How Long It Really Takes to Pay Off a Credit Card
The debt payoff formula explained, with a real example showing how fixed payments interact with high APRs.
Credit card interest compounds monthly, and because APRs are often 20%+, the math behind "how long will this take to pay off" is less intuitive than most people expect.
The formula
n = −ln(1 − (Balance × r) / Payment) / ln(1 + r)
where r is the monthly rate (APR ÷ 12), and n is the number of months to payoff.
Worked example
A $5,000 balance at 22% APR with a fixed $200 monthly payment: the monthly rate r = 0.22/12 ≈ 0.018333. Balance × r = 5,000 × 0.018333 ≈ $91.67 — that's the interest charged in month one alone. Plugging into the formula gives n ≈ 33.8 months, just under 2 years 10 months.
Why the formula can "break"
If the monthly payment is less than or equal to the first month's interest charge, the formula has no solution — the balance would never actually shrink, since the payment doesn't even cover the interest accruing. In the example above, if the payment were dropped to $90 (below the $91.67 monthly interest), the balance would grow indefinitely rather than ever reaching zero, which is exactly the trap of paying only "the minimum" on a high-APR card.
The hidden cost of the minimum payment trap
Card issuers often set minimum payments around 1-3% of the balance. On a $5,000 balance, a 2% minimum payment is just $100/month — barely above the $91.67 monthly interest in this example, meaning payoff would take an extremely long time and rack up enormous cumulative interest. Doubling the payment to $200/month, as in the worked example, cuts payoff time dramatically precisely because a much larger share of each payment attacks principal instead of just covering interest.
A quick sensitivity check
Raise the payment from $200 to $300/month on that same $5,000/22% balance, and payoff time drops to roughly 18 months — nearly half the time — because a larger fixed payment shrinks the principal faster, which in turn reduces the next month's interest charge, compounding the payoff acceleration in your favor.
Common mistakes to avoid
- Comparing credit card APR directly to investment returns without accounting for the fact that guaranteed debt payoff (avoiding ~20%+ APR) usually beats uncertain market returns
- Ignoring that new purchases on the card reset the effective payoff clock, since they add to the balance the payment formula is working against
- Assuming a balance transfer with a temporary low rate solves the problem — it only helps if paired with a real payoff plan before the promotional rate ends
Run your own numbers with the credit card payoff calculator, and check your overall debt load with the debt-to-income ratio calculator.