Find the total installment cost and the finance charge for an installment loan with these conditions.

\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]$3000 & \$[/tex]500 & \[tex]$3500 & 12 & \$[/tex]275 & \[tex]$ & \$[/tex] \\
\hline
\end{tabular}

The total installment cost is \[tex]$\_\_\_\_. The finance charge is \$[/tex]\_\_\_\_.



Answer :

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].