select the correct answer. to have $25,000 to spend on a new car in five years, how much money should jill…

Explanation:

Step1: Recall compound - interest formula

The compound - interest formula is $A = P(1+\frac{r}{n})^{nt}$, where $A$ is the future value, $P$ is the principal amount (initial investment), $r$ is the annual interest rate (in decimal), $n$ is the number of times interest is compounded per year, and $t$ is the number of years. Here, $A = 25000$, $r=0.08$, $n = 12$ (monthly compounding), and $t = 5$. We need to solve for $P$, so $P=\frac{A}{(1 +\frac{r}{n})^{nt}}$.

Step2: Substitute the values

First, calculate $(1+\frac{r}{n})^{nt}$. Substitute $r = 0.08$, $n=12$, and $t = 5$ into $(1+\frac{r}{n})^{nt}$: [ \begin{align*} (1+\frac{0.08}{12})^{12\times5}&=(1+\frac{0.08}{12})^{60}\ &\approx(1 + 0.00667)^{60}\ \end{align*} ] Using a calculator, $(1 + 0.00667)^{60}\approx1.49083$. Then, $P=\frac{25000}{1.49083}\approx16770\approx16780$.

Answer:

C. $16,780$