A landscaping company buys a new bulldozer for 561,000.00.
The company makes a down payment of $15,000.00 and finances the balance at 6.0% APR over 60 months.
The monthly payment is $889.33.
A split second after making the 12th payment, the company owner decides to pay the remaining balance on the loan.
What is the total amount due to pay off the balance? Use the actuarial method.
To calculate the total amount due to pay off the remaining balance on the loan after the 12th payment, we need to determine the remaining principal balance at that point.
The loan amount is $561,000.00 - $15,000.00 = $546,000.00
The interest rate is 6.0% per year, or 0.5% per month.
The number of payments remaining after the 12th payment is 60 - 12 = 48 months.
To find the remaining balance after the 12th payment, we use the actuarial method formula:
Remaining balance = P * (1 - (1 + r)^-n) / r
Where:
P = principal balance after the down payment = $546,000.00
r = monthly interest rate = 0.5%
n = number of remaining payments = 48
Remaining balance = $546,000.00 * (1 - (1 + 0.005)^-48) / 0.005
Remaining balance = $546,000.00 * (1 - 0.69547) / 0.005
Remaining balance = $546,000.00 * 0.30453 / 0.005
Remaining balance = $33,116.38
Therefore, the total amount due to pay off the remaining balance on the loan after the 12th payment is $33,116.38.