An insurer sells a one-year policy to people with the following loss distributions: Size of loss Probability of loss
11,000 0.05
30,000 0.01
10,000 0.02
5,000 0.05
0 0.915

Assume:

a. The fair premiums, the administrative expenses and the profit loading are all paid at the beginning of the year.
b. The claims are paid one year later; 3) The interest rate is 10%
c. The administrative expenses are assumed to be 10% of the expected claim cost
d. The profit loading is assumed to be 2% of the expected claim costs.

Required:
Find the fair premium for the policy.