4. Bruce Wayne is 48 years old and will retire ate the age of 53. He wishes to provide retirement income for himself and is considering an annuity contract with the Targaryen Insurance Company. Such a contract pays him an equal-dollar amount each year between his retirement and death. For this cash-flow stream, he must put up a specific amount of money at the beginning of his retirement. According to actuary tables, his life expectancy is 25 years (age: 78) from the time he retires, and that is the duration on which the insurance company bases its calculations regardless of how long he actually lives.

: a. If Targaryen uses a compound annual interest rate of 7 percent in its calculations, what must Bruce pay at the start 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 25 years.)

b. How much will Bruce need today as a single amount to provide the fund calculated in part (a) if you earn only 12% per year during the 5 years preceding retirement?