Question 3 of 5
This quiz: 5 point(s) possible
This questiont 1 point(s) posstble
Determine the monthly payment for the installment loan.
\begin{tabular}{|c|c|c|c|}
\hline \begin{tabular}{l}
Amount \\
Financed (P) \\
$\$ 15.000$
\end{tabular} & \begin{tabular}{l}
Annual \\
Percentage \\
Rate (r) \\
\end{tabular} & \begin{tabular}{l}
Number of \\
Payments per \\
Year $(n)$
\end{tabular} & \begin{tabular}{l}
Time in \\
Years (t)
\end{tabular} \\
\hline$\$ 15,000$ & $5.5 \%$ & 12 & 4 \\
\hline
\end{tabular}

Click the icon to view the partial APR table.

The monthly payment is $\$ \square$.
(Round to the nearest cent as needed.)
Finance Rates

Step 1 ：Given the amount financed \(P = \$15000\), the annual percentage rate \(r = 5.5\% = 0.055\), the number of payments per year \(n = 12\), and the time in years \(t = 4\).

Step 2 ：We first convert the annual interest rate to a monthly interest rate by dividing it by 12. So, \(r_{monthly} = \frac{r_{annual}}{12} = \frac{0.055}{12} = 0.004583333333333333\).

Step 3 ：Then, we calculate the total number of payments, which is the number of payments per year times the number of years. So, \(n = 12 \times 4 = 48\).

Step 4 ：We substitute these values into the formula for the monthly payment of an installment loan: \(M = P \times \frac{r_{monthly} \times (1 + r_{monthly})^n}{(1 + r_{monthly})^n - 1}\).

Step 5 ：Substituting the given values, we get \(M = 15000 \times \frac{0.004583333333333333 \times (1 + 0.004583333333333333)^{48}}{(1 + 0.004583333333333333)^{48} - 1} = 348.84712840864455\).

Step 6 ：Rounding to the nearest cent, we get \(M \approx \$348.85\).

Step 7 ：So, the monthly payment for the installment loan is approximately \$348.85. Therefore, the final answer is \(\boxed{348.85}\).