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A life insurance company sells annuities to men aged exactly 60. Each policyholder pays a single net premium, P, and then receives an annuity of $30,000 a year in arrear (so that the first annuity payment is on the 61st birthday). Assume that mortality follows the Standard Select Life Table, and that the interest rate is 5% per year. (a) Calculate P. (b) Calculate the probability that the present value of profit on a single policy is positive.

A life insurance company sells annuities to men aged exactly 60. Each policyholder pays a single net premium, P, and then receives an annuity of $30,000 a year in arrear (so that the first annuity payment is on the 61st birthday). Assume that mortality follows the Standard Select Life Table, and that the interest rate is 5% per year. (a) Calculate P. (b) Calculate the probability that the present value of profit on a single policy is positive.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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3. (AMLCR) 6.16. A life insurance company sells annuities to men aged exactly 60. Each policyholder pays a single net premium, P, and then receives an annuity of $30,000 a year in arrear (so that the first annuity payment is on the 61st birthday). Assume that mortality follows the Standard Select Life Table, and that the interest rate is 5% per year. (a) Calculate P. (b) Calculate the probability that the present value of profit on a single policy is positive. (c) Calculate the standard deviation of the present value of profit on a single policy. (d) Now suppose that the office sells 1,000 such annuities simultaneously to independent lives. Calculate the value of P such that the probability that the present value of the profit to the insurance company is positive is 95%.
Transcribed Image Text:3. (AMLCR) 6.16. A life insurance company sells annuities to men aged exactly 60. Each policyholder pays a single net premium, P, and then receives an annuity of $30,000 a year in arrear (so that the first annuity payment is on the 61st birthday). Assume that mortality follows the Standard Select Life Table, and that the interest rate is 5% per year. (a) Calculate P. (b) Calculate the probability that the present value of profit on a single policy is positive. (c) Calculate the standard deviation of the present value of profit on a single policy. (d) Now suppose that the office sells 1,000 such annuities simultaneously to independent lives. Calculate the value of P such that the probability that the present value of the profit to the insurance company is positive is 95%.
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