A married couple with a new child wish to save for the child’s college education

Question

A married couple with a new child wish to save for the child’s college education. The current price of a 4-year degree today $88,000. They couple expect that inflation on tuition will be 4% per year for the next 18 years when the child will enter college.

The couple begins with a $10,000 investment in a mutual fund that is expected to earn 7% per year for the next 18 years. How much more will they need to invest (assuming 7%/year return) at the end of each of the 18 years to have an amount equal to pay for the cost of a 4-year education in 18 years? Round your answer to the nearest whole dollar.

Explanation / Answer

First year cost in 18 years, C1 = 88,000 x (1 + 4%)^18 = $178,272

Second year cost, C2 = 178,272 x 1.04 = $185,403

Third year cost, C3 = 185,403 x 1.04 = $192,819

Final year cost, C4 = 192,819 x 1.04 = $200,532

Present Value of cost in 18 years, PV = C1 + C2 / (1 + r) + C3 / (1 + r)^2 + C4 / (1 + r)^3

= 178,272 + 185,403 / 1.07 + 192,819 / 1.07^2 + 200,532 / 1.07^3

= $683,654

Now, annual savings can be calculated using PMT function on a calculator

N = 18, I/Y = 7%, PV = 10,000, FV = -683,654

=> Compute PMT = $19,114

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