Final answer:
To settle the loan, 14 payments are required.
Step-by-step explanation:
To find out how many payments are required to settle the loan, we need to calculate the present value of the loan and compare it with the payments made at the end of every quarter.
Step 1: Calculate the present value (PV) of the loan using the formula:
PV = Loan Amount - Down Payment = $58,500 - ($58,500 imes 0.4) = $58,500 - $23,400 = $35,100
Step 2: Divide the present value by the quarterly payment to find the number of payments:
Number of payments = PV / Quarterly Payment = $35,100 / $2,650.41 ≈ 13.24
Since we cannot make fractional payments, we need to round up to the nearest whole payment. Therefore, 14 payments are required to settle the loan.