A farmer buys a new tractor for $38,000. He makes a down payment of $10,000 and finances the balance at 8.5% APR over 48 months. Before making the 12th payment, the farmer decides to pay the remaining balance on the loan. How much interest will the farmer save (use the actuarial method)?

Question

A farmer buys a new tractor for $38,000. He makes a down payment of $10,000 and finances the balance at 8.5% APR over 48 months. Before making the 12th payment, the farmer decides to pay the remaining balance on the loan. How much interest will the farmer save (use the actuarial method)?

Answer 1

I need help on this one please

Answer 2

Sorry -- but I know nothing about the actuarial method.

Answer 3

ok, thanks anyway

Answer 4

To calculate the interest saved by paying off the loan early using the actuarial method, we need to consider the remaining balance at the time of payment.

First, let's calculate the loan amount by subtracting the down payment from the original purchase price:

Loan Amount = Purchase Price - Down Payment
Loan Amount = $38,000 - $10,000
Loan Amount = $28,000

Next, let's calculate the interest rate per month by dividing the annual percentage rate (APR) by 12:

Monthly Interest Rate = APR / 12
Monthly Interest Rate = 8.5% / 12 = 0.0070833

We can now use the formula for calculating the remaining balance on a loan with the actuarial method:

Remaining Balance = Loan Amount * (1 + Monthly Interest Rate)^Number of Payments - Payment Amount * [(1 + Monthly Interest Rate)^Number of Payments - 1] / Monthly Interest Rate

Since the farmer decides to pay off the remaining balance after making 12 payments, we'll substitute Number of Payments with 12. We'll also set Payment Amount to 0 since the farmer pays off the remaining balance.

Remaining Balance = $28,000 * (1 + 0.0070833)^12 - 0 * [(1 + 0.0070833)^12 - 1] / 0.0070833

Calculating this equation will give us the remaining balance on the loan after 12 months. Let's perform the calculation:

Remaining Balance = $28,000 * (1 + 0.0070833)^12 - 0 * [(1 + 0.0070833)^12 - 1] / 0.0070833
Remaining Balance = $24,745.73

Now, to calculate the interest saved, we subtract the remaining balance from the original loan amount:

Interest Saved = Loan Amount - Remaining Balance
Interest Saved = $28,000 - $24,745.73
Interest Saved = $3,254.27

Therefore, the farmer will save $3,254.27 in interest by paying off the loan early using the actuarial method.