Loans & Mortgages
Payoff time with extra
Solves the amortisation formula for the number of months at the higher payment.
The Formula
n = -ln(1 - r x balance / (payment + extra)) / ln(1 + r)
Solves the amortisation formula for the number of months at the higher payment.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| B | Balance | currency | Amount still owed. |
| P | Payment | currency | Required monthly payment. |
| E | Extra | currency | Additional principal each month. |
| r | Monthly rate | rate | Annual rate divided by twelve. |
What Each Symbol Means
Bcurrency
Balance
Amount still owed.
Pcurrency
Payment
Required monthly payment.
Ecurrency
Extra
Additional principal each month.
rrate
Monthly rate
Annual rate divided by twelve.
See It Worked With Real Numbers
A formula on its own does not tell you which number goes where. The how to calculate mortgage payoff 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 Mortgage Payoff, filed under Finance. Every number the guide produces comes from substituting into this one line.