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Credit Card Payoff Time Calculator

Paying a fixed amount every month retires a revolving balance on a predictable schedule — and that schedule can be written as a closed-form equation rather than simulated line by line. The catch is a boundary condition the formula cannot cross: pay only the interest and the balance never falls.

Months to pay off

36.3273

First month's interest
$124.53
Total of all payments
$9,081.82
Total interest
$2,581.82

Values update as you type. This calculator covers the single scenario its formula assumes — see Common Mistakes for what it leaves out.

The formula this calculator uses

n = -ln(1 - (rm x B) / P) / ln(1 + rm)

n
Number of monthly payments to reach zero
B
Current balance owed
rm
Monthly periodic rate — APR divided by 12
P
Fixed monthly payment
ln
Natural logarithm

How to check the result by hand

  1. 1

    Convert the APR to a monthly periodic rate

    Divide by 12 and by 100. An APR of 22.99% becomes 0.2299 / 12 = 0.0191583. Many issuers accrue daily, but for a fixed balance without new purchases the monthly approximation lands within a few cents.

  2. 2

    Check that the payment exceeds the monthly interest

    Compute rm x B. Here 0.0191583 x $6,500 = $124.53. If your payment is at or below this, stop — the balance will not fall and the formula has no real result. This is exactly what the requirement that the logarithm's argument stay positive means.

  3. 3

    Build the logarithm's argument

    Divide the monthly interest by the payment and subtract from one: 1 - (0.0191583 x $6,500 / $250) = 1 - 0.4981167 = 0.5018833. The closer this sits to zero, the more slowly principal is falling.

  4. 4

    Divide the two natural logarithms

    Take ln of that argument and ln of (1 + rm): ln(0.5018833) = -0.6893876 and ln(1.0191583) = 0.0189771. Negate the first and divide: 0.6893876 / 0.0189771 = 36.3273 months.

  5. 5

    Round up and price the total

    Thirty-seven payments of $250 come to $9,250.00, of which $2,750.00 above the $6,500 balance is interest. Using the unrounded 36.3273 gives the theoretically exact $9,081.82 — the $168.18 difference is the overshoot in that final partial month.

For worked examples, common mistakes and the limits of this formula, read the full How To Calculate Credit Card Payoff Time page.