Today is your 30th birthday and you have a dream of retiring on your 65th birthday. You want to put aside however much is necessary on your 31st through 65th birthdays (35 annual payments) to have enough to retire. You’ve estimated that you will live until you are 90 and you want the first withdrawal to occur on your 66th birthday, with the last payment occurring on your 90thbirthday. You think that you will need $150,000 per year to spend during retirement. You estimate constant interest rates of 11.25%. Assuming that you currently have $7,500 deposited in your retirement account, how much must you put aside each year in order to have sufficient money to retire at age 65?


John Keene recently invested $5,000 in a project that is promising to return 6.5 percent per year. The cash flows are expected to be as follows:

End of CashYear Flow 1 $1000 2 950 3 875 4 ???

5 850

Note that the 4th year cash flow is unknown. Assuming the present value of this cash flow stream is $5,000(that is, CF0 = -5000), what is the missing cash flow value (that is, what is the cash flow at the end of the 4th year)?