10.6) Question 1 of 15 This quir: 15 point(s) possible This questlon: 1 point(s) possible Submit quiz Determine the monthly payment for the installment loan. \begin{tabular}{|c|c|c|c|} \hline \begin{tabular}{l} Amount \\ Financed (P) \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$\$ 18,000$ & $55 \%$ & 12 & 3 \\ \hline \end{tabular} Click the icon to view the partial APR table. The monthly payment is $\$$. (Round to the nearest cent as needed.) Finance Rates \begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|} \hline \multirow{3}{*}{\begin{tabular}{l} Number of \\ payments \end{tabular}} & \multicolumn{11}{|c|}{ Annual Percentage Rate Table for Monthly Payment Plans } & \multicolumn{2}{|c|}{ Annual Percentage Rate } \\ \hline & $4.0 \%$ & $4.5 \%$ & $5.0 \%$ & $5.5 \%$ & $6.0 \%$ & $6.5 \%$ & & $7.5 \%$ & $8.0 \%$ & $8.5 \%$ & $9.0 \%$ & $9.5 \%$ & $10.0 \%$ \\ \hline & \multicolumn{13}{|c|}{ (Finance charge per $\$ 100$ of amount financed) } \\ \hline 6 & 1.17 & 1.32 & 1.46 & 1.61 & 1.76 & 1.90 & 2.05 & 2.20 & 2.35 & 2.49 & 2.64 & 279 & 2.93 \\ \hline 12 & 2.18 & 2.45 & 2.73 & 3.00 & 3.28 & 3.56 & 3.83 & 4.11 & 4.39 & 466 & 4.94 & 5.22 & 5.50 \\ \hline 18 & 3.20 & 3.60 & 4.00 & 4.41 & 4.82 & 5.22 & 563 & 6.04 & 6.45 & 686 & 7.28 & 7.69 & 8.10 \\ \hline 24 & 4.22 & 4.75 & 5.29 & 5.83 & 6.37 & 6.91 & 7.45 & 8.00 & 8.54 & 9.09 & 9.64 & 10.19 & 10.75 \\ \hline 30 & 5.25 & 5.92 & 6.59 & 7.26 & 7.94 & 8.61 & 9.30 & 9.98 & 10.66 & 11.35 & 12.04 & 12.74 & 13.43 \\ \hline 36 & 6.29 & 7.09 & 7.90 & 8.71 & 9.52 & 10.34 & 11.16 & 11.98 & 12.81 & 13.64 & 14.48 & 15.32 & 16.16 \\ \hline 48 & 8.38 & 9.46 & 10.54 & 11.63 & 12.73 & 13.83 & 1494 & 1606 & 17.18 & 18.31 & 19.45 & 20.59 & 21.74 \\ \hline 60 & 10.50 & 11.86 & 13.23 & 14.61 & 16.00 & 17.40 & 1881 & 20.23 & 21.66 & 23.10 & 2455 & 26.01 & 27.48 \\ \hline \end{tabular} Print Done Next MacBookPro
Solution
Step 1 ：Convert the annual interest rate to a monthly rate: \(\frac{r}{n} = \frac{55\%}{12} = 0.0458333\) or 4.58333%
Step 2 ：Substitute the given values into the formula: \(M = 18000 \times \left[\frac{0.0458333}{1 - (1 + 0.0458333)^{-12 \times 3}}\right]\)
Step 3 ：Calculate the denominator: \(1 + \frac{r}{n} = 1 + 0.0458333 = 1.0458333\)
Step 4 ：Calculate the power: \((1 + \frac{r}{n})^{-n \times t} = (1.0458333)^{-36} = 0.0301539\)
Step 5 ：Subtract from 1: \(1 - (1 + \frac{r}{n})^{-n \times t} = 1 - 0.0301539 = 0.969846\)
Step 6 ：Calculate the numerator: \(P \times \frac{r}{n} = 18000 \times 0.0458333 = 825\)
Step 7 ：Divide the numerator by the denominator to find the monthly payment: \(M = \frac{825}{0.969846} = 850.37\)
Step 8 ：\(\boxed{M = 850.37}\)
