Loan
Fixed loan payment (amortization)
Standard amortization. Produces the level payment that retires principal exactly over n periods at a periodic rate r.
The Formula
M = P x r(1 + r)^n / ((1 + r)^n - 1)
Standard amortization. Produces the level payment that retires principal exactly over n periods at a periodic rate r.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| P | Principal borrowed | currency | The amount financed, after down payment and excluding any financed fees unless they were rolled in. |
| r