Solve the problem.
-The average cost of a 4-year college education is projected to be $120,000 in 16 years. How much money should be invested now at 6%, compounded quarterly, to provide $120,000 in 16 years?

Question

Quizplus · Accepted Answer

To find the present value (the amount that should be invested now) to achieve a future value of $120,000 in 16 years at an interest rate of 6% compounded quarterly, we use the formula for the present value of a single sum: $PV = \frac{FV}{(1 + r)^n}$, where PV is the present value, FV is the future value, r is the quarterly interest rate (annual rate divided by 4), and n is the total number of compounding periods (years times 4). Here, FV = $120,000, annual interest rate = 6% or 0.06, so r = 0.06/4 = 0.015, and n = 16 * 4 = 64. Plugging these values into the formula gives $PV = \frac{120,000}{(1 + 0.015)^{64}}$, which calculates to approximately $46,275.86.

Solve the Problem. -The Average Cost of a 4-Year College Education Is Projected