The Credit Card Payoff Formula
The number of months to pay off a balance is calculated using:
n = −ln(1 − r×P/M) ÷ ln(1+r)
n = months | r = monthly rate (APR ÷ 12) | P = balance | M = monthly payment
For a $6,500 balance at 22.77% APR:
- Monthly rate: 22.77% ÷ 12 = 1.8975%
- At $200/month: 52 months, $3,900 total interest
- At $300/month: 29 months, $2,200 total interest
- Difference: $1,700 saved, 23 months sooner
- On minimum payment (~$130/month): 159 months, $14,170 total interest
The minimum payment trap is severe at 22.77% APR — paying only the minimum turns a $6,500 balance into a $20,670 total cost over 13.3 years. Any amount above the minimum dramatically reduces both timeline and total interest paid.