## (Solved) Uneven cash flow James Street's son, Harold, is 10 years old today.

Uneven cash flow

James Streetâ€™s son, Harold, is 10 years old today. Harold, a studious young fellow, is already making plans to go to college on his 18th 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 Haroldâ€™s 11th birthday, one year from now, and the last on his 18th 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 Haroldâ€™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 â€œplanningâ€ account each year to provide for Haroldâ€™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. Â Â

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

Â Â Â Â Â Â Â Â Â Â Â  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 xâ€™s

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