Auto loan calculator

How the formula works

A car payment is an amortized loan, the same closed form as a mortgage: a fixed monthly payment \(M\) that pays the balance to zero over \(N\) months. The work is in the balance you start from — the amount financed \(A\) — which is rarely the sticker price:

where \(P\) is the vehicle price, \(T\) the sales tax, \(F\) the title and doc fees, \(D\) your cash down payment, \(V\) the trade-in's value and \(O\) the loan still owed on it. The term \(V - O\) is the trade-in's net equity: what it actually knocks off the loan. In most US states the sales tax is charged on the price after the trade-in is subtracted — the trade-in tax credit:

Once \(A\) is known, the payment is the standard amortization form:

The trade-in tax credit is real money: taxing \(P-V\) instead of \(P\) saves you the tax rate times the trade-in's value. On a $5,000 trade at 6.5% that is $325 you never finance. A handful of states (and private-party sales in some) tax the full price with no credit — check your state before trusting the number.

Negative equity is the mirror image. If you still owe more than the trade-in is worth, \(V - O\) is negative, so subtracting it adds to the loan — you are financing the new car plus the leftover balance on the old one. Rolling that shortfall forward is common and quietly expensive: you pay interest on a car you no longer own, and you start the new loan already underwater.

What each input means

Vehicle price — \(P\)

The agreed sale price of the car, before tax and fees. This is the number you negotiate; it is not the amount you finance.

Down payment — \(D\)

Cash you put in up front. Every dollar down is a dollar you neither finance nor pay interest on, and it is the fastest way to stay out of negative equity as the car depreciates.

Trade-in value — \(V\)

What the dealer credits you for your old vehicle. In most states it also reduces the taxable amount, so a trade-in cuts the loan twice — once directly, once through the tax.

Owed on trade-in — \(O\)

Any loan balance still outstanding on the car you are trading in. The dealer pays it off and the difference, \(V-O\), is your net equity — positive if the car is worth more than you owe, negative if you are upside-down.

Sales tax rate — \(\tau\)

Your state and local motor-vehicle sales tax. Applied here to the price after the trade-in credit. Rates and rules vary widely by state.

Title & doc fees — \(F\)

Title, registration and the dealer's documentation fee, financed into the loan. This model does not include optional add-ons like GAP insurance or an extended warranty.

Interest rate — APR

The annual percentage rate on the loan, set by your credit. The payment is computed at \(i = \mathrm{APR}/12\) a month.

Term

How many months the loan runs. A longer term lowers the payment but raises the total interest, because the balance falls more slowly.

A worked example

The worksheet's defaults: a $35,000 car with $3,000 down and a $5,000 trade-in that still owes $2,000, at 6.5% sales tax and $400 in fees, financed at 7.5% APR over 72 months.

• Net trade-in equity: $5,000 − $2,000 = $3,000 — positive, so it reduces the loan.
• Sales tax (trade-in credit applied): ($35,000 − $5,000) × 6.5% = $1,950. Taxing the full price would have cost $2,275 instead.
• Amount financed: $35,000 + $1,950 + $400 − $3,000 − $3,000 = $31,350.
• Monthly rate: \(i = 7.5\%/12 = 0.006250\); over \(N = 72\) months the growth factor is \((1+i)^{72} = 1.5661\).
• Payment: $31,350 × 0.006250 × 1.5661 / (1.5661 − 1) = $542.05 a month.

Over the full 72 months that is $39,027 paid in all — $7,677 of it interest on top of the $31,350 financed.

Assumptions and limits

• Sales-tax rules vary by state. Most credit the trade-in as modeled here; some tax the full price, and a few charge no vehicle sales tax at all. This tool applies one flat rate to the price after the trade-in credit.
• No GAP insurance, extended warranty, service contracts or other dealer add-ons are financed. Each of those, if rolled in, raises the amount financed and the payment.
• The APR is whatever your credit earns and is held fixed for the term. A lower score means a higher rate and a higher payment on the same car.
• Fees vary by dealer and state; the single fee input stands in for title, registration and documentation. This is arithmetic, not advice.

Questions people ask

Does a longer loan term save money?

No — it lowers the monthly payment but raises the total interest. On the worked example, $31,350 at 7.5% costs $975 a month over 36 months and $542 over 72, which feels like a saving. But the 36-month loan pays $3,756 of interest and the 72-month loan pays $7,677 — nearly 2 times as much. A longer term buys a smaller payment with more interest and more time spent owing more than the car is worth.

How does a trade-in cut my sales tax?

In most states the motor-vehicle sales tax is charged on the price minus the trade-in allowance, not the full price — the trade-in tax credit. On the worked example the tax is charged on $35,000 − $5,000 = $30,000, so at 6.5% you pay $1,950 instead of $2,275 — a $325 saving purely from how the tax is figured. Selling the car yourself may fetch more for it but usually forfeits this credit, so compare the two on the after-tax number.

What is negative equity, or being upside-down?

You are upside-down when you owe more on the car than it is worth — the loan balance exceeds the trade-in value. It is common early in a loan because cars depreciate fastest in the first year or two while the balance is still high. When you trade an upside-down car in, the leftover balance does not disappear: the dealer rolls it into the new loan, so you finance the new car plus the old shortfall and start the new loan already underwater.

Should I put money down?

A down payment lowers the amount financed dollar for dollar, so it cuts both the payment and the total interest, and it is the simplest way to avoid negative equity as the car depreciates. There is no rule you must — some borrowers with a strong rate and cash better used elsewhere choose not to — but putting nothing down on a long term is the fastest route to owing more than the car is worth. This calculator shows the trade-off for your own numbers; it does not tell you what to do.

Is the advertised price the amount I finance?

No. The advertised price is the starting point; the loan is that price plus sales tax and title and doc fees, minus your down payment and trade-in equity. On the worked example a $35,000 car finances $31,350 after $1,950 of tax and $400 of fees, offset by $3,000 down and $3,000 of trade equity. Tax and fees push the number up; cash and equity pull it down.