A life insurer has a group of 100 term life insurance policies, each with a face

Question

A life insurer has a group of 100 term life insurance policies, each with a face value of $25,000. The policies in the group are written on single and distinct lives that are assumed to be independent. The probability of a death claim on any given policy in the group during the coming year is .01 . Suppose that the insurer would like to be 99% condent that total premiums exceed total claims. Determine the premium P that must be charged to each policy holder. (Remark: Each policyholder is charged the same amount P and you want to make P as small as you possibly can.)

Explanation / Answer

Sigma = sqrt(npq) = sqrt(100*0.01*0.99) = 0.995

At the 99% confidence level we have z=2.807

Upper bound of no of claims = Mean + z* sigma/sqrt(n) = 100*0.01 + 2.807*0.995/10 = 1.279

Total premium amount = Payout in paying policies

Or, P* 100 = 1.279*25000

P = 319.75

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