Paying off $4,500 at 22.9% APR with $200 a month takes 30 months and costs $1,500 in interest. The time to clear a balance with a fixed monthly payment follows from a logarithm: n = −ln(1 − Br/M) / ln(1+r), where B is the balance, r the monthly rate, and M the payment — and if the payment does not even cover the first month's interest, the balance never falls.
Your 22.9% is above the average APR on credit cards carrying a balance of 21.52%. Federal Reserve G.19, as of Q1 2026.
Suppose you put the default values into Credit Card Payoff Calculator:
Plug those into the formula n = −ln(1 − Br/M) / ln(1+r) and the result is:
At the defaults the monthly rate is 22.9% / 12 ≈ 1.908%, so the first month accrues about $85.87 of interest — $200 covers it with $114.13 left for principal. The formula gives n ≈ 29.7, rounded up to 30 months, or 2.5 years. Total paid is 30 × $200 = $6,000 against a $4,500 balance, so interest costs $1,500 — a third of the original debt.
| Monthly payment | Months to payoff | Total interest |
|---|---|---|
| $150 | 45 | $2,250 |
| $200 | 30 | $1,500 |
| $300 | 18 | $900 |
| $400 | 13 | $700 |
| $500 | 10 | $500 |
Each month the balance accrues interest at APR / 12, then the payment is subtracted; the formula solves in closed form for how many such months reach zero, consistent with CFPB repayment methodology. The month count is rounded up (in practice the final payment is smaller), total paid is payment × months, and interest is the excess over the starting balance. The model treats the card as frozen — no new purchases, fees, or rate changes — and makes the mathematical floor explicit: when M ≤ B × r, the entire payment is absorbed by interest and the payoff time is infinite, which the calculator reports as Never.
References: CFPB methodology.
Last reviewed July 2, 2026 · Editorial policy