How credit card interest actually compounds
Your card doesn't charge interest once a month — it charges it every day. The issuer divides your APR by 365 to get a daily periodic rate (22% APR → about 0.06% per day), multiplies it by that day's balance, and adds it to what you owe. Tomorrow's interest is charged on today's interest: that's compounding, and it's why balances grow faster than the sticker APR suggests. This calculator simulates month by month (APR ÷ 12) because it's easier to sanity-check against your statement; the difference versus daily compounding is small — a few dollars a year on typical balances — and always in the direction of your real card being slightly worse.
The formula
n is the number of monthly payments, B the balance, r the monthly rate (APR ÷ 12 ÷ 100), and P your fixed payment. If B × r ≥ P there is no solution — your payment doesn't cover the interest, and the balance grows forever. Flip the same formula around and you get the payment needed to be done in n months: P = B × r(1 + r)n ÷ ((1 + r)n − 1).
Worked example
A $5,000 balance at 22% APR, paying $150 a month: r = 22 ÷ 12 ÷ 100 ≈ 0.01833, so the first month's interest is $91.67 and only $58.33 of that first payment touches the principal.
Result: 52 payments (4 years 4 months), $2,798.05 of interest, $7,798.05 paid in total.
Want out in 24 months instead? The required payment is $259.39 — and total interest drops to $1,225.38.
The minimum payment trap
A typical minimum payment is that month's interest plus 1% of the balance, with a floor around $25 (formulas vary by issuer — check your cardholder agreement). It's engineered to always be affordable, which is exactly the problem: it shrinks as your balance shrinks, so your progress slows down over time. On a $3,000 balance at 22% APR, the first minimum is just $85 — and riding the minimum takes 180 payments (15 years) and $4,433.12 in interest, more than the original debt. The fix costs nothing extra on day one: freeze your payment at that first $85 instead of letting it shrink, and you're done in 58 months with $1,872.86 of interest — $2,560 saved by refusing to slow down.
The 0% balance-transfer play
Balance-transfer cards offer 0% for 12–21 months in exchange for a fee of 3–5% of the amount moved. The math usually favors the transfer if you can finish inside the window. Take the $5,000 balance: a 3% fee costs $150 up front, and clearing $5,150 over an 18-month promo takes about $286 a month with no interest at all. The same $286 a month at 22% APR would cost $1,083.18 in interest — so the transfer saves roughly $930. The play fails when the promo ends with a balance still on the card: the leftover starts accruing at the new card's full rate, and serial transfers pay the fee again each time. Commit to the payment that finishes the job before you move the debt.
More than one card? Order matters
When you're juggling several balances, pay minimums on everything and aim every spare dollar at the card with the highest APR — the "avalanche" order, which is mathematically optimal. The rival "snowball" method (smallest balance first) costs a bit more in interest but pays out quick wins that keep people going, and the best plan is the one you'll actually stick to. Compare both orderings with your real numbers in our debt snowball calculator.