Why do I enter the taxable amount instead of letting the calculator derive it?

Tax treatment can differ by location and transaction. An explicit tax base avoids silently assuming whether a rebate, trade-in, or fee is taxable.

What happens when I owe more than my trade-in is worth?

The difference is negative equity. If it is rolled into the new loan, it increases the amount financed and you pay interest on that added balance.

Does an extra payment change my contractual monthly payment?

No. The planner keeps the contractual payment from the original amount, rate, and term, then adds your chosen extra amount to the schedule. The last payment is reduced to the exact remaining balance and interest.

What does the A/B comparison send to the loan comparison tool?

It sends Scenario A's amount financed as a common principal plus each scenario's rate and term. Purchase incentives, taxes, trade-in details, and extra payments stay on this page so financing terms are not confused with transaction differences.

How does negative trade equity affect the new loan?

When balance owed exceeds trade value, the difference is added to amount financed; 8,500 owed on a 6,000 trade adds 2,500.

Which inputs does Auto loan calculator use?

It uses the visible fields Vehicle price, Cash incentive, Down payment, Trade in value, Trade in balance, Taxable amount, Sales tax percent, Fees, Sales tax payment, Fees payment, Annual interest rate, Term months, Extra monthly payment. No hidden value is substituted for an omitted required input.

What happens when Auto loan calculator receives an invalid or extreme value?

The page rejects missing, ambiguous, out-of-range, or non-finite values and refuses to display a non-finite result.

Why can Auto loan calculator differ from another result?

Different unit conventions, endpoint policies, fee or rate assumptions, formula domains, and premature rounding can produce a different answer.

Can I use Auto loan calculator as professional advice?

No. It is an educational estimate, not financial, tax, investment, accounting, or lender advice.

How can I verify the Auto loan calculator result?

Recalculate the two evaluated examples without rounding intermediate values and compare the declared formula or convention with OpenStax Principles of Finance.

Auto loan calculator

Plan the purchase and loan

Estimated loan result454.72Planned monthly payment

Contract monthly payment454.72Amount financed23,240.00Estimated payoff60 months

Total interest: 4,043.04
Interest saved with extra payments: 0.00
Cash due at signing: 5,000.00
Purchase cost before interest: 31,240.00
Cash and loan payments: 32,283.04

Cash and loan payments exclude the value of the vehicle you surrender as a trade-in.

Balance, principal and interest

Loan balance falls while cumulative principal and cumulative interest rise across the payoff schedule.

Remaining balanceCumulative principalCumulative interest

Complete amortization schedule

Complete amortization schedule — Yearly
Period	Payment	Principal	Interest	Remaining balance
1	5,456.61	4,065.71	1,390.89	19,174.29
2	5,456.61	4,338.00	1,118.60	14,836.28
3	5,456.61	4,628.53	828.08	10,207.76
4	5,456.61	4,938.51	518.10	5,269.25
5	5,456.61	5,269.25	187.36	0.00

Local A/B scenarios

Save the current inputs in this browser, then load or compare them later.

Scenario inputs stay in this browser. Nothing is uploaded.

Save both A and B to compare them.

Estimate only—not a lender quote, tax advice or financial advice. Confirm APR, fees, tax treatment and payment timing in your contract.

Formula

Auto loan calculator evaluates the registered expression “P=x₁−x₂−x₃−x₄+x₅+F_tax(x₆,x₇,x₉)+F_fee(x₈,x₁₀); i=x₁₁/1200; n=x₁₂; M={P/n:i=0;P·i(1+i)^n/((1+i)^n−1):i≠0}; planned=M+x₁₃; x₁=Vehicle price; x₂=Cash incentive; x₃=Down payment; x₄=Trade in value; x₅=Trade in balance; x₆=Taxable amount; x₇=Sales tax percent; x₈=Fees; x₉=Sales tax payment; x₁₀=Fees payment; x₁₁=Annual interest rate; x₁₂=Term months; x₁₃=Extra monthly payment” with the validated inputs. Full calculation precision is retained until the result is formatted for display.

