Answer to Question #73429 in Financial Math for Jacob

Question

A person wants to buy a life insurance policy that would yield a large enough sum of money to provide semiannual payments for 20 years of $25,000 to surviving members of the family. The payments would begin 6 months from the time of death. It is assumed that interest could be earned on the sum received from the policy at a rate of 8 percent per year compounded semiannually. What amount of insurance should be taken out as to ensure the desired annuity? How much interest will be earned on the policy benefits over the 20 year period?

Answer 1

If it is assumed that interest could be earned on the sum received from the policy at a rate of 8 percent per year compounded semiannually, then using the formula for annuity the amount of insurance is:
PV = 25,000*((1 - 1/1.08^39)/0.08) = $296,965.