Credit & Debt
Payments needed to clear a balance
Setting the balance after n payments to zero and solving for n gives the number of payments directly. The argument of the logarithm must be positive, which is the condition that the payment covers the interest.
The Formula
n = -ln(1 - r x B / P) / ln(1 + r)
Setting the balance after n payments to zero and solving for n gives the number of payments directly. The argument of the logarithm must be positive, which is the condition that the payment covers the interest.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| r | Monthly rate | percent | Annual rate divided by twelve. |
| B | Balance | currency | The amount outstanding at the start. |
| P | Payment | currency | The fixed payment made each month. |
| n | Payments | payments | How many payments clear the balance. |
What Each Symbol Means
rpercent
Monthly rate
Annual rate divided by twelve.
Bcurrency
Balance
The amount outstanding at the start.
Pcurrency
Payment
The fixed payment made each month.
npayments
Payments
How many payments clear the balance.
See It Worked With Real Numbers
A formula on its own does not tell you which number goes where. The how to pay off debt 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 Pay Off Debt, filed under Finance. Every number the guide produces comes from substituting into this one line.