Credit Card Payoff Formula

Finance Formula • Published on July 30, 2026 • Last updated August 09, 2026

Mathematical Equation

$$N = -\frac{\ln\left(1 - \frac{i \cdot B}{P}\right)}{\ln(1 + i)}$$

Variable Definitions

N

Number of months required to completely pay off the balance

B

Current outstanding credit card balance

P

Fixed monthly payment amount (must exceed monthly interest)

i

Monthly interest rate (Annual APR / 12 / 100)

Detailed Explanation

In-Depth Guide

Key Concept

The Credit Card Payoff Formula determines the exact number of months (N) required to liquidate a revolving credit card balance (B) at an annual interest rate (i) with a fixed monthly payment (P).

Because interest compounds monthly on unpaid balances, making only minimum payments significantly extends the payoff timeline and inflates total interest costs.

Paying even a small amount above the minimum drastically reduces N and cuts total interest paid.

How to Calculate: Step-by-Step

1. Identify the current credit card balance ($B$). 2. Calculate the monthly interest rate ($i = \text{Annual APR} / (12 \times 100)$). 3. Determine your fixed monthly payment ($P$). Note: $P$ must be strictly greater than $i \times B$, otherwise the balance will grow continuously. 4. Compute $1 - \frac{i \cdot B}{P}$. 5. Take the natural logarithm $\ln\left(1 - \frac{i \cdot B}{P}\right)$. 6. Divide by $\ln(1 + i)$ and negate the result to calculate the total months ($N$).

Worked Calculation Example

Suppose you have a credit card balance of $10,000 at an annual APR of 24% and you commit to paying $400 per month: - Balance ($B$) = $10,000 - Monthly Rate ($i$) = 24% / 12 / 100 = 0.02 - Monthly Payment ($P$) = $400 - Monthly interest charge = $10,000 \times 0.02 = $200 - Compute $1 - \frac{0.02 \times 10000}{400} = 1 - 0.5 = 0.5$ - Compute $\ln(0.5) \approx -0.69315$ - Compute $\ln(1 + 0.02) = \ln(1.02) \approx 0.01980$ - Apply formula: $$N = -\frac{-0.69315}{0.01980} \approx 35.01\text{ months (approx 2 years 11 months)}$$ - Total Payments Made = $400 \times 35 = $14,000 - Total Interest Paid = $14,000 - $10,000 = $4,000

Common Use Cases

  • Credit card debt payoff timeline calculation
  • Minimum payment interest trap evaluation
  • Comparing credit card balance transfer savings
  • Budget planning for revolving debt liquidation

Frequently Asked Questions

Credit card minimum payments are usually set to 2% to 3% of the remaining balance (or interest plus 1%). As the balance decreases, the required minimum drops, extending the payoff timeline over 20 to 30 years.

If your payment is less than interest accrued, negative amortization occurs: unpaid interest is added back to your balance, causing your debt to grow continuously.

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