The debt payoff formula determines how many months until a balance reaches zero, given a fixed monthly payment and interest rate. It is the same calculation used by banks and credit card issuers — but understanding it puts you in control of your debt timeline.
The Core Formula
The standard formula for calculating payoff months is:
Where:
- B = current balance (dollars)
- r = monthly interest rate (APR ÷ 12 ÷ 100)
- P = fixed monthly payment (dollars)
- log = natural logarithm
Important: P must be greater than B × r. If your monthly payment equals or is less than the monthly interest charge, the balance never decreases.
Step-by-Step Example
Assume: $8,500 balance, 18.99% APR, $300/month payment.
- Calculate monthly rate: r = 18.99 / 12 / 100 = 0.015825
- Calculate monthly interest charge: B × r = 8,500 × 0.015825 = $134.51 (minimum needed to reduce the balance)
- Apply the formula:months = −log(1 − (8,500 × 0.015825) / 300) / log(1 + 0.015825)= −log(1 − 0.44837) / log(1.015825)= −log(0.55163) / 0.015700= 0.59481 / 0.015700≈ 37.9 months → 38 months
- Total paid = 38 × $300 = $11,400 (last payment slightly less)
- Total interest = $11,400 − $8,500 = approximately $2,900
Reverse Formula: Finding the Required Payment
To find the monthly payment needed to pay off a balance in exactly n months:
Example: Pay off $8,500 at 18.99% APR in exactly 24 months.
The Minimum Payment Trap
The table below shows how dramatically monthly payment size affects total cost on an $8,500 balance at 18.99% APR.
| Monthly Payment | Payoff Time | Total Interest | Total Paid |
|---|---|---|---|
| $170 (2% min) | 8+ years | $8,200+ | $16,700+ |
| $250 | 50 months | $3,900 | $12,400 |
| $300 | 37 months | $2,583 | $11,083 |
| $450 | 23 months | $1,330 | $9,830 |
Why Monthly Rate Matters
Credit cards compound monthly. A 24% APR is not 24% per year effective — it is 2% per month, which compounds to an effective annual rate of (1.02)^12 − 1 = 26.82%. This makes high-APR debt significantly more expensive than the stated rate implies.
The practical implication: paying down a 24% APR card is equivalent to earning a guaranteed 26.82% return on that money — well above any savings account or low-risk investment.
Common Mistakes When Using the Formula
- Using the annual rate instead of the monthly rate — always divide APR by 1,200, not 100
- Forgetting the formula breaks down if your payment is less than or equal to monthly interest
- Not accounting for minimum payment changes as the balance decreases
- Ignoring new charges added to the balance each month