Credit Card Payoff Formula

Finance Formula • Published on September 01, 2026 • Last updated September 01, 2026

Mathematical Equation

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

Variable Definitions

Number of months required to completely pay off the balance

Current outstanding credit card balance

Fixed monthly payment amount (must exceed monthly interest)

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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