How to calculate a car payment

The formula

Car payment = P × r ÷ (1 − (1 + r)^−n), where P is the amount financed, r is the monthly interest rate (APR divided by 12) and n is the number of months.

Example: $25,000 at 7% for 60 months. The monthly rate is 0.07 ÷ 12 = 0.005833. (1.005833)^−60 is about 0.7054, so the denominator is 1 − 0.7054 = 0.2946. The payment is 25,000 × 0.005833 ÷ 0.2946 = $495.03.

From payment to total cost

Multiply the payment by the number of months to get the total repaid: $495.03 × 60 = $29,701.80. Subtract the amount financed to get the interest: $4,701.80. In the first month, interest is 25,000 × 0.005833 = $145.83 and $349.20 goes to principal. Each month the interest portion shrinks a little as the balance falls.

$25,000 financed: payment by loan length

At 7% APR, financing $25,000 costs $495.03 a month over 60 months and $377.32 over 84 months. The longer loan lowers the payment by $117.71 but adds $1,993 in interest. Going the other way, 36 months raises the payment to $771.93 and cuts total interest to $2,789.

How the interest rate changes a 5-year loan

On the same $25,000 over 5 years, each full percentage point of APR moves the payment by about $11.88 and total interest by about $713. Rates depend on your credit score, the loan term and whether the car is new or used, so get a pre-approval from a bank or credit union before you walk into a dealership.

What a bigger down payment does

A down payment reduces what you finance, which cuts both the payment and the interest, and it protects you from owing more than the car is worth early in the loan, when new cars depreciate fastest. Here is the same $25,000 car at 7% over 5 years with different down payments.

Paying extra

Adding $100 a month to this loan would pay it off 11 months sooner and save $939 in interest, as long as your lender applies extra money to principal and charges no prepayment penalty. Ask before you start.

Can you afford a $25,000 car?

A common rule of thumb, the 20/4/10 guideline, suggests 20% down, a term of at most 4 years and total car costs under 10% of gross income. On payment alone, $495.03 a month points to a gross income of roughly $59,400 a year to stay at 10%, before insurance, fuel and maintenance. Here the down payment is 0% rather than 20% and the term of 60 months is longer than 48, which means a smaller monthly payment in exchange for more interest and a longer period of debt.

Will you owe more than the car is worth?

New cars commonly lose around 20% of their value in the first year and roughly 15% a year after that, though this varies by model. Using that rough rule on a $25,000 car, you would likely owe more than the car is worth until about year 2. Gap insurance can cover the difference if the car is totaled while you are underwater.