What is the formula for a car loan payment?

It is the same PMT formula every fixed-rate loan uses: PMT = P × [r(1+r)^n] / [(1+r)^n − 1], where P is the amount financed, r is the monthly interest rate (annual rate divided by 12), and n is the total number of monthly payments. For a 6-year loan, n = 72.

How much is the monthly payment on a $32,000 car loan at 7.5% for 6 years?

About $553.28 per month. Over 72 payments that totals roughly $39,836, meaning you pay about $7,836 in interest on top of the $32,000 you borrowed.

Should I take the dealer's 0% financing or the rebate?

Run both numbers. A $3,000 rebate financed at 7% for 60 months on a $30,000 car beats 0% financing on the full $33,000 in most cases — the interest you would pay on the smaller balance is usually less than $3,000 of cash in hand today. The dealer offers you one or the other because they know the rebate-plus-outside-loan path is often the cheaper deal.

Does a trade-in lower my monthly payment?

Yes, by reducing the amount financed. If your trade-in is worth $5,000 and you owe nothing on it, the amount the loan covers drops by $5,000 and your monthly payment drops accordingly. If you still owe more on the trade-in than it is worth — negative equity — that gap usually gets rolled into the new loan, increasing the amount financed.

Is a longer car loan better because the payment is lower?

Lower payment, more total interest, and a real risk of going underwater on the loan. A 72-month or 84-month auto loan keeps the monthly number tolerable but charges thousands more in interest and almost guarantees you owe more than the car is worth for the first 2–3 years. 48 to 60 months is the practical sweet spot for most buyers.

What is amount financed and how is it different from the car's price?

Amount financed is the number the PMT formula uses: vehicle price + sales tax + title and registration fees + dealer fees − down payment − net trade-in value. The sticker price is just the starting point. Sales tax alone often adds 6–9% before any of the other adjustments.

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How to Calculate a Car Loan Payment (With Trade-In, Down Payment, and a Worked Example)

Walk into a dealership and the finance manager will quote you a monthly payment in about ten seconds. What they won't show you is the formula behind it — or the four lines on the sales contract that quietly raise the number you're actually borrowing. Here's the math, worked all the way through on a $32,000 sedan, plus how trade-in equity, sales tax, and a rebate-versus-0%-financing offer all collide on the same equation.

Try the calculator → /financial.html — set P/Y = 12, plug in N, I/Y, and PV, and solve for PMT in three keystrokes.

Last updated: May 20, 2026.

A calculator next to a stack of $100 bills wrapped in a gold band labeled AUTO LOAN, with Visa and Mastercard credit cards fanned out beside it on a dark wood desk

The formula is the same one mortgages use

Auto loans, mortgages, student loans, and personal loans all share a single equation. It's called the PMT formula because it solves for the fixed monthly payment that drives the balance to zero on the last month:

PMT = P × [r(1+r)ⁿ] / [(1+r)ⁿ − 1]

Three inputs, nothing else:

P — the amount financed. Not the vehicle's sticker price. We'll get to the difference in a minute, and it's important.
r — the monthly interest rate. Take the quoted annual rate (APR) and divide by 12. A 7.5% APR becomes 0.075 / 12 = 0.00625.
n — the total number of monthly payments. A 6-year loan is 6 × 12 = 72.

If you've already worked through how to calculate a mortgage payment, you've already done this. The only thing that changes is the size of P, the typical rate, and the term — which together are why a $32,000 car at 7.5% for 6 years and a $300,000 house at 6.5% for 30 years feel like totally different products even though one formula generates both.

The number you actually plug in: amount financed, not sticker price

The biggest mistake people make on car-loan math is using the window-sticker number as P. The bank doesn't lend you the sticker price. The bank lends you the amount financed, which is the sticker price after a half-dozen adjustments:

Amount financed = Vehicle price + Sales tax + Title/registration/doc fees − Down payment − Net trade-in value

Take a realistic example. You're buying a $30,000 sedan in a state with 7% sales tax. The dealer's doc fee is $400 and title/registration runs $200. You're putting $4,000 down and trading in your old car for $5,000 (you own it outright). The math:

Vehicle price: $30,000
Sales tax (7% of $30,000): +$2,100
Title, registration, doc fees: +$600
Down payment: −$4,000
Trade-in (net of payoff): −$5,000
Amount financed: $23,700

That's the number the PMT formula needs — not $30,000. Forget the adjustments and you'll underestimate the payment by 20–25%.

