How much should be set aside each month to accumulate $10 000 at the end of year 3 under 12% annual interest rate compounded monthly?
A)$222.14
B)$232.14
C)$242.14
D)$252.14
E)$277.78

Question

Quizplus · Accepted Answer

To accumulate $10,000 at the end of year 3 (36 months) under a 12% annual interest rate compounded monthly, we use the future value of an annuity formula: $FV = P \times \frac{(1 + r)^n - 1}{r}$, where FV is the future value, P is the monthly payment, r is the monthly interest rate (annual rate divided by 12), and n is the total number of payments. Here, r = 0.12/12 = 0.01, n = 36, and FV = $10,000. Rearranging the formula to solve for P gives us $P = FV \times \frac{r}{(1 + r)^n - 1}$. Plugging in the values gives $P = 10000 \times \frac{0.01}{(1 + 0.01)^{36} - 1}$, which calculates to approximately $232.14.

How Much Should Be Set Aside Each Month to Accumulate