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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.

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ajeigbeibraheem

Answer:

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.

[tex]= [50000 \times 0.005] + [30000 \times 0.01] + [10000 \times 0.02] + [5000 \times 0.05] + [0 \times0.915][/tex]

[tex]= 250 + 300 + 200 + 250 + 0[/tex]

[tex]= 1000[/tex]

Following the given assumptions:

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

[tex]X= \dfrac{Expected \ Claim }{(1 + interest \ rate ) }+(Administrative \ Exp.\times X )+ exp. \ profit \ percentage[/tex]

[tex]X= \dfrac{1000}{(1 + 8\%)}+(10 \%\times X) +( 5\% \times 1000)[/tex]

[tex]X= \dfrac{1000}{(1 + 0.08)}+(0.1 X) + 50[/tex]

[tex]X-0.1X= \dfrac{1000}{(1.08)}+ 50[/tex]

0.9 X = 975.9259

X = 975.9259/0.9

Fair Premium (X) = 1084.36

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