Credit Card Payoff Calculator: Months to Pay Off and Interest

This calculator works out how long a fixed monthly payment takes to clear a credit card balance and how much interest that costs. Enter the balance, the card’s APR and the payment you plan to make every month.

Formula

n = −ln(1 − r × B ÷ M) ÷ ln(1 + r), rounded up, with r = APR ÷ 1200. The last payment is the balance after n − 1 payments plus one month of interest. Total interest = M × (n − 1) + last payment − B.

Worked Example

A $5,000 balance at 22% APR, paying $200 a month.

1. r = 0.018333; r × B ÷ M = 0.4583
2. n = −ln(0.5417) ÷ ln(1.018333) = 33.7, so 34 months
3. Total interest = $1,749.88; total paid = $6,749.88

Assumptions

• No new purchases, fees or rate changes while you pay it off.
• Interest compounds monthly at APR ÷ 12; card issuers usually use a daily balance, which gives a slightly different figure.
• The same payment every month (not a minimum that falls with the balance).

How to read the result

If the payment is not more than one month’s interest, the balance never falls and the result is “Cannot compute”. A higher payment shortens the time sharply.

Limits and common mistakes

• Minimum payments that shrink with the balance take much longer than a fixed payment.
• A promotional 0% period is not modelled.

Frequently Asked Questions

How long does $200 a month take to pay off $5,000 at 22%?

About 34 months, with about $1,750 of interest.

Why “Cannot compute”?

The payment does not cover the monthly interest, so the balance does not go down.

Does paying more help a lot?

Yes. At $300 a month the same balance clears in 21 months.

in b | Card balance | $ | 5000 | 1 | 10000000
in apr | Card APR | % | 22 | 0.01 | 100
in m | Monthly payment | $ | 200 | 0.01 | 10000000
out n | Months to pay off | months | ceil(round(-ln(1 - (apr / 1200) * b / m) / ln(1 + apr / 1200), 6)) | 0
out int | Total interest | $ | m * (n - 1) + (b * (1 + apr / 1200) ^ (n - 1) - m * ((1 + apr / 1200) ^ (n - 1) - 1) / (apr / 1200)) * (1 + apr / 1200) - b | 2
out tot | Total paid | $ | b + int | 2