Credit & Debt
Number of payments to zero
Requires P > rm x B. Round the result up, because a partial final month is still a full calendar month of payments.
The Formula
n = -ln(1 - (rm x B) / P) / ln(1 + rm)
Requires P > rm x B. Round the result up, because a partial final month is still a full calendar month of payments.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| B | Balance owed | currency | The current outstanding balance. Assumes no new purchases during the payoff period. |
| r(m) | Monthly periodic rate | decimal | APR divided by 12, expressed as a decimal: 22.99% becomes 0.2299 / 12 = 0.0191583. |
| P | Monthly payment | currency | A fixed amount paid every month. Must exceed the first month's interest or the balance never clears. |
| n | Number of payments | months | Months until the balance reaches zero, rounded up to the next whole month. |
What Each Symbol Means
Bcurrency
Balance owed
The current outstanding balance. Assumes no new purchases during the payoff period.
r(m)decimal
Monthly periodic rate
APR divided by 12, expressed as a decimal: 22.99% becomes 0.2299 / 12 = 0.0191583.
Pcurrency
Monthly payment
A fixed amount paid every month. Must exceed the first month's interest or the balance never clears.
nmonths
Number of payments
Months until the balance reaches zero, rounded up to the next whole month.
See It Worked With Real Numbers
A formula on its own does not tell you which number goes where. The how to calculate credit card payoff time page applies this equation to a concrete case, shows every intermediate step, and names the mistakes that produce a wrong answer even when the algebra is right.
Where This Formula Appears
This equation is the working core of How To Calculate Credit Card Payoff Time, filed under Finance. Every number the guide produces comes from substituting into this one line.