How to Calculate Monthly Payment for a Fixed Installment Loan

What is the monthly payment for a 36-month fixed installment loan with a 4% interest rate?

Given that Michael purchases a used car for $16,000, makes a 25% down payment, and finances the balance with a 36-month fixed installment loan at a 4% interest rate, what would be the monthly payment?

Monthly Payment Calculation

The monthly payment for Michael's 36-month fixed installment loan is approximately $353.61. He financed $12,000 at a 4% interest rate, making a 25% down payment on the $16,000 used car.

Explanation

To determine the monthly payment for Michael's 36-month fixed installment loan, we need to calculate the loan amount and then use the formula for calculating monthly payments on a fixed installment loan.

First, let's calculate the loan amount. Michael purchased a used car for $16,000 and paid 25% down. To find the loan amount, we subtract the down payment from the purchase price:

Loan amount = Purchase price - Down payment

Loan amount = $16,000 - (25% of $16,000)

Loan amount = $16,000 - ($4,000)

Loan amount = $12,000

Now that we have the loan amount, we can use the formula for calculating monthly payments on a fixed installment loan. The formula is:

Monthly payment = (Loan amount * Monthly interest rate) / (1 - (1 + Monthly interest rate)^(-Number of months))

In this case, the loan amount is $12,000, the monthly interest rate is 4%, and the number of months is 36.

To convert the annual interest rate of 4% to a monthly interest rate, we divide it by 12:

Monthly interest rate = 4% / 12 = 0.003333

Now, we can substitute these values into the formula and calculate the monthly payment for the loan.

Please note that this calculation assumes monthly compounding interest and no additional fees or charges on the loan.