Worked derivation
How long minimum payments take, and when they never finish
There is one line of arithmetic that decides it, and it is not the one most calculators show you.
Does not clear
$3,000.00 at 29.99% APR, paying $30.00 a month, never reaches zero.
Interest in month one: $74.98. Payment: $30.00. The balance is $44.98 higher after the payment than before it — and higher again the month after.
Computed on this page by the same engine the calculator runs, at build time.
The only line that matters
A card charges interest on what you owe, then your payment arrives. So the balance moves by the difference between the two:
interest this month = balance × (APR ÷ 12)
balance next month = balance + interest − payment
Everything else follows from that. If the payment is larger than the interest, the balance falls and the card eventually clears. If it is smaller, the balance rises and the card never clears, no matter how long you keep paying. There is no third case.
The payment that exactly equals the interest is the hinge. On $3,000.00 at 29.99% that is $74.98 a month — and it pays off nothing whatsoever. It holds the balance exactly where it is, indefinitely. Only the money above that figure reduces the debt.
That is why two cards with similar balances can behave completely differently. The question is never "is the minimum small". It is "is the minimum bigger than the interest", and by how much.
Four cards, same arithmetic
Every row below is computed by running the engine, not looked up. The only thing that changes between the first two rows is the payment.
| Balance | APR | Paid monthly | Interest, month 1 | Time to clear | Interest paid |
|---|---|---|---|---|---|
| $3,000.00 | 29.99% | $30.00 | $74.98 | never clears | unbounded |
| $3,000.00 | 29.99% | $90.00 | $74.98 | 73 months (6y 1m) | $3,526.99 |
| $6,000.00 | 22.99% | $150.00 | $114.95 | 77 months (6y 5m) | $5,492.03 |
| $6,000.00 | 22.99% | $250.00 | $114.95 | 33 months (2y 9m) | $2,113.21 |
"Never clears" means a balance remains after 50 years, which is where the engine stops simulating. There is no payment schedule beyond it — the balance is rising, not falling.
Two numbers worth keeping
Interest can exceed the debt
$3,000.00 at 29.99%, paid $90.00 a month, costs $3,526.99 in interest.
That is $526.99 more than the balance itself, over 6y 1m. The card is repaid roughly 2.2 times over.
What $100.00 a month removes
Paying $250.00 instead of $150.00 on $6,000.00 removes 44 months and $3,378.82.
Same balance, same 22.99% rate, same card. 6y 5m becomes 2y 9m.
Why a real minimum is worse than this
The table above assumes a fixed monthly payment. Most issuers do not work that way: a minimum is commonly the greater of a small flat amount or a percentage of the balance, so it shrinks every month as the balance falls.
That matters more than it sounds. Paying a fixed $150.00 clears $6,000.00 at 22.99% in 77 months. Following a percentage minimum down as the balance falls takes longer, because the amount reaching the principal falls with it.
So the figures on this page are the optimistic case. Where a row says a card never clears, a declining percentage minimum does not rescue it — it is smaller still.
Check this against your own statement
You do not have to take this page's word for any of it, and you should not. If you have a US card, your statement carries a repayment disclosure required under Regulation Z: a box stating how long the balance takes to clear making only minimum payments, and what it costs.
Compare it with the arithmetic above. The two figures will usually differ, and the reason is stated rather than hidden: your issuer models the percentage minimum your agreement specifies, while this page models a fixed payment. When they disagree, your statement is describing your card — this page is describing what the arithmetic does to any card.
The one figure you can check exactly, with a pocket calculator: month-one interest. Take your balance, multiply by your APR, divide by twelve. On $3,000.00 at 29.99% that is $74.98. If your minimum payment is below that number, your balance is growing.
What this page does not model
Rounding happens to the cent every month, the way a statement does it, and the final payment is reduced to clear the balance exactly rather than overshooting.
Not modelled: new spending on the card, promotional or introductory rates, penalty APRs triggered by a late payment, fees, cash-advance rates charged separately from purchase rates, or a percentage-based minimum that changes month to month. Each of those moves the real answer, none of them changes the rule at the top of this page, and none of them is something a calculator can know about your account.
Common questions
- Can a credit card really never be paid off?
- Yes, and it needs no unusual numbers. If the minimum payment is smaller than the interest charged that month, the balance is larger after the payment than before it. On $3,000.00 at 29.99% the card charges $74.98 in month one; a $30.00 payment leaves $44.98 of unpaid interest added to what you owe. The balance grows every month, forever.
- What payment makes the balance stand still?
- Exactly the monthly interest: balance × (APR ÷ 12). On $3,000.00 at 29.99% that is $74.98 a month, which pays off nothing at all — it holds the balance where it is. Every cent above that figure, and only the cents above it, reduce what you owe.
- My statement says a number of years. Why is yours different?
- Both can be right. US statements are required to show a payoff estimate under Regulation Z, and it assumes the percentage-based minimum your issuer actually uses, which shrinks as the balance falls. This page models a fixed monthly payment, which is the more optimistic case. If the figures differ, your statement is describing your card and this page is describing the arithmetic.
- Why does a percentage minimum take longer than a fixed one?
- Because it shrinks as you pay. A minimum of 2% of the balance starts high and falls every month, so the amount going to principal falls too, and the tail of the debt stretches out. Paying the same fixed amount every month — the figure your minimum started at — clears the balance sooner than following the minimum down.
- Does this account for new spending on the card?
- No. Every figure here assumes nothing further is charged to the card. New spending is added to the balance and charged interest in the same way, so it moves the answer in one direction only.
- Is a minimum payment the same everywhere?
- No. How a minimum is set is a matter of the cardholder agreement, not of any single rule, and it differs by issuer and by country. The arithmetic on this page does not depend on which formula your issuer uses — it depends only on whether the payment is larger than the interest.
Sources
- CFPB — What is a minimum payment? — retrieved 2026-08-12
- Regulation Z, Appendix M1 — Repayment Disclosures — retrieved 2026-08-12
- Every figure on this page is produced at build time by the same engine the debt payoff calculator runs, from the balances, rates and payments shown beside it. Nothing is transcribed from a third party. The sources above are cited for what they describe — how a minimum payment is set, and what a statement must disclose — not for any number here.
Written and maintained by Vikash Singh. Last verified 2026-08-12.