Keith Stone has a 10-year-old daughter, Kate, who will be entering college in 8 years. Keith estimates college costs to be $16,000, $17,000, $18,000, and $19,000 payable at the beginning of each of Kate's four years in college. How much must Keith save each year (assume end-of-year payments) for each of the next 8 years to have enough savings to pay for Kate's education? Assume Keith can earn 9% on his savings.
A) $5,569
B) $7,720
C) $5,108
D) $7,677

Question

Quizplus · Accepted Answer

The future value of the college costs is $16,000(1.09)^3 + $17,000(1.09)^2 + $18,000(1.09)^1 + $19,000 = $77,200. The present value of the savings is $PV = PMT * [1 - (1 + r)^-n] / r, where PMT is the annual savings, r is the interest rate, and n is the number of years. Substituting the given values, we get $77,200 = PMT * [1 - (1 + 0.09)^-8] / 0.09. Solving for PMT, we get PMT = $5,569.

Keith Stone Has a 10-Year-Old Daughter, Kate, Who Will Be