Car loan calculator: payment and total cost

Enter the amount you are financing, the annual rate on the loan and the term in years. It returns the monthly payment, the total you hand over by the last payment, the interest inside that total, and what you still owe after twelve payments.

The figure to enter is the amount financed, not the sticker price. In the United States, sales tax, registration and dealer fees are commonly rolled into the loan, and so are the products sold at the finance desk: gap cover, an extended warranty, credit life or disability cover. A deposit or a trade-in comes off. What is left after all of that is the number the payment is calculated from, so the payment on a car you thought cost one amount is set by a different, usually larger one. Elsewhere the split differs, and in some places tax falls due up front and never enters the loan at all, so work from the amount financed printed on your own agreement rather than from the price on the window.

A car loan is a level payment loan, the same shape as a mortgage over a much shorter term:

$$M = P \times \frac{i}{1 - (1 + i)^{-n}}$$

$P$ is the amount financed, $i$ is the monthly rate, and $n$ is the number of monthly payments. A 5 year loan at 8.5 percent has $i = 0.085/12 = 0.00708333$ and $n = 60$.

Dividing by 12 is what makes that a monthly rate, and it only works because the quoted figure is a nominal annual rate rather than an effective one. Twelve months of 0.708333 percent compound to 8.84 percent, so the headline 8.5 percent and the rate the balance actually grows at are two different numbers. In the United States a car loan is quoted as an APR, which is nominal and folds certain finance charges in, while a deposit account is quoted as an APY, which is effective and folds compounding in. The APR against APY calculator shows the size of that gap. Enter the rate the way the lender wrote it and let the formula do the dividing.

The payment stays the same every month, but the job it does changes. Interest is charged on what you still owe, so the interest share is largest at the start and shrinks only as the balance falls. How amortisation works walks through that split payment by payment.

Two numbers come out of any loan offer, and they answer different questions. The monthly payment says whether the loan fits your month. The total repaid says what the car actually cost you.

The term pulls those two apart. On the worked examples below, the same $32,000 at the same rate costs $7,391.74 in interest over five years and $10,568.47 over seven, while the monthly payment drops from $656.53 to $506.77. Nothing about the car changed. Lenders in the United States often price a longer term at a higher rate as well, which widens the gap further than these figures show.

So compare offers on the total repaid, then check the payment fits. The general version of this maths is the loan payment calculator, and whether the payment fits your income at all is the debt-to-income calculator.

A car loan is a secured loan, and the car is the collateral. That collateral loses value with age and mileage, which is what makes a long car loan a different animal from a long mortgage.

Two lines move at once. Your balance falls a little slower than the calendar, because part of every payment goes to interest and that part is at its largest while the balance is. The car loses value fastest when it is new. If the value line drops below the balance line you are underwater: selling the car would not clear the loan, and you would owe the difference in cash.

One thing gets imported wrongly from mortgages here. On a 30 year loan the early payments really are almost all interest. On a five year car loan they are not: the first payment on the loan below is about 35 percent interest and 65 percent principal, and the last is under 1 percent interest. The balance comes down from payment one. What opens the underwater gap is mostly the car's side of the picture, not the loan's.

A longer term still keeps you there for longer, because it slows the one line you control. After twelve payments on the five year loan below, the balance is still $26,635.87, under 17 percent of the way down. The seven year version is under 11 percent down over the same twelve payments.

That position only bites when something forces the issue, such as a write-off after an accident or a trade-in before the loan is finished. A larger deposit and a shorter term are the two levers that close the gap sooner.