How the minimum payment is calculated
Each simulated month, interest accrues on the current balance at the monthly rate (APR ÷ 12). The minimum payment is the greater of the stated percentage of the new balance (including that month's interest) or the dollar floor, and it declines as the balance declines because it is recalculated as a percentage each month. Federal law requires credit card statements to disclose the estimated time to pay off the balance, and the total interest that would cost, if only the minimum is paid — the same figures below.
- Each month: interest = balance × (APR ÷ 100 ÷ 12); minimum payment = max(minPct% × (balance + interest), floor); balance = balance + interest − minimum payment
- Never-pays-off condition: minimum % ≤ monthly periodic rate (APR ÷ 12)
Worked example: $5,000 at 24% APR
On a $5,000 balance at 24% APR with a 3% minimum (floor $25), the balance takes 224 months (about 18.7 years) to reach zero, with total interest of $8,413.92 and a first minimum payment of $153.00. That total interest is nearly 68% more than the original balance — a direct result of a long payoff period combined with interest compounding on a slowly declining balance.
| Minimum payment % | Outcome at 24% APR on $5,000 |
|---|---|
| 2% (equal to the monthly periodic rate) | The balance never decreases — every payment is absorbed by that month's interest |
| 3% (floor $25) | Payoff in 224 months (≈18.7 years); total interest $8,414 |
| A higher fixed payment above the minimum | Payoff time and total interest both fall sharply |
The case where the balance never falls
If the minimum payment percentage does not exceed the monthly periodic interest rate, the balance never decreases under that minimum — every dollar paid is absorbed by interest. For a 24% APR card, the monthly periodic rate is 2% (24% ÷ 12), so a card with only a 2% minimum-payment policy on a 24% APR balance would never amortize through minimum payments alone. This is a mathematical description of the payment schedule, not a statement about any specific cardholder's ability to pay more.
Why the payment keeps shrinking
Because the minimum is typically a percentage of the current balance, the required dollar amount declines as the balance declines, which means minimum payments shrink over time even as interest keeps accruing — this is a central reason minimum-payment payoff schedules stretch out for years, far longer than a fixed payment of the same starting size would take. The Consumer Financial Protection Bureau requires issuers to print the payoff-time and total-interest disclosure on every statement precisely so cardholders can see this effect for their actual balance.
よくある質問
How long does it take to pay off a credit card making only the minimum payment?
On a $5,000 balance at 24% APR with a 3% minimum payment (floor $25), it takes 224 months — about 18.7 years — with total interest of $8,414 over that period.
Why does my minimum payment get smaller over time?
Most issuers calculate the minimum as a percentage of the current outstanding balance each month, so as the balance declines, the required dollar minimum declines with it — even while interest keeps accruing on what remains.
Can a credit card balance never pay off with minimum payments?
Yes, mathematically, if the minimum payment percentage does not exceed the monthly periodic interest rate (APR ÷ 12). At a 24% APR, that monthly rate is 2%, so a 2% minimum-payment policy would never reduce the balance.
Is minimum-payment total interest really more than the original balance?
It can be. On the $5,000-at-24%-APR example, total interest of $8,414 is nearly 68% more than the original balance — a result of a long payoff period combined with interest compounding on a slowly declining balance.
参考文献
- Consumer Financial Protection Bureau (CFPB) — What is the minimum payment on my credit card statement? https://www.consumerfinance.gov/
- Federal Reserve Board — Regulation Z (Truth in Lending Act), minimum payment disclosure requirements under the CARD Act of 2009. https://www.federalreserve.gov/
- Federal Trade Commission (FTC) — Understanding credit card terms. https://consumer.ftc.gov/