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How car loan payments work

A car loan uses the level-payment formula. Finance $32,000 at 8.5 percent over 5 years and the payment is $656.53 a month. You hand over $39,391.74, so interest is $7,391.74. Stretch the same loan to 7 years and the payment falls to $506.77 while interest rises to $10,568.47.

Monthly payment

$656.53

Over 60 payments you hand over $39,391.74 in total.

Total interest
$7,391.74
Interest as a share of the amount financed
23.10%
Total repaid
$39,391.74
Still owed after 12 payments
$26,635.87
$

Price plus tax, fees and any add-ons rolled in, less deposit or trade-in.

%

The nominal rate the lender quotes, such as an APR. Not an effective annual rate.

yr

A longer term lowers the payment and raises the total repaid.

On this page

In short

  • Finance $32,000 at 8.5 percent over 5 years, monthly, and the payment is $656.53. Total repaid is $39,391.74. Interest is $7,391.74.
  • After 12 payments the balance is $26,635.87. That month's interest is $191.96 and principal is $464.57. Most of an early payment is still interest.
  • The same $32,000 over 7 years drops the payment to $506.77. Total repaid rises to $42,568.47. Interest is $10,568.47, more than on the five-year sheet.
  • The payment is not the price. The price is what the dealer charged. The payment is what the rate, the term and the amount financed produce.
  • A car is a wasting asset. Stretching the term to cut the payment is how the loan can outlast the car. Car finance and depreciation is that pairing.

The payment is a formula, not a sticker

A car loan is the same level-payment identity as any other amortising loan:

M=P×i1−(1+i)−nM = P \times \frac{i}{1 - (1 + i)^{-n}}

PP is the amount financed, not the sticker. ii is the monthly rate, the nominal annual rate divided by 12. nn is months.

Finance $32,000 at 8.5 percent over 5 years: i=0.085/12i = 0.085/12, n=60n = 60, and MM is $656.53. Over 60 payments you hand over $39,391.74. Interest is $7,391.74, which is 23.1 percent of the amount financed.

The car loan calculator on this page is that formula. The loan payment calculator is the same identity on a mortgage-sized principal. How amortisation works is the long form of what each payment is doing to principal.

APR on a car offer can include fees packed into the rate. Type the rate the contract actually compounds at, or the payment will describe a different loan.

The formula on this page holds the rate still. A dealer offer that starts lower and then follows an index is a different input. Fixed against variable rates is when that opening gap is a bargain and when it is a reset waiting to happen.

After a year, most of the car is still owed

After 12 payments on the five-year sheet, the balance is $26,635.87. Month 12 charges $191.96 of interest and $464.57 of principal. You have been paying $656.53 for a year and still owe about 83 percent of the $32,000.

That is amortisation, not a trick. Early payments are mostly interest because the balance is still large. The amortisation explorer is the picture of that split moving.

A longer term cuts the payment and raises the cost

Keep $32,000 and 8.5 percent. Stretch the term to 7 years. The payment falls to $506.77. Total repaid rises to $42,568.47. Interest is $10,568.47, more than on the five-year sheet.

The payment fell. The cost of the debt rose, because 24 extra payments at a still-high early-interest split more than ate the lower monthly figure. On a car, the term also has to sit inside how long the car will be worth more than the balance. A seven-year loan on a car that is sold in year five is a balance due at the sale.

What this page is not doing

It is not a dealer quote, not tax and title, and not a residual on a lease. The three sheets are $32,000 at 8.5 percent over 5 years ($656.53, interest $7,391.74), the balance after a year ($26,635.87), and the same principal over 7 years ($506.77, interest $10,568.47). This is educational material, not financial advice.

Worked examples

A five year loan on a \$32,000 car

You finance $32,000 at 8.5 percent over 5 years, paid monthly. What is the payment, and what does the loan cost?

  1. Find the rate for one month: i=0.085/12=0.00708333i = 0.085/12 = 0.00708333.
  2. Count the payments: n=5×12=60n = 5 \times 12 = 60.
  3. Work out the discount term: (1+i)−60=0.654750(1 + i)^{-60} = 0.654750, so 1−0.654750=0.3452501 - 0.654750 = 0.345250.
  4. Apply the formula: M=32000×0.007083330.345250M = 32000 \times \frac{0.00708333}{0.345250}, which is $656.53 a month.
  5. Multiply the unrounded payment by the 60 payments to get everything you hand over: $39,391.74. Rounding to the cent first and multiplying 656.53 by 60 comes out six cents higher, so totals are worked from the full figure rather than from the displayed one.
  6. Subtract the amount financed to isolate the interest: $39,391.74 minus $32,000.

The payment is $656.53 a month. Over 60 payments you hand over $39,391.74, so the finance costs $7,391.74 on top of the $32,000 you borrowed, which is 23.1 percent of the amount financed.

What you still owe after a year

Same loan. After twelve payments, how much of the $32,000 have you actually cleared?

  1. Each month the interest charge is the balance times i=0.00708333i = 0.00708333, and the rest of the payment comes off the balance.
  2. Walk the schedule forward twelve months. The interest charge in month 12 is $191.96.
  3. That leaves $464.57 of the payment to reduce what you owe.
  4. Carry the balance to the end of month 12: $26,635.87.

After a full year of payments the balance is $26,635.87, so under 17 percent of the amount financed is gone. Month 12 sends $191.96 of the $656.53 payment to interest and $464.57 to the balance, a bit under 71 percent of it doing the work, and a car is usually worth a good deal less after its first year than it was on the day you drove it away.

The same car over seven years

Keep $32,000 at 8.5 percent and stretch the term to 7 years. What happens to the payment, and what happens to the total?

  1. The monthly rate is unchanged at i=0.00708333i = 0.00708333, but now n=84n = 84.
  2. (1+i)−84=0.552721(1 + i)^{-84} = 0.552721, so the divisor becomes 1−0.552721=0.4472791 - 0.552721 = 0.447279.
  3. M=32000×0.007083330.447279M = 32000 \times \frac{0.00708333}{0.447279}, which is $506.77 a month.
  4. Multiply the unrounded payment by the 84 payments: $42,568.47 in total. Multiplying the rounded 506.77 by 84 instead overstates it by about 21 cents.
  5. Take off the $32,000 financed to isolate the interest.

The payment falls to $506.77, nearly 23 percent lighter each month. The total repaid rises to $42,568.47 and the interest rises to $10,568.47, roughly 43 percent more than the five year version costs. The smaller payment is bought with two more years of interest on a car that is two years older by the end.

Common questions

Is the payment the cost of the car?

No. The payment is what the amount financed, the rate and the term produce. On the first sheet, $656.53 a month is the cost of borrowing $32,000 at 8.5 percent for 5 years. The car's price is a different number, and a large deposit changes the amount financed rather than the formula.

Why does a longer term cost more if the payment is smaller?

Because you pay interest for more months. The seven-year sheet drops the payment from $656.53 to $506.77 and raises interest from $7,391.74 to $10,568.47. The extra 24 payments more than fill the monthly gap.

What rate should I type?

The nominal annual rate the contract compounds at, monthly. An APR that packs in fees is a different object. If the contract quotes a monthly payment already, this page is for seeing what that payment implies, not for replacing the contract.

Keep reading

This page is educational material, not financial advice. The figures come from the formula shown and assume the inputs you enter hold for the whole term. Your own rate, fees, taxes and timing will differ, so treat the output as arithmetic to check a decision against, not as a recommendation.