You need to have $15,000 in five years to pay off a home equity loan. You can invest in an account that pays 5.75 percent compounded quarterly. How much will you have to invest today to attain your target in five years? (Round to the nearest dollar.)
A) $4,903
B) $11,275
C) $13,184
D) $12,250

Question

Quizplus · Accepted Answer

To find out how much you need to invest today to reach a future sum with an account that compounds interest quarterly, you can use the formula for the present value of a future sum: $PV = \frac{FV}{(1 + r)^n}$, where PV is the present value (amount you need to invest today), FV is the future value ($15,000), r is the quarterly interest rate (annual rate divided by 4), and n is the total number of compounding periods (years times 4, since it compounds quarterly). Given an annual interest rate of 5.75%, the quarterly rate is $0.0575 / 4 = 0.014375$, and with 5 years of compounding quarterly, $n = 5 \times 4 = 20$. Plugging these values into the formula gives $PV = \frac{15,000}{(1 + 0.014375)^{20}}$, which when calculated and rounded to the nearest dollar, gives approximately $11,275.

You Need to Have $15,000 in Five Years to Pay