An insurer sells a one-year policy to many people with the following loss distributions:Size of loss Probability of loss50,000 0.00530,000 0.0110,000 0.025,000 0.050 0.915Assume:1) The fair premiums, the administrative expenses and the profit loading are all paid at the beginning of the year;2) The claims are paid one year later;3) The interest rate is 8%;4) The administrative expenses are assumed to be 10% of the fair premiums;5) The profit loading is assumed to be 5% of the expected claim costs. Find the fair premium for the policy.

Explanation:

The table can be computed as follows:

Size of loss       Probability of loss

50000                 0.005

30000                  0.01

10000                  0.02

5000                    0.05

0                           0.915

The expected claim for the cost can be calculated by multiply each of the loss sizes with their corresponding probability loss.

i.e.

Following the given assumptions:

The fair premium(X) of the policy is calculated as follows:

0.9 X = 975.9259

X = 975.9259/0.9

Fair Premium (X) = 1084.36

you have to put the parentheses like this:

in fact, you have to perform the operation inside parentheses first, and then proceed in order: