Vehicle finance / consumer lending

Auto loan payment

Turn a sticker price into a real monthly payment: sales tax, trade-in credit, down payment and dealer fees all change the amount financed. The term comparison shows what stretching the loan actually costs.

APR7.20%Sales tax$2,030Interest per dollar0.194×

Monthly payment

$549.72

60 monthly payments

Amount financed

$27,630

After down payment, trade-in, tax and fees

Total interest

$5,353

19.4% of the amount financed

Total cost

$39,983

Down payment plus all payments

Drive-off cost breakdown

Every line that turns a sticker price into an amount financed.

60 months

Drive-off cost breakdown
Line item	Amount	Note
Vehicle price	$32,000	Negotiated price, before tax
Trade-in credit	-$3,000	Reduces both cash due and the taxable base
Down payment	-$4,000	Cash paid at signing
Sales tax	$2,030	7.00% on $29,000
Dealer / title fees	$600.00	Documentation, registration, title
Amount financed	$27,630	Principal on the loan
Total interest	$5,353	At 7.20% APR
Total cost of ownership	$39,983	Down + payments + trade-in value

Some states tax the full price rather than the trade-in-adjusted base — check your state’s rule, it moves the financed amount materially.

What the money buys

Price against tax, fees and the amount actually financed.

Loan balance

Outstanding principal across the term.

Canonical equations

The exact relationships implemented by this engine.

B = max(0, Price − Trade-in) · trade-in credit reduces the taxed amount

F = Price − Down − Trade + Tax + Fees · the principal on the note

PMT = F·i / (1 − (1+i)⁻ⁿ) · i = APR/12, n = term in months

Down + n·PMT + Trade · what the vehicle really costs you

Show model notation and computationOpen the symbolic form, the variable definitions, and the step-by-step derivation when you need the detail.

A clear path from inputs to results.

The monthly payment on a car is not the sticker price divided by the term. Sales tax, a trade-in credit, cash down and dealer fees all change the amount financed, and the term changes how much interest that amount costs. This engine builds the payment from the drive-off numbers.

Step-by-step methodWorked exampleAssumptions explained

How to use

Enter the negotiated vehicle price, not the sticker.

Add the trade-in value — it reduces both the cash due and, in most states, the taxable amount.

Enter the cash down payment.

Set the sales tax rate for your jurisdiction and add dealer, title and registration fees.

Set the APR and the term in months.

Compare the term options: the shortest affordable term usually has the lowest total cost.

The formula

F = \text{Price} - \text{Down} - \text{Trade} + \text{Tax} + \text{Fees}, \qquad \mathrm{PMT} = \frac{F \cdot i}{1-(1+i)^{-n}}, \qquad i = \frac{\mathrm{APR}}{12}

Reference: Standard vehicle-retail financing under Regulation Z (12 CFR §1026) APR disclosure; state motor-vehicle sales-tax treatment of trade-ins.

Worked example

$32,000 car with trade-in and 7% tax (default inputs)

Inputs

Vehicle price $32,000, trade-in $3,000, down payment $4,000.
Sales tax 7% on the trade-in-adjusted price; fees $600.
APR 7.2% over 60 months.

Calculation path

1
Taxable base: 32,000 − 3,000 = $29,000; tax = $2,030.
2
Amount financed: 32,000 − 4,000 − 3,000 + 2,030 + 600 = $27,630.
3
Monthly rate 0.6%; payment = 27,630 × 0.006 / (1 − 1.006^−60) = $549.72.
4
Total interest over 60 months: 60 × 549.72 − 27,630 = $5,353.
5
Total cost including the down payment: $36,983.

Result

Monthly payment $549.72 · financed $27,630 · total interest $5,353 · total cost $36,983.

Interpreting the result

The car costs $36,983 in cash terms against a $32,000 price — the difference is tax, fees and interest. Stretching to 84 months would cut the payment to roughly $455 but add about $1,400 of interest, and leave the loan underwater for longer as the car depreciates. The term comparison chart exists to make that trade-off visible rather than rhetorical.

Assumptions & limitations

Trade-in reduces the taxable base. A minority of states tax the full price — check locally, it moves the financed amount by the tax rate times the trade-in.

No manufacturer rebate is modelled. Rebates and subsidised APRs are usually mutually exclusive, so compare total cost.

The APR is fixed for the term and no promotional rate expires mid-loan.

Insurance, fuel, maintenance and depreciation are excluded — this is the financing cost, not the cost of ownership.

Fees are paid at signing or financed; either way they are included in the amount financed here.

Frequently asked questions

Does a trade-in reduce sales tax?

In most US states, yes: tax is charged on the price difference after the trade-in. A few states tax the full purchase price. The difference is the tax rate times the trade-in value, which can be several hundred dollars.

Should I take the rebate or the low APR?

Compare total cost both ways. A cash rebate with a normal loan often beats a 0% APR with no rebate, especially if you plan to keep the car. Run both through the calculator and compare the total.

What about gap insurance?

It covers the difference between the loan balance and the insurance payout if the car is written off. It matters most on long terms with small down payments, where negative equity is largest.

Is a longer term always worse?

It lowers the payment and raises the total interest. The real risk is negative equity: cars depreciate faster than a long loan amortises, so you can owe more than the car is worth for years.

How is the payment affected by the down payment?

Every dollar down reduces the amount financed directly, and therefore reduces both the payment and the total interest. It also reduces negative-equity risk.

Why is my dealer’s number different?

Common causes: tax on the full price rather than the trade-in difference, documentation fees not disclosed up front, add-ons financed into the loan, or a different APR tier based on credit score.