Question No. 2

Part a

Assume that you will be opening a savings account today by depositing $100,000. The savings account pays 5 percent compound annual interest, and this rate is assumed to remain in effect for all future periods. Four years from today you will withdraw R dollars. You will continue to make additional annual withdrawals of R dollars for a while longer - making your last withdrawal at the end of year 9 - to achieve the following pattern of cash flows over time. (Note: Today is time period zero; one year from today is the end of time period 1; etc.)

How large must R be to leave you with exactly a zero balance after your final R withdrawal is made at the end of year 9? (Tip: Making use of an annuity table or formula will make your work a lot easier!)

Part b

"Want to win a million dollars? Here's how. . . . One winner, chosen at random from all entries, will win a $1,000,000 annuity." That was the statement announcing a contest on the World Wide Web. The contest rules described the "million-dollar prize" in greater detail: "40 annual payments of $25,000 each, which will result in a total payment of $1,000,000. The first payment will be made January 1; subsequent payments will be made each January thereafter." Using a compound annual interest rate of 8 percent, what is the present value of this "million-dollar prize" as of the first installment on January 1?

Part c

Pick a financial intermediary with which you are familiar and explain its economic role. Does it make the financial markets more efficient?