A few gotchas baked into that calculation:

Sales tax is usually charged on the post-trade-in price in trade-credit states (most states do this — your $5,000 trade-in lowers the taxable price too). In a few states (Virginia, Kentucky, parts of Hawaii) tax is charged on the full sticker. Check before you sign.
Negative equity rolls in. If you still owe $7,000 on the trade-in but it's only worth $5,000, the $2,000 gap doesn't disappear — it gets added to the new loan. Amount financed jumps by $2,000, your payment goes up, and you start the new loan already underwater.
Dealer fees vary wildly. A $400 doc fee is normal in most of the country; some states cap it at $75, a few dealerships will try $799 or more. It's negotiable. It just usually isn't negotiated.

A worked example: $32,000 at 7.5% for 6 years

Let's solve a clean version. You financed exactly $32,000 — the amount on the loan paperwork, all adjustments already made — at 7.5% APR for 72 months. Plug into the formula:

P = 32,000. r = 0.00625. n = 72.

First compute (1 + r)ⁿ:

(1.00625)⁷² ≈ 1.5661

Then the numerator: 0.00625 × 1.5661 ≈ 0.009788

And the denominator: 1.5661 − 1 = 0.5661

Divide: 0.009788 / 0.5661 ≈ 0.017290

Multiply by principal: 32,000 × 0.017290 ≈ $553.28

That's your monthly payment. Over 72 months you'll pay 553.28 × 72 ≈ $39,836, meaning about $7,836 in interest on top of the $32,000 you borrowed. A car you "bought" for $32,000 actually costs you closer to $40,000 by the time you own the title outright.

Same loan, four different terms

Dealers love to negotiate on monthly payment because they can change n while you focus on it. Here's what happens to the same $32,000 at 7.5% as you stretch the term:

36 months (3 yr): $995 / month, $3,834 total interest.
48 months (4 yr): $774 / month, $5,139 total interest.
60 months (5 yr): $641 / month, $6,473 total interest.
72 months (6 yr): $553 / month, $7,836 total interest.
84 months (7 yr): $491 / month, $9,229 total interest.

Stretching from 36 to 84 months drops the monthly payment by about half — and almost triples the interest you pay. It also keeps you underwater on the loan for years. New cars depreciate roughly 20% in year one and another 10–15% in year two. On a 7-year loan, the balance falls so slowly that you'll owe more than the car is worth until somewhere around month 36–48. If the car is totaled or you need to sell before then, you write a check just to walk away.

The 48–60 month range is where most buyers land in practice — payment is manageable, interest stays under $7K on a typical loan, and you cross over to positive equity in year 2.

The dealer-financing trap: 0% vs cash rebate

The single most common math trick at the closing desk: "0% APR financing or a $3,000 cash rebate." They sound equivalent — a discount one way or no interest the other. They're not. Run the numbers.

Option A: Take the 0% on a $30,000 car for 60 months. Payment = $500/month. Total paid = $30,000.

Option B: Take the $3,000 rebate, financing $27,000 instead. Get an outside loan from a credit union at, say, 7% for 60 months. PMT works out to about $534.63/month. Total paid = $32,078.

On paper, Option A wins by about $2,078. So why is this called a trap? Two reasons:

0% offers usually come with a shorter max term and stricter credit requirements. The 0% might be capped at 36 months, where the payment is $833/month — almost twice the rebate-option payment.
Real outside-loan rates are often 5–6%, not 7%. At 5.5% for 60 months on $27,000, the payment is $516/month and total interest is $3,944. Total paid = $30,944. Still a hair more than the 0% — but now you're holding $3,000 in cash today, which is worth real money in an emergency fund or a higher-yield account.

The honest answer: always run both. Don't trust the dealer's framing. The PMT formula gives you the apples-to-apples comparison; the salesperson is incentivized to obscure it.

What "amortization" looks like on a 6-year loan

Same $32,000 at 7.5% for 72 months. In month 1, you owe the full $32,000. Interest charged that month:

32,000 × 0.00625 = $200.00

Your $553.28 payment splits into $200.00 interest and $353.28 principal. Balance after month 1: $31,646.72. In month 2 you owe slightly less, the interest portion drops by about a dollar, the principal portion rises by about a dollar. Repeat 70 more times and the balance lands at zero.

At three points on this loan:

Month 1 — payment $553.28 = $200.00 interest + $353.28 principal. Balance after: $31,646.72.
Month 36 (halfway) — payment $553.28 ≈ $111 interest + $442 principal. Balance: about $17,800.
Month 72 (final) — payment $553.28 ≈ $3 interest + $550 principal. Balance: $0.

