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 in terest rate is 6 percent. Calculate the dis- counted 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?

a) $2000

b)  $1,886.7925

C) $2,036.7925

Explanation:

First, the question states to determine the expected claim cost per policy

Expected Claim Cost represents the fund required to be paid by an insurer for a particular contract or a group of contracts as the case maybe. This is usually based on the policy taken.

A) Expected Claim Cost per policy

= (Policy Loss Value A x its probability) + (Policy Loss Value B x its probability) + (Policy Loss Value C x its probability)+(Policy Loss Value D x its probability)+ (Policy Loss Value E x its probability)

= ( (100000 x 0.005 )+ (60000 x 0.010) + (20000 x 0.02) + (10000 x 0.05) + 0 = $2000

Part B: discounted expected claim cost per policy

Since, the sum of $2000 is expected to be paid by the insurer by the end of the year, the interest to be earned based on the rate  (discounting used)

=$2,000 ÷ (1  + 0.06)

= $1,886.7925

Part C:: Determine the Fair Premium

Fair Premium is calculated as follows

The discounted policy claim cost + the Processing Cost per application + The fair profit loading

= $1,886.7925+ $100+50 = $2,036.7925

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