Evaluate. Round dollar amounts to the nearest cent and other answers to the nearest thousandth when necessary.
-$$1,000 \left( 1 + \frac { \mathrm { r } } { \mathrm { k } } \right) ^ { \mathrm { kn } } \text { for } \mathrm { n } = 7 , \mathrm { r } = 5 \% , \mathrm { k } = 2$$
A) $412.97
B) $1412.97
C) $1407.10
D) $1378.51

Question

Quizplus · Accepted Answer

The formula given is for compound interest: $A = P\left(1 + \frac{r}{k}\right)^{kn}$, where $A$ is the amount of money accumulated after n years, including interest, $P$ is the principal amount (\$1,000), $r$ is the annual interest rate (5%, or 0.05 as a decimal), $k$ is the number of times that interest is compounded per year (2), and $n$ is the number of years (7). Plugging in the values: $A = 1000\left(1 + \frac{0.05}{2}\right)^{2*7} = 1000\left(1 + 0.025\right)^{14} = 1000(1.025)^{14} \approx \$1412.97$.

Evaluate Round Dollar Amounts to the Nearest Cent and Other