Car loans amortize fast compared to mortgages because the term is short. By the halfway point of a 6-year loan you've actually paid down about 45% of the principal, versus only 28% by halfway on a 30-year mortgage. Short term, fast amortization — but the rate is usually higher than a mortgage, which is why the total interest as a percent of borrowed amount can still be hefty.

Solving it on the financial calculator (TVM keys)

The TVM keys on any financial calculator are designed for exactly this. For the $32,000 at 7.5% for 6 years:

P/Y = 12 (12 payments per year)
N = 72
I/Y = 7.5
PV = 32,000 (the lender hands this to you, so it's positive)
FV = 0 (loan is paid off at the end)
Solve for PMT → −$553.28 (negative because it's leaving your pocket)

Same five keys solve "how much car can I afford?" — set PMT to your target monthly number and solve for PV. They also solve "what rate am I actually getting?" if the dealer hands you a payment and a term but you suspect the APR isn't what they're claiming. Just plug in PV, PMT, N, and FV, and let the calculator solve for I/Y.

The thing most people get wrong: APR vs the monthly payment number

The car salesperson is going to ask you "what monthly payment are you comfortable with?" before they ask anything else. That's not a friendly question. It's an information-gathering question. Once they know your target payment, they have three knobs to hit it: lower the price, stretch the term, or play with the APR. They will almost always reach for term first because it's the cheapest one for them.

Negotiate on price first (the number you'll plug in as P), rate second (the r), and term last (the n). The monthly payment is the output of those three inputs. If you negotiate the output directly, the dealer will move whichever input gives them the most margin, which is term. A 60-month loan and a 72-month loan can both produce "around $550/month" payments on different P and r combinations — but one of them costs you $1,300 more in interest.

And while we're on the subject of rates: the APR they quote you is a regulated number that's supposed to include most of the loan's costs. It usually does. The thing it doesn't always include is GAP insurance, extended warranties, and any dealer add-ons financed into the loan — those raise P but don't change the disclosed APR. Pull them out before signing.

Frequently asked questions

Is dealer financing always worse than a credit-union loan?

Not always — promotional 0% or 1.9% manufacturer-subsidized rates from a dealer can genuinely beat a credit union when they're real. But the standard non-promotional dealer rate is often 1–2 percentage points higher than what a credit union offers the same buyer, because the dealer marks up the bank's wholesale rate as a profit center. Get pre-approved at a credit union first, then let the dealer try to beat it. If they can, take theirs. If they can't, you've got a backup that's already approved.

Should I make a 20% down payment?

20% on a new car and 10% on a used car is the rule of thumb. The reason is the depreciation cliff: a new car loses ~20% of its value in year one, and if your down payment is smaller than the year-one depreciation, you're underwater the moment you drive off the lot. A 20% down payment keeps you at-or-above the curve from day one and lowers the financed amount enough to drop your payment by a meaningful number.

Can I pay off a car loan early without a penalty?

Almost always yes for auto loans in the US — prepayment penalties on consumer car loans are uncommon and in some states outright illegal. Always confirm by reading the actual contract (look for "prepayment penalty" or "minimum interest charge" in the terms). If there's no penalty, extra principal payments early in the loan kill off huge amounts of future interest, the same way they do on a mortgage — just on a smaller scale.

What's a "buy rate" and why do I care?

The buy rate is the actual interest rate the dealer's lender will accept on your credit profile. The dealer is allowed to mark it up (typically 1–2 points) and pocket the difference as dealer reserve. You usually can't see the buy rate, but you can shop the dealer's quote against an outside lender — if your credit union offers 6.5% and the dealer is pitching 8.5%, the dealer's buy rate is probably 6.5–7% and the markup is going into their pocket. Showing up with a pre-approval is the cleanest way to compress that markup.

Lease or buy?

Different math problem entirely. A lease isn't a loan — it's paying for the depreciation between the start and end of the lease term, plus a financing charge (the money factor). The PMT formula doesn't quite apply the same way. Rule of thumb: leases make sense if you cycle cars every 2–3 years anyway, drive under the mileage cap, and want a luxury vehicle you couldn't afford to buy outright. Buying with a loan makes sense if you want to own the car at the end and amortize the cost over a longer ownership horizon.

Try it yourself

Punch your own numbers into the financial calculator — your real amount financed, the rate from your pre-approval, and a term you can actually live with. Then try the same loan at 12 months longer and 12 months shorter and watch the trade-off between payment and total interest play out in real time. The dealership is doing this math in their head while they talk to you. There's no reason you shouldn't be doing it too.

This article is for general education and is not financial advice. See our Terms.