5) choose the closest correct answer. how muc...
5) choose the closest correct answer. how much will the monthly payment be for a 5 - year - old used car with 56,235 miles that is priced at $10,995? the current finance rate is 36 months at 4.35%. $105.42 $325.15 $245.27 $518.70
Answer
# Explanation:
## Step1: Identify loan - related values
Loan amount $P = 10995$, number of months $n=36$, annual interest rate $r = 4.35\%=0.0435$, monthly interest rate $i=\frac{r}{12}=\frac{0.0435}{12}= 0.003625$.
## Step2: Use the loan - payment formula
The formula for the monthly payment of a loan is $M = P\times\frac{i(1 + i)^n}{(1 + i)^n-1}$.
Substitute the values:
\[
\begin{align*}
M&=10995\times\frac{0.003625\times(1 + 0.003625)^{36}}{(1 + 0.003625)^{36}-1}\\
\end{align*}
\]
First, calculate $(1 + 0.003625)^{36}$. Let $x=(1 + 0.003625)^{36}$. Using the formula $a^n=e^{n\ln(a)}$, we have $\ln(x)=36\times\ln(1.003625)\approx36\times0.003618 = 0.130248$, so $x = e^{0.130248}\approx1.1399$.
\[
\begin{align*}
M&=10995\times\frac{0.003625\times1.1399}{1.1399 - 1}\\
&=10995\times\frac{0.003625\times1.1399}{0.1399}\\
&=10995\times\frac{0.004125}{0.1399}\\
&=10995\times0.029486\\
&\approx325.15
\end{align*}
\]
# Answer:
$325.15$