How the Debt Calculator works
This calculator answers one question: if you pay a fixed amount every month toward a balance that charges interest, how long until it reaches zero — and how much of what you pay along the way is interest rather than principal? It uses the standard loan-payoff formula, the same math that sets the number of payments on an amortizing loan, solved here for time instead of payment size.
The formula
For a starting balance B, a monthly interest rate i (annual rate ÷ 12), and a fixed total monthly payment P (your regular payment plus any extra), the number of months n to reach a zero balance is:
n = −ln(1 − i·B / P) / ln(1 + i)
If the interest rate is 0%, this collapses to n = B / P — the balance simply divided by the payment. The formula only produces an answer when the payment exceeds the interest charged in the first month (i × B); if it does not, the balance can never shrink no matter how many months pass, and the calculator flags that case instead of returning a number.
Worked example
Take a $12,000 balance at 18% APR, paid down with $400 per month and no extra payment. The monthly rate is 18% / 12 = 1.5% (0.015), and the first month's interest is 0.015 × $12,000 = $180 — well under the $400 payment, so the balance does shrink over time. Solving the formula gives n ≈ 40.2, which rounds up to 41 monthly payments (about 3 years 5 months) to reach zero, since the final payment is a smaller, partial one. Over that stretch the total paid is around $16,060, of which roughly $4,060 is interest and the remaining $12,000 is the original balance.
What moves the payoff time and interest cost most
- Interest rate: a higher APR means more of each payment is consumed by interest before it touches principal, stretching out the payoff and raising the total interest owed.
- Payment size: even a modest increase shortens the timeline by more than a proportional amount, because it is the marginal dollar above the interest charge that actually reduces principal.
- Extra payments: any amount added on top of the regular payment goes entirely toward principal, since the interest portion is already covered — which is why extra payments are disproportionately effective at cutting both time and total interest.
What this calculator does not model
The projection assumes a fixed starting balance, a constant APR, and a payment that does not change from month to month, with no new charges added. It does not account for new purchases on a credit card, promotional or variable rates that change mid-payoff, minimum-payment formulas that shrink as the balance shrinks, or fees. If your card sets a minimum payment as a percentage of the balance rather than a fixed dollar amount, your actual payoff will differ from this fixed-payment projection — for a closer estimate, re-run the calculator periodically with your current balance and payment.