Uneven cash flow

James Street?s son, Harold, is 10 years old today. Harold, a studious young fellow, is already making plans to go to college on his 18^th birthday, and his father wants to start putting money away now for that purpose. Street estimates that Harold will need $18,000, $19,000, $20,000 and #21,000 for his freshman, sophomore, junior, and senior years, respectively. He plans on making these amounts available to Harold at the beginning of each of these years.

Street would like to make eight annual deposits (the first of which would be made on Harold?s 11^th birthday, one year from now, and the last on his 18^th birthday, the day he leaves for college) in an account earning 10 percent annually. He wants the account to eventually be worth enough to just pay for Harold?s college expense. Any balance remaining in the account will continue to earn the 10 percent.

How much will Street have to deposit in this ?planning? account each year to provide for Harold?s education? Hints: Calculate the present value of all the year-end needs. The 8-year deposit (year-end payment) is an annuity. The present value of the annuity should equal to the present value of the college expenses.

The present value of year-end needs (Y) = ?

Hint: the sum of the present value for each piece of withdraw.

The year-end payment (x) = ?

Hint: with the result of (Y) from previous step, you can transform the questions into an annuity problem, with Y as the present value of the annuity of x?s