The formula
Credit card interest is charged once a month, on the balance you owe at that moment. The formula has two parts. First, the monthly rate: divide the APR by 12. At 24% APR the monthly rate is 24% divided by 12, which is 2% a month. Second, the month’s interest: multiply the balance by the monthly rate. On a $10,000 balance at 2% a month, the first month’s interest is $200.00. Then subtract the payment from the balance plus the interest, and repeat next month on the new balance. That is the whole formula — interest on the balance, every month, until the balance is gone.
Step 1 — Write down your balance
Start with what you owe right now. In our worked example that is $10,000. If you carry a balance from month to month, that is the number the interest is charged on — not your credit limit, and not what you spent this month.
Step 2 — Turn the APR into a monthly rate
The APR is a yearly number, but the card charges monthly, so divide it by 12. At 24% APR the monthly rate is 24% divided by 12, which is 2% a month. At 18% APR it is 1.5% a month. This one division is where most people go wrong — they multiply the balance by the full APR and get a number twelve times too big.
Step 3 — Work out one month’s interest
Multiply the balance by the monthly rate. On $10,000 at 2% a month, the first month’s interest is $10,000 times 2%, which is $200.00. That $200.00 is added to the balance before your payment comes off, so the balance the payment fights is $10,200.00, not $10,000.00.
Step 4 — Apply the payment
Subtract the monthly payment from the balance plus the interest. Our example pays $322.67 a month — the same payment as a 10% personal loan on the same $10,000. After the first month the balance is $10,000.00 plus $200.00 of interest minus $322.67, which is $9,877.33. The payment beat the interest by $122.67, so the balance fell by that much.
Step 5 — Repeat until the balance is gone
Next month the interest is charged on the new, smaller balance: $9,877.33 times 2% is $197.55, so the balance becomes $10,074.88 and the $322.67 payment takes it to $9,752.21. Every month the interest shrinks a little and the payment eats a little more of the balance. Keep going — 48 full payments of $322.67 and a final $271.00 payment — and the card is clear in 49 months. The total paid is $15,759.16 and the interest is $5,759.16.
Step 6 — Compare the total with a loan
The same $10,000 on a 10% personal loan at the same $322.67 a month costs $1,616.12 in interest over 36 months — $4,143.04 less than the card, and 13 months sooner. The loan is cheaper because the rate is lower and the term is fixed: the card’s 24% rate is what stretches the payoff to 49 months. If the rate is the only difference, the rate is the whole story.
The worked example
Setup: $10,000 balance, 24% APR, $322.67 a month. Line 1: the monthly rate is 24% divided by 12, which is 2%. Line 2: the first month’s interest is $10,000 times 2%, which is $200.00. Line 3: the balance after the first payment is $10,000.00 plus $200.00 minus $322.67, which is $9,877.33. Line 4: repeat — 48 full payments of $322.67 and a final $271.00 payment clear the card in 49 months. Line 5: the total paid is $15,759.16 and the interest is $5,759.16. Check it against the calculator on the personal loan vs credit card page and you will get the same numbers.
How the numbers change
Two changes show what matters most. First, pay more: at $500 a month instead of $322.67, the same $10,000 at 24% clears in 26 months and costs $2,898.75 in interest — $2,860.41 less interest and 23 months sooner. The payment is the lever you control. Second, pay less: at $100 a month the card never pays off at all, because the first month’s interest is $200.00 — more than the payment — so the balance grows every month instead of shrinking. A payment below the monthly interest is not a slow payoff; it is no payoff.
Working backwards
Sometimes the question runs the other way: you know the target and want the input. To clear $10,000 in 36 months at 24% APR, the smallest whole-dollar payment is $393 a month — the exact formula payment is 392.3285, and at the displayed $392.33 the card takes 36 months and costs $4,123.78 in interest. And if the target is the rate: a card APR of 10.00% is the flip point against a 10% personal loan — at 10.00% the card takes 37 months and costs $1,616.20 in interest, so the loan wins by $0.08; below 10% the card wins. Both are worked out in full on the calculator page.
What the calculation leaves out
The formula assumes one fixed APR and the same payment every month, and real cards are messier than that. It ignores annual fees, late fees, and penalty APRs, which can push the rate higher after a missed payment. It ignores new purchases, which add to the balance and restart the interest on the new amount. It ignores balance transfers and 0% introductory periods, which change the rate for a while. And it ignores minimum payments — usually 1 to 2% of the balance — which stretch the payoff far longer than a fixed $322.67. Use it to see what the rate and the payment do — then check your statement for the fees and the real minimum before you act on it.
What to do next
Run your own numbers on personal loan vs credit card: put in your debt, your rates, and your payment, and it will give you the interest and the payoff time on each side — and it will work backwards from any target you set. If you want the payoff date for a card on its own, credit card payoff calculator works out the months and the interest from your balance and payment. And if you want the loan side of the comparison, loan payoff calculator prices any fixed loan the same way.