Why revolving debt behaves differently from a loan
An instalment loan tells you when it ends. The note fixes the payment and the number of payments, and the two are consistent by construction. A credit card fixes neither: it sets a rate and a minimum, and the payoff date is whatever your behaviour makes it.
That is why the same balance can cost wildly different amounts. On $6,500 at 22.99%, paying $250 a month clears the card in 37 months and costs $2,582 in interest. Paying $500 clears it in 16 months and costs $1,047.05. The balance is identical; the payment decision changed the cost by a factor of two and a half.
The mechanism is that interest is charged on the balance you are still carrying, so every month you remain in debt is a month you pay for. Cards compound this monthly on a balance calculated by the average daily method, and the periodic rate is the APR divided by twelve — 22.99% becomes 1.9158% a month.
The number that surprises people most is the break-even payment: interest, new charges and any monthly share of the annual fee. On a $5,000 balance at 24% that is $100 a month, so a $100 payment leaves the balance exactly where it started, forever. Anything below it and the debt grows while you are paying.
The two questions and their two formulas
How long will this take? Rearranging the annuity identity for n gives n = −ln(1 − r·B / M) / ln(1 + r), rounded up to a whole month. Read the argument of the logarithm carefully: r·B is the first month's interest, so r·B/M is the share of your payment that interest consumes. When that share reaches one, the logarithm's argument reaches zero and n goes to infinity — the algebra's way of stating the break-even condition.
What payment finishes by a date? That is the ordinary loan formula run forward: M = B·r / (1 − (1 + r)−n), the same identity behind the personal loan calculator. On $6,500 at 22.99% over 12 months it gives $611.46.
Both closed forms assume nothing else happens. Once you add new monthly charges or an annual fee, the cash flows are no longer a clean annuity, so the calculator simulates the account month by month instead and finds the required payment by bisection. The simulation is also what lets it detect the case where no payment reaches your target — which happens whenever ongoing charges are large relative to the horizon.
Worked example: $6,500 at 22.99% paying $250 a month
Take the defaults and follow the first month, then jump to the closed form.
- Monthly periodic rate. 22.99 ÷ 100 ÷ 12 = 0.01915833.
- Month one interest. 6,500 × 0.01915833 = $124.53. Nearly half of a $250 payment is consumed before it touches the debt.
- Month one principal. 250 − 124.53 = $125.47, leaving a balance of $6,374.53.
- Now the whole schedule. r·B/M = 124.5292 ÷ 250 = 0.4981167, so 1 − that = 0.5018833.
- Take logarithms. ln(0.5018833) = −0.6893877 and ln(1.01915833) = 0.01897696. Dividing gives n = 36.33, which rounds up to 37 months.
- Total cost. Interest over those 37 months is $2,582.35, so you pay $9,082.35 in total — 28.4% of everything you hand over goes to interest.
Change one thing. Raise the payment to $500 and the card clears in 16 months with $1,047.05 of interest: double the payment, well under half the time, and 59.5% less interest. That non-linearity is the single most useful fact about revolving debt, and it is why the marginal dollar sent to a card is worth more than almost anything else you can do with it.
Reading the result and choosing a payment
Start with the interest share. At 28.4% on the default case, roughly two dollars in seven go to the issuer rather than to the debt. Below about 10% the payment is doing its job; above 25% the schedule is long enough that the rate is compounding meaningfully against you.
Then compare the break-even payment against your minimum. Card minimums are typically the greater of a fixed dollar amount and a small percentage of the balance — commonly 1% of principal plus that month's interest and fees, or 2% to 3% of the balance. That is deliberately just above break-even, which is why minimum payments produce payoff horizons measured in decades. The reference table below shows the effect starkly: at 26% APR, paying 2% of a $5,000 balance never clears it at all, because $100 does not cover $108.33 of interest.
If the payment you can manage produces an uncomfortable answer, there are two structural fixes rather than behavioural ones. A balance transfer to a promotional 0% card converts interest into a one-off transfer fee, typically 3% to 5% of the amount moved — on $6,500 that is $195 to $325, against $2,582 of interest, so the arithmetic is usually overwhelming. The catch is the promotional window: whatever remains when it ends reverts to a normal rate, so divide the balance plus the fee by the number of promotional months and check that you can pay it.
A fixed-rate consolidation loan is the other route. It converts revolving debt into an instalment loan with a real end date, usually at a materially lower rate — the personal loan calculator prices one including its origination fee. Both fixes fail in the same way: if the card balance goes back up afterwards, you now have two debts.
And if you are carrying several cards, the ordering question matters more than the payment size. The debt avalanche calculator shows which balance to attack first and what the alternative orderings cost.
Months to clear a $5,000 balance, by APR and payment
| APR | $100 (2%) | $150 (3%) | $200 (4%) | $250 (5%) |
|---|---|---|---|---|
| 12% | 70 | 41 | 29 | 23 |
| 18% | 94 | 47 | 32 | 24 |
| 22% | 137 | 52 | 34 | 26 |
| 26% | never | 60 | 37 | 27 |
| 30% | never | 73 | 40 | 29 |
The two “never” cells are not a formatting choice: at 26% the monthly interest on $5,000 is $108.33 and at 30% it is $125, both above the $100 payment, so the balance rises every month. Notice also how much more the APR matters at low payments than at high ones — from 12% to 30% the $250 column moves by six months and the $150 column by thirty-two.
What this model simplifies
- Interest is computed monthly here, on the balance at the start of the month. Real cards use the average daily balance method, often with compounding applied daily, so a real statement can differ by a few dollars a month. The direction of the difference depends on when in the cycle you pay.
- The grace period is ignored. If you pay the statement balance in full each month, purchases carry no interest at all. That grace disappears the moment you carry a balance, and on most cards it does not return until the balance is cleared for a full cycle.
- Cash advances and balance transfers usually have their own rates, often higher, and no grace period. Run those portions separately.
- Payment allocation is set by law, not by choice. Under the CARD Act, amounts above the minimum must be applied to the highest-rate balance first — helpful if you carry both purchases and a cash advance, and something no calculator can override.
- Minimum payments fall as the balance falls. This calculator assumes a fixed dollar payment, which is the only assumption under which a card clears in reasonable time. Paying the declining minimum is what produces the decades-long horizons in the fine print.
- Penalty APRs are not modelled. A payment more than 60 days late can trigger a substantially higher rate on the existing balance.
- Rewards are not netted off. No cash-back rate approaches a carried-balance APR, so rewards on a revolving balance are not a saving.
Where card debt sits, and why it is almost always first
Credit card interest is generally the most expensive money a household holds — well above auto loans, personal loans and mortgages, in that order. That ordering follows directly from collateral: nothing secures a card balance, so nothing limits the issuer's loss except the rate.
The practical consequence is that clearing card debt beats almost every other use of a marginal dollar. Paying down a 22.99% balance is a guaranteed, tax-free 22.99% return with no market risk, which no investment offers reliably. The two things that legitimately come first are an employer retirement match, because a match is an immediate return no rate matches, and a minimal cash buffer, because a household with no buffer simply puts the next emergency back on the card.
Two structural points worth knowing. Utilisation — your balance divided by your credit limit — is a significant input to credit scores, and it is measured on the balance the issuer reports, usually the statement balance. Paying before the statement date can therefore improve a score even when you always pay in full. And closing a paid-off card reduces total available credit, which raises utilisation on everything else; keeping it open with no balance is normally the better move.
Finally, a note on order. If your card balance is what is keeping your debt-to-income ratio high, it is also constraining any mortgage you apply for — the home affordability calculator shows how much purchasing power each $100 of monthly debt payment costs.