Question
Alex wishes to take out an installment loan to finance the purchase of a lawn mower costing \( \$ 715 \). Her loan requires a \( 2.75 \% \) down payment and equal monthly payments of \( \$ 125.78 \) for 9 months. What is the amount of the finance charge on this loan? Select one: a. \( \$ 425.47 \) b. \( \$ 417.02 \) c. \( \$ 430.64 \) d. \( \$ 436.68 \)
Ask by Mcdonald Santiago. in the United States
Mar 12,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The finance charge on the loan is \$436.68.
Solution
1. Calculate the down payment:
\[
\text{Down Payment} = 0.0275 \times 715 = 19.6625 \approx \$19.66
\]
2. Determine the amount financed (the principal of the loan):
\[
\text{Principal} = 715 - 19.66 = \$695.34
\]
3. Calculate the total amount paid over 9 months:
\[
\text{Total Payments} = 125.78 \times 9 = \$1\,132.02
\]
4. Compute the finance charge by subtracting the principal from the total amount paid:
\[
\text{Finance Charge} = 1\,132.02 - 695.34 = \$436.68
\]
Thus, the amount of the finance charge on the loan is \( \$436.68 \), which corresponds to option d.
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Beyond the Answer
First, let's calculate the down payment Alex needs to make on the lawn mower. The down payment amount is calculated as \(2.75\% \) of \( \$ 715 \): \[ \text{Down Payment} = 0.0275 \times 715 = 19.6625 \approx \$ 19.66 \] Next, we find out how much Alex will need to finance. Subtract the down payment from the total cost: \[ \text{Amount Financed} = 715 - 19.66 = 695.34 \] Now, let's calculate the total payments Alex will make over the 9 months: \[ \text{Total Payments} = 125.78 \times 9 = 1132.02 \] The finance charge is the total payments minus the amount financed: \[ \text{Finance Charge} = 1132.02 - 695.34 \approx 436.68 \] So you should choose option d: \( \$ 436.68 \).
