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25 September, 22:22

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?

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  1. 25 September, 23:47
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    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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