calculate-loan

06 Auto loans

Auto Loan Calculator With Trade-In and Amount Owed (Negative Equity)

Calculator No. 06-0034 · Updated · Formula and assumptions shown below

Monthly payment $578.03
Amount financed
$34,000.00
From the formula below, to the cent
Negative equity rolled in
$2,000.00
From the formula below, to the cent
Total interest
$7,618.16
= Monthly payment × term − amount financed
Section
Auto loans
You enter
Vehicle price ($), Cash down payment ($), Trade-in value ($), Amount owed on the trade-in ($), Interest rate (APR) (%), Term (months)
You get
Monthly payment ($), Amount financed ($), Negative equity rolled in ($), Total interest ($)
Rounding
2 dp

Estimate for education, not financial advice. The result follows from the numbers you enter and the formula shown. It is not a quote or an offer, and it does not include fees, taxes or insurance unless the calculator asks for them. Ask your lender for the exact figures.

This calculator works out a car loan when you trade in a vehicle that still has a loan on it. Enter the new vehicle price, your cash down payment, the trade-in value, what you still owe on the trade, the APR and the term; you get the payment, the amount financed, any negative equity rolled into the new loan and the total interest.

Formula

Amount financed = price − down payment − trade-in value + amount owed on the trade-in. Negative equity = amount owed − trade-in value, when that is above zero. M = financed × r ÷ (1 − (1 + r)−n).

Worked Example

A $35,000 vehicle, $3,000 down, an $8,000 trade-in with $10,000 still owed, 6.9% APR for 72 months.

  1. Financed = 35,000 − 3,000 − 8,000 + 10,000 = $34,000.00
  2. Negative equity = 10,000 − 8,000 = $2,000.00
  3. r = 0.00575; M = 34,000 × 0.00575 ÷ (1 − 1.00575−72) = $578.03
  4. Total interest = 578.03 × 72 − 34,000 = $7,618.16

Assumptions

  • The payment is rounded to the cent and totals use the rounded payment; a lender’s final payment can differ by a few cents.
  • Fixed interest rate for the whole term; payments of equal size at the end of each month.
  • Interest compounds monthly at APR ÷ 12.
  • No fees, taxes or insurance unless the calculator has a field for them.
  • Sales tax, title and fees are not included. In many states tax is charged on the price minus the trade-in; check yours.
  • The dealer pays off the old loan in full.

How to read the result

Negative equity is debt from the old car carried into the new loan, so you pay interest on it for the whole new term.

Limits and common mistakes

  • Use the payoff amount from your current lender for “amount owed”, not the last statement balance.
  • If the trade-in is worth more than you owe, the difference lowers the amount financed.

Frequently Asked Questions

What is negative equity on a trade-in?

Owing more on the old car than it is worth; here $2,000.

What is the payment in this example?

About $578.03 a month for 72 months on $34,000.

Is sales tax included?

No. Tax rules on trade-ins differ by state, so add any tax to the price yourself.

Formula used
in price | Vehicle price | $ | 35000 | 1 | 10000000
in dp | Cash down payment | $ | 3000 | 0 | 10000000
in tr | Trade-in value | $ | 8000 | 0 | 10000000
in owe | Amount owed on the trade-in | $ | 10000 | 0 | 10000000
in apr | Interest rate (APR) | % | 6.9 | 0.01 | 100
in n | Term | months | 72 | 1 | 120
out pmt | Monthly payment | $ | round((price - dp - tr + owe) * (apr / 1200) / (1 - (1 + apr / 1200) ^ -n), 2) + 0 * sqrt(price - dp - tr + owe) | 2
out fin | Amount financed | $ | price - dp - tr + owe | 2
out neq | Negative equity rolled in | $ | max(0, owe - tr) | 2
out int | Total interest | $ | pmt * n - fin | 2

Each line is one input (in, sel, list) or one result (out: label, unit, formula, decimals). How the calculators work

Method: the standard loan formula for this calculation, fixed rate and monthly compounding unless stated, rounded as each result states. Not financial advice; no lender, rate or product is recommended. See formulas and assumptions, the disclaimer or report an error.

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