Adrea wishes to take out an installment loan to finance the purchase of a small antique dinning set costing \( \$ 71,500 \). Her loan requires a \( 22.5 \% \) down payment and equal payments of \( \$ 2,557 \) for 40 months. What is the amount of the finance charge on this loan. Select one: a. \( \$ 46,867.50 \) b. \( \$ 45,695.27 \) c. \( \$ 43,580.64 \) d. \( \$ 48,350.00 \)

To calculate the amount of the finance charge on this installment loan, we first need to determine the total cost of the loan with the down payment and the payments made over the loan term. The down payment is \( 22.5\% \) of \( \$71,500 \), which is: \[ \text{Down Payment} = 0.225 \times 71,500 = 16,087.50 \] The total payments over 40 months at \( \$ 2,557 \) each is: \[ \text{Total Payments} = 2,557 \times 40 = 102,280 \] The total amount financed (which is the purchase price minus the down payment) is: \[ \text{Amount Financed} = 71,500 - 16,087.50 = 55,412.50 \] Now, to find the finance charge, we subtract the amount financed from the total payments: \[ \text{Finance Charge} = \text{Total Payments} - \text{Amount Financed} = 102,280 - 55,412.50 = 46,867.50 \] Thus, the finance charge on this loan is \( \$ 46,867.50 \), leading us to option (a).