Let's walk through the problem step-by-step to find the total installment cost and the finance charge.
### Given Information
1. Amount Financed: \[tex]$3000
2. Down Payment: \$[/tex]500
3. Cash Price: \[tex]$3500
4. Number of Payments: 12
5. Amount of Payment: \$[/tex]275
### Definitions
1. Total Installment Cost: This is the total amount paid over the duration of the loan, including interest and the principal amount financed.
2. Finance Charge: This is the additional amount paid over the amount financed, which typically includes interest and any other fees.
### Total Installment Cost Calculation
First, we calculate the total installment cost by multiplying the number of payments by the amount of each payment.
[tex]\[
\text{Total Installment Cost} = \text{Number of Payments} \times \text{Amount of Payment}
\][/tex]
Given:
[tex]\[
\text{Number of Payments} = 12
\][/tex]
[tex]\[
\text{Amount of Payment} = \$275
\][/tex]
So,
[tex]\[
\text{Total Installment Cost} = 12 \times 275 = \$3300
\][/tex]
### Finance Charge Calculation
Next, we calculate the finance charge by subtracting the amount financed from the total installment cost.
[tex]\[
\text{Finance Charge} = \text{Total Installment Cost} - \text{Amount Financed}
\][/tex]
Given:
[tex]\[
\text{Total Installment Cost} = \$3300
\][/tex]
[tex]\[
\text{Amount Financed} = \$3000
\][/tex]
So,
[tex]\[
\text{Finance Charge} = 3300 - 3000 = \$300
\][/tex]
### Conclusion
- The total installment cost is [tex]\(\$3300\)[/tex].
- The finance charge is [tex]\(\$300\)[/tex].
Therefore, the completed table would look like this:
\begin{tabular}{|c|c|c|c|c|c|c|}
\hline \begin{tabular}{c}
Amount \\
Financed
\end{tabular} & \begin{tabular}{c}
Down \\
Payment
\end{tabular} & \begin{tabular}{c}
Cash \\
Price
\end{tabular} & \begin{tabular}{c}
Number of \\
Payments
\end{tabular} & \begin{tabular}{c}
Amount of \\
Payment
\end{tabular} & \begin{tabular}{c}
Total \\
Installment \\
Cost
\end{tabular} & \begin{tabular}{c}
Finance \\
Charge
\end{tabular} \\
\hline[tex]$\$[/tex] 3000[tex]$ & $[/tex]\[tex]$ 500$[/tex] & [tex]$\$[/tex] 3500[tex]$ & 12 & $[/tex]\[tex]$ 275$[/tex] & [tex]$\$[/tex]3300[tex]$ & $[/tex]\[tex]$300$[/tex] \\
\hline
\end{tabular}
Thus, the total installment cost is [tex]\(\$3300\)[/tex] and the finance charge is [tex]\(\$300\)[/tex].
