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

Explanation:

Step1: Identify the compound - interest formula for present value

The compound - interest formula for present value $PV$ is $PV=\frac{FV}{(1 + \frac{r}{n})^{nt}}$, where $FV$ is the future value, $r$ is the annual interest rate (in decimal form), $n$ is the number of times compounded per year, and $t$ is the number of years.

Step2: Convert the given values to the appropriate form

We have $FV = 25000$, $r=0.08$ (since $8%=0.08$), $n = 12$ (compounded monthly), and $t = 5$.

Step3: Substitute the values into the formula

$PV=\frac{25000}{(1+\frac{0.08}{12})^{12\times5}}$. First, calculate the value inside the parentheses: $\frac{0.08}{12}\approx0.00667$, and $1+\frac{0.08}{12}=1.00667$. Then, calculate the exponent: $12\times5 = 60$. So, $(1.00667)^{60}\approx1.489859$. Finally, $PV=\frac{25000}{1.489859}\approx16780$.

Answer:

C. $16,780$