A car loan, or auto loan, is a contract between a borrower and a lender, where the lender provides cash to a borrower to purchase a vehicle on the condition that the borrower pays the lender back with the principal and interest over a certain period of time. The borrower makes payments that are calculated by using the formula for an ordinary annuity. The formula to calculate auto loan payments is shown below:
- PMT = loan payment
- PV = present value (loan amount)
- i = period interest rate expressed as a decimal
- n = number of payments
Suppose you wish to purchase a car that costs $32,000 after tax. The trade-in value of your current car is $10,000, and right now, you only have enough saved to be able to make a down payment of $2,000, which means that you will be financing the remaining $20,000. The bank you are working with has offered you a fixed interest rate of 5.0% annually on a 60-month, $20,000 loan.
We will use the ordinary annuity formula to calculate each monthly payment. The present value here is $20,000, which is the value of the loan. The annual interest rate is 5.0%, so the monthly rate is 5.0% divided by twelve. The number of auto loan payments is 60. The work to calculate monthly payments is shown below:
This means that every month you will pay $377.42 for your shiny new car.