The cost of a four-year college education at a public university is expected to

Question

The cost of a four-year college education at a public university is expected to be $7,000 a year in 18 years. How much money should be invested now at 7% so that the balance of the account after 18 years covers the cost a college education?

Hint: Assume that the payments for college are made once a year for four years, so that if, e.g., college costs $N per year in Y years, that a payment of $N will be made in Y years from now; another payment of $N will be made Y+1 years from now; etc.

I'm not getting the answer, which is $7,506.13.

Explanation / Answer

If you go to an annuity table and look up the value of a 7,000 payment for 4 years at 7%, you will get a factor of 3.38721. Multiply this by 7,000 and you will get 23,710.47. This is the amount you have to have at the end of 17 years. So the amount you must invest now to have 23710.47 at the end of 17 years is 23710.47/(1.07)^17. This amount comes out to the 7,506.13 you say is the correct answer.

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