Thelma 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, assuming th expenses incur only at the end of the year. How much must Thelma 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

To solve this, we use the present value of an annuity formula, which is PV = PMT * [(1 - (1 + r)^-n) / r], where PMT is the annual payment ($5,000), r is the annual interest rate (8% or 0.08), and n is the number of periods (4 years). However, since the withdrawals start in 5 years, we also need to discount the result back to today, which is done by dividing by (1 + r)^n, where n in this case is 5 years. The calculation is as follows: PV = $5,000 * [(1 - (1 + 0.08)^-4) / 0.08] = $16,319.48 as the present value of the annuity at the beginning of the college period. To find how much Thelma must deposit today, we discount this amount back 5 years: $16,319.48 / (1 + 0.08)^5 = $11,270.

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