Negative Equity Car Calculator

Equity in a vehicle is its market value minus what you still owe:

$E = V - B$

• $V$ — market value, whatever a buyer or dealer will actually pay today
• $B$ — the payoff: the outstanding balance plus interest accrued since the last payment, which is slightly more than the balance shown on a statement

$E > 0$ is positive equity; $E < 0$ is negative equity, also called being upside down or underwater. There is no formula for $V$ — it comes from a valuation guide or an offer. The math starts once you have it.

Negative equity appears because the two curves move differently. A loan balance falls slowly at first, since early payments are mostly interest:

$B_k = P(1+r)^k - M\cdot\frac{(1+r)^k - 1}{r}$

while value falls fast and early, roughly geometrically:

$V_k = V_0 (1-d)^{k/12}$

with $d$ the annual depreciation rate. A small down payment, a long term and a high rate all push the crossover later.

When a car with negative equity is traded, the shortfall does not disappear — it is added to the new loan:

$A = \text{Price} + \text{Tax and fees} - \text{Down} - \text{Trade-in allowance} + \text{Old payoff}$

The last two terms are the whole story. If the allowance exceeds the payoff you subtract net equity; if the payoff exceeds the allowance you add the difference, and now you are financing part of a car you no longer own.

The payment on the result is the ordinary amortised-loan formula:

$M = A\cdot\frac{r(1+r)^n}{(1+r)^n - 1}, \qquad r = \frac{\text{APR}}{12}$

and the total interest is $nM - A$.

Two things worth computing before signing

1. The starting equity of the new deal: $\text{new car value} - A$. Rolling a shortfall in guarantees this starts negative.
2. The break-even month: the first $k$ where $V_k \ge B_k$.

Whether sales tax applies to the full price or to the price net of the trade-in is a jurisdictional rule, and it changes $A$. Use the rule that applies where you are.

• Using the statement balance as the payoff: the payoff includes interest accrued since the last payment. It is always a little higher.
• Confusing the trade-in allowance with the car's value: a generous-looking allowance paired with a higher price is arithmetic sleight of hand. Compare $A$ across offers, never the allowance alone.
• Believing a longer term makes the shortfall smaller: stretching to 84 months lowers $M$ but raises $nM - A$ and delays the break-even month, which is what created the negative equity in the first place.
• Netting equity the wrong way round: negative equity is added to the amount financed, not subtracted.
• Assuming straight-line depreciation: value drops fastest in the first year. A linear estimate makes the underwater period look shorter than it is.
• Forgetting gap coverage exists as a separate question: if the car is written off while $B > V$, the shortfall is still owed. That is an insurance matter, not a calculation.