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The payment formula, and the three numbers it needs

Every fixed rate installment loan uses the same payment formula: P x r / (1 - (1 + r)^-n), where P is the amount financed, r is the annual percentage rate divided by 12, and n is the number of monthly payments. The rate has to be divided by 12 before it goes in, and the exponent has to be negative, or the answer comes out as a nonsense figure.

Three inputs decide everything. The amount financed is the price minus down payment, trade in and rebate plus tax, title and fees. The APR is the yearly cost of credit including lender fees. The term is how many months you agree to pay, and it is the input where buyers give away the most money without noticing.

For 28,000 at 7.47 percent over 60 months, r is 0.006225 and the payment works out at 560.66. Over the full term that is 5,640 of interest, which is 201.42 for every 1,000 borrowed.

The car loan calculator builds the amount financed from the sticker price, trade in, rebate and sales tax, which is the step before this one. This page starts where that one ends: the loan exists, and now the questions are the price of the term, the interest inside each payment and the cost of paying it off early.

Payment per 1,000 borrowed, by term and rate

Dealers and lenders quote payments rather than total costs, so a short table of payments per 1,000 borrowed makes offers comparable in your head. Multiply the figure by the number of thousands you are financing.

Read the last column before the others. Moving from 36 to 84 months cuts the payment by 51 percent and raises the interest by 141 percent, so a longer term is not a discount, it is a rental of cash flow at the lender's price.

The rate column matters just as much. Two percentage points on a 60 month loan add about 0.92 per 1,000 borrowed each month, which on 28,000 is 25.76 a month and 1,545.60 over five years, enough to be worth one afternoon of rate shopping.

Worked example: 28,000 at 7.47 percent for 60 months

Take a loan of 28,000 at an APR of 7.47 percent over five years. The monthly rate is 0.6225 percent, the payment is 560.66, and the 60 payments add up to 33,640, of which 5,640 is interest.

That interest is not spread evenly. The balance at the start is the whole 28,000, so the first payment carries 174.30 of interest and only 386.36 of principal. By the final year the balance is small, so the same payment is almost all principal.

More than a third of the interest is paid in the first twelve months. That is the arithmetic behind the advice to avoid long terms: the loan is expensive while the balance is high, and the balance stays high for years.

What you still owe after two years

After 24 payments of 560.66, the balance on this loan is 18032.15. The payments total 13,456, but only 9,968 of that went to principal, because 3,488 of it was interest and interest buys no equity in the car.

That gap is the reason a car can be worth less than the loan two or three years in. Vehicles lose value fastest in the first years, and a 60 month loan repays principal slowest in exactly the same window. The two curves cross, and the owner is upside down until the principal line rises above the value line.

The practical check before signing is to ask what the car will be worth in 24 months and compare it with this balance. Trade in values are published in guides and dealer quotes, and the comparison takes a minute. If the projected value sits below the balance, a larger down payment or a shorter term is the fix, because a longer term makes the gap wider.

The debt payoff calculator handles the same amortization logic when there are several balances competing for the same monthly money.

Extra payments: what 100 a month changes

An extra 100 a month goes entirely to principal, which removes both the principal and every future interest charge on it. On the 28,000 loan the payoff moves from 60 months to 50, and interest falls from 5,640 to 4,608, a saving of 1,032.

The saving is smaller than the total interest suggests because the loan ends earlier rather than cheaper per month. In effect the extra payments buy the last ten months of interest, and those are the cheapest months of the loan, which is why the saving looks modest compared with the first-year interest figure.

Ask the lender to apply extra money to principal and to keep the regular payment date, and confirm in writing that it is not being treated as a prepayment of the next installment. Some contracts treat extra money that way by default, which delays the payoff instead of shortening it.

Biweekly payment plans offered by third parties usually charge a setup fee to do the same arithmetic, and the same result is available for free by adding one twelfth of the payment each month.

Rolling negative equity into the new loan

Trading a car that is worth less than its payoff does not erase the difference. The lender adds it to the new loan, so a 28,000 purchase with 3,000 of negative equity becomes a 31,000 loan at the same terms.

The payment rises from 560.66 to 620.73, which is 60.07 more each month, and total interest rises by 604.27 over the term. The new car also starts its own depreciation with a loan that is already above its value, so the gap is wider than before.

Two alternatives usually beat rolling the debt forward: paying the difference in cash at the time of sale, or keeping the current car until the balance falls below its value. Gap insurance covers the difference after a total loss, which is a separate product and is not a fix for negative equity.

APR is not the same as the interest rate

The interest rate prices the money. The APR prices the money plus the fees the lender charges to provide it, expressed as a yearly rate. The Consumer Financial Protection Bureau explains the difference and requires lenders to disclose both on the Truth in Lending statement.

A 400 origination fee on a 28,000 loan at 6.9 percent over 60 months raises the APR to 7.51 percent even though the quoted rate never moves. The payment stays at 553.11, but the borrower receives 27,600 and repays as if 28,000 had been lent.

Fees matter more on short terms. The same 400 spread over 36 months adds about one percent to the APR, while over 84 months it adds around 0.4 percent, so a fee that looks trivial on a long loan is expensive on a short one.

Compare offers on APR and total of payments, not on the monthly figure. A dealer can match a payment by stretching the term, and the offer then costs more in total while looking identical on the contract's headline number.

What the payment leaves out, and where rates stand

The payment covers principal and interest only. Insurance, registration, fuel, maintenance, tires and repairs are separate, and the CFPB points out that these ownership costs can be higher on a new vehicle than an older one because insurance and registration are priced on value.

A useful rule is to budget the payment plus about 30 percent for those other costs. On a 560.66 payment that is roughly 168 a month of ownership cost that never appears on the loan paperwork.

Rates move monthly. The Federal Reserve Bank of St. Louis publishes the average finance rate on 48 month new car loans at commercial banks as series TERMCBAUTO48NS, and the August 2026 reading was 7.47 percent, published on 7 October 2026. That is an average of bank loans, not a quote, and dealer financing and credit unions often land on either side of it.

Credit history moves the rate more than shopping does. The CFPB comparison guide also notes that terms beyond five years are more likely to leave a borrower owing more than the vehicle is worth, which is the same arithmetic as the two-year balance above, extended.

For the rebate against low rate question, the cash back or low interest calculator compares the two offers directly, and the simple interest calculator covers loans that do not amortize.