Find the amount of each regular payment to provide $14,000 in 10 years, at an annual rate r = 8%, compounded annually.
A)$1,458.28
B)$966.41
C)$979.21
D)$971.86
E)$977.96

Question

Quizplus · Accepted Answer

To find the amount of each regular payment (PMT) to provide a future value (FV) of $14,000 in 10 years at an annual interest rate (r) of 8%, compounded annually, we use the future value of an annuity formula: $FV = PMT \times \frac{(1 + r)^n - 1}{r}$, where $n$ is the number of periods (years in this case), $r$ is the annual interest rate as a decimal, and $PMT$ is the payment amount per period. Rearranging the formula to solve for PMT gives us: $PMT = FV \times \frac{r}{(1 + r)^n - 1}$. Plugging in the values: $PMT = 14000 \times \frac{0.08}{(1 + 0.08)^{10} - 1}$, calculating this gives us approximately $966.41, which matches option B.

Find the Amount of Each Regular Payment to Provide $14,000