Chris is planning for her son's college education to begin five years from today. She estimates the yearly tuition, books, and living expenses to be $5,000 per year for a four year degree. How much must Chris deposit today, at an interest rate of 8 percent, for her son to be able to withdraw $5,000 per year for four years of college?

Question

Quizplus · Accepted Answer

The first thing we need to do is calculate the future value of the college expenses in five years, using the formula:

FV = PV x (1 + r)^n

Where FV is the future value, PV is the present value, r is the interest rate, and n is the number of years.

FV = $5,000 x 4 x (1 + 0.08)^4 = $27,657.60

This means that in five years, Chris will need $27,657.60 to pay for her son's college expenses over four years.

Now we need to calculate the present value of this future amount, again using the formula:

PV = FV / (1 + r)^n

PV = $27,657.60 / (1 + 0.08)^5 = $19,419.50

So Chris would need to deposit $19,419.50 today at an interest rate of 8 percent in order for her son to be able to withdraw $5,000 per year for four years of college.

The closest answer choice to this amount is D, $12,172, which is clearly too low. Answer choice C, $20,000, is too high. Answer choice A, $13,620, is also too low. The only answer choice remaining is B, $39,520, which is clearly too high. Therefore, the correct answer is D, $12,172.

Chris Is Planning for Her Son's College Education to Begin