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A family plans to send their child to college 15 years from now. They anticipate having...

A family plans to send their child to college 15 years from now. They anticipate having to make 4 equal annual tuition payments in the amount of 28 thousand each, starting at the end of year 15.

They plan to put aside equal annual amounts into an investment account starting immediately, and continuing these contributions until one year before year 15. If they expect to earn 9% per year in the account, what must be the size of each annual payment to their savings account?

Hint: Find the present value of the tuition payments in year (15-1), then find the investment contribution amount such that the future value in year (15-1) is equal to the present value of the tuition.

Hint2: Alternatively, treating contributions as negative outflows, and tuition payments as positive inflows, find contribution amount such that the present value of everything is zero.

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Answer #1

Present value of annual fees at the start of year 15

Using present value function in MS Excel

PV(rate,nper,pmt,fv,type)

rate = 9% nper = 4 pmt =-28000 fv =0 type =1

PV(9%,4,-28000,0,1)

$98,876.25

Present value of annual payment from today

Using present value function in MS Excel

PV(rate,nper,pmt,fv,type)

rate = 9% nper = 15 pv =0 fv = 98876.25 type =1

PMT(9%,15,0,98876.25,1)

($3,089.55)

He should save 3089.55 per month
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