P=x₁−x₂−x₃−x₄+x₅+F_tax(x₆,x₇,x₉)+F_fee(x₈,x₁₀); i=x₁₁/1200; n=x₁₂; M={P/n:i=0;P·i(1+i)^n/((1+i)^n−1):i≠0}; planned=M+x₁₃; x₁=Vehicle price; x₂=Cash incentive; x₃=Down payment; x₄=Trade in value; x₅=Trade in balance; x₆=Taxable amount; x₇=Sales tax percent; x₈=Fees; x₉=Sales tax payment; x₁₀=Fees payment; x₁₁=Annual interest rate; x₁₂=Term months; x₁₃=Extra monthly payment

OpenStax Principles of Finance

What this calculator answers

Use this planner to separate the purchase transaction from its financing. It estimates a fixed-rate loan from values you enter, shows where negative trade equity goes, and compares saved scenarios without recommending a lender or a vehicle.

Input definitions

Vehicle price and cash incentive: The negotiated vehicle price and a cash rebate that directly reduces that price. A promotional interest rate is not a cash incentive.
Down payment and trade-in: Cash paid at signing, the value credited for the old vehicle, and the outstanding balance that must still be paid. Trade-in equity equals value minus balance owed.
Taxable amount, tax rate, and fees: Enter the tax base supplied by the quote or applicable local rule. Choose separately whether calculated tax and entered fees are financed or paid upfront.
Rate, term, and extra payment: The annual percentage rate used as APR divided by 12, the whole-number term in months, and an optional amount added to each scheduled payment.

Formulas and variables

Amount financed

P = V − R − D − T + B + financed tax + financed fees

V = vehicle price
R = cash incentive
D = cash down payment
T = trade-in value
B = balance owed on trade-in

Because T − B is trade equity, a balance larger than the trade value increases the new loan as negative equity.

Sales tax

tax = taxable amount × tax rate / 100

taxable amount is entered explicitly
tax rate is entered as a percent

The planner does not infer whether rebates, trade-ins, or fees change the legal tax base.

Contract monthly payment

M = P × r(1+r)ⁿ / ((1+r)ⁿ − 1)

P = amount financed
r = annual rate / 1200
n = contractual months

When r = 0, M = P / n. Extra payments do not change M; they change the actual payoff schedule.

Monthly amortization

interestₖ = balanceₖ₋₁ × r; principalₖ = paymentₖ − interestₖ

paymentₖ includes the optional extra amount except for the final smaller payment

The next balance is the previous balance minus principal. Full precision is retained until display and CSV formatting.

Assumptions and rounding

The loan has a fixed annual rate, monthly compounding, and end-of-month payments. Daily-interest loans, irregular first periods, add-ons, insurance, and balloon payments are outside this model.
Extra payments are applied immediately to principal without a fee or prepayment penalty. Confirm that treatment with the lender.
All money entries use one currency. The tool performs no exchange-rate conversion and displays monetary results to two decimals while the engine retains full precision.
Taxes and fees use exactly the user-entered amounts and financed/upfront choices; they are estimates, not jurisdiction-specific tax advice.

Worked examples

Positive trade equity with taxes and fees financed

Vehicle 30,000; rebate 1,000; down payment 5,000; trade value 4,000 with 1,000 owed; taxable amount 29,000 at 6%; fees 500; 6.5% for 60 months.

Calculation

Trade equity: 4,000 − 1,000 = 3,000.
Tax: 29,000 × 6% = 1,740.
Amount financed: 30,000 − 1,000 − 5,000 − 4,000 + 1,000 + 1,740 + 500 = 23,240.
Fixed monthly payment from the annuity formula is about 454.72.

Result: Estimated contract payment: 454.72 for 60 months; total interest is about 4,043.04.

Negative equity, upfront charges, and an extra payment

Vehicle 32,000; rebate 2,000; down payment 3,000; trade value 8,000 with 10,500 owed; tax 2,030 and fees 650 paid upfront; 7% for 72 months plus 100 extra monthly.

Calculation

Trade equity: 8,000 − 10,500 = −2,500, so 2,500 is added to financing.
Amount financed: 32,000 − 2,000 − 3,000 − 8,000 + 10,500 = 29,500.
Contract payment is about 502.95; planned payment is 602.95.
The schedule pays off in about 58 months and saves about 1,376.93 in interest versus the contractual schedule.

Result: The upfront cash estimate is 5,680; the accelerated schedule totals about 5,335.16 in interest.

Questions people ask

Why do I enter the taxable amount instead of letting the calculator derive it?: Tax treatment can differ by location and transaction. An explicit tax base avoids silently assuming whether a rebate, trade-in, or fee is taxable.
What happens when I owe more than my trade-in is worth?: The difference is negative equity. If it is rolled into the new loan, it increases the amount financed and you pay interest on that added balance.
Does an extra payment change my contractual monthly payment?: No. The planner keeps the contractual payment from the original amount, rate, and term, then adds your chosen extra amount to the schedule. The last payment is reduced to the exact remaining balance and interest.
What does the A/B comparison send to the loan comparison tool?: It sends Scenario A's amount financed as a common principal plus each scenario's rate and term. Purchase incentives, taxes, trade-in details, and extra payments stay on this page so financing terms are not confused with transaction differences.

Boundaries and common mistakes

Do not enter a promotional 0% rate as a cash rebate; dealer offers may require choosing one or the other.
Do not subtract the trade-in value without also entering its outstanding balance, or negative equity will be hidden.
A lower monthly payment from a longer term can still produce more total interest and a longer period of negative equity.
Confirm whether extra payments reduce principal and whether taxes or fees are financed before relying on the estimate.

Sources and scope

Consumer Financial Protection Bureau — Auto loansApplies to: APR, term, amount financed, trade-in and loan-comparison concepts; not a source for local tax treatment.
Federal Trade Commission — Auto trade-ins and negative equityApplies to: How an unpaid trade-in balance can be rolled into a new loan and increase its cost.

Variables, defaults, and limits

Vehicle price: Vehicle price is a number input. The displayed starter value is 30,000; it is an example, not a hidden assumption.; Default: 30,000; Accepted values: Minimum: 0.01. Numeric entries must be finite and unambiguous.
Cash incentive: Cash incentive is a number input. The displayed starter value is 1,000; it is an example, not a hidden assumption.; Default: 1,000; Accepted values: Minimum: 0. Numeric entries must be finite and unambiguous.
Down payment: Down payment is a number input. The displayed starter value is 5,000; it is an example, not a hidden assumption.; Default: 5,000; Accepted values: Minimum: 0. Numeric entries must be finite and unambiguous.
Trade in value: Trade in value is a number input. The displayed starter value is 4,000; it is an example, not a hidden assumption.; Default: 4,000; Accepted values: Minimum: 0. Numeric entries must be finite and unambiguous.
Trade in balance: Trade in balance is a number input. The displayed starter value is 1,000; it is an example, not a hidden assumption.; Default: 1,000; Accepted values: Minimum: 0. Numeric entries must be finite and unambiguous.
Taxable amount: Taxable amount is a number input. The displayed starter value is 29,000; it is an example, not a hidden assumption.; Default: 29,000; Accepted values: Minimum: 0. Numeric entries must be finite and unambiguous.
Sales tax percent: Sales tax percent is a number input. The displayed starter value is 6; it is an example, not a hidden assumption.; Default: 6; Accepted values: Allowed range: 0 to 1,000. Numeric entries must be finite and unambiguous.
Fees: Fees is a number input. The displayed starter value is 500; it is an example, not a hidden assumption.; Default: 500; Accepted values: Minimum: 0. Numeric entries must be finite and unambiguous.
Sales tax payment: Sales tax payment is a choice input. The displayed starter value is financed; it is an example, not a hidden assumption.; Default: financed; Accepted values: The field has no narrower HTML limit, but it must still satisfy the documented formula domain and produce a finite result. Available choices: financed, upfront.
Fees payment: Fees payment is a choice input. The displayed starter value is financed; it is an example, not a hidden assumption.; Default: financed; Accepted values: The field has no narrower HTML limit, but it must still satisfy the documented formula domain and produce a finite result. Available choices: financed, upfront.
Annual interest rate: Annual interest rate is a number input. The displayed starter value is 6.5; it is an example, not a hidden assumption.; Default: 6.5; Accepted values: Allowed range: 0 to 100. Numeric entries must be finite and unambiguous.
Term months: Term months is a number input. The displayed starter value is 60; it is an example, not a hidden assumption.; Default: 60; Accepted values: Allowed range: 1 to 1,200. Numeric entries must be finite and unambiguous.
Extra monthly payment: Extra monthly payment is a number input. The displayed starter value is 0; it is an example, not a hidden assumption.; Default: 0; Accepted values: Minimum: 0. Numeric entries must be finite and unambiguous.

Worked examples