Question 3 (2 points) Solomon is taking out a \( \$ 15,320,2 \)-year loan with an APR of \( 3.29 \% \). What will be the finance charge for this loan to the nearest dollar? a \( \$ 315 \) b \( \$ 351 \) \& \( \$ 531 \)

To calculate the finance charge for Solomon's loan, we'll use the formula for the total finance charge on an installment loan: \[ \text{Finance Charge} = \text{Total Payments} - \text{Principal} \] **Given:** - **Principal (P):** \$15,320 - **Annual Percentage Rate (APR):** 3.29% - **Loan Term:** 2 years (24 months) **Step 1: Calculate the Monthly Interest Rate** \[ \text{Monthly Rate} = \frac{3.29\%}{12} = 0.2742\% \text{ per month} \] \[ \text{Monthly Rate (decimal)} = 0.002742 \] **Step 2: Calculate Monthly Payment using the Amortization Formula** \[ \text{Monthly Payment} = P \times \frac{r(1 + r)^n}{(1 + r)^n - 1} \] Where: - \( r \) = monthly interest rate - \( n \) = total number of payments \[ \text{Monthly Payment} = 15320 \times \frac{0.002742(1 + 0.002742)^{24}}{(1 + 0.002742)^{24} - 1} \approx \$661 \] **Step 3: Calculate Total Payments Over the Loan Term** \[ \text{Total Payments} = \$661 \times 24 \approx \$15,864 \] **Step 4: Determine the Finance Charge** \[ \text{Finance Charge} = \$15,864 - \$15,320 = \$544 \] Rounding to the nearest dollar, the finance charge is approximately **\$544**. The closest provided option is: **Answer:** & \( \$ 531 \)