Loans
Payment sized on the full amortisation term
The ordinary level payment for the full schedule, even though only n of them will be made.
The Formula
PMT = P x i / (1 - (1 + i)^-N)
The ordinary level payment for the full schedule, even though only n of them will be made.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| PMT | Payment | currency per month | The level payment implied by the full schedule. |
| P | Principal | currency | The amount borrowed. |
| i | Period rate | fraction per month | The annual rate divided by twelve. |
| N | Amortisation term | months | The full number of payments the payment is sized on. |
What Each Symbol Means
PMTcurrency per month
Payment
The level payment implied by the full schedule.
Pcurrency
Principal
The amount borrowed.
ifraction per month
Period rate
The annual rate divided by twelve.
Nmonths
Amortisation term
The full number of payments the payment is sized on.
See It Worked With Real Numbers
A formula on its own does not tell you which number goes where. The how to calculate a balloon payment 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 A Balloon Payment, filed under Finance. Every number the guide produces comes from substituting into this one line.