elyn Cohen is 63 years old and recently retired. He wishes to provide retirement income

for himself and is considering an annuity contract with the Philo Life Insurance

Company. Such a contract pays him an equal-dollar amount each year that he lives. For

this cash-flow stream, he must put up a specific amount of money at the beginning.

According to actuary tables, his life expectancy is 15 years, and that is the duration on

which the insurance company bases its calculations regardless of how long he actually

lives.

a. If Philo Life uses a compound annual interest rate of 5 percent in its calculations,

what must Cohen pay at the outset for an annuity to provide him with $10,000 per

year? (Assume that the expected annual payments are at the end of each of the

15 years.)

b. What would be the purchase price if the compound annual interest rate is 10 percent?

c. Cohen had $30,000 to put into an annuity. How much would he receive each year if

the insurance company uses a 5 percent compound annual interest rate in its calculations? A 10 percent compound annual interest rate?