Paul Springer plans to save for a down payment for a house in 10 years. He will be able to invest $12,000 today in a money market account that will pay him an annual interest rate of 5.50 percent on a monthly basis. How much will he have at the end of 10 years?
A) $12,640
B) $20,773
C) $24,859
D) $23,080

Question

Quizplus · Accepted Answer

To find the future value of a single sum, we use the formula FV = PV(1 + r)^n, where FV is the future value, PV is the present value (initial investment), r is the annual interest rate divided by the number of compounding periods per year, and n is the total number of compounding periods. Here, PV = $12,000, r = 5.50% or 0.055 (annual interest rate), and since the interest is compounded monthly, we divide the annual rate by 12 and multiply the number of years by 12 to get n. Thus, r = 0.055/12 per month, and n = 10*12 = 120 months. Plugging these into the formula gives FV = $12,000 * (1 + 0.055/12)^(120) ≈ $20,773.

Paul Springer Plans to Save for a Down Payment for a House