number of policies to people with the following loss distribution:
$100,000 with probability 0.005
$ 60,000 with probability 0.010
Loss = $ 20,000 with probability 0.020
$ 10,000 with probability 0.05
$ 0 with probability 0.915
a. Calculate the expected claim cost per policy.
b. Assume claims are paid one year after premiums are received and that the interest rate is 6 percent. Calculate the discounted expected claim cost per policy.
c. Assume that the only administrative cost is the cost of processing an application, which equals $100 per policy, and that the fair profit loading is $50. What is the fair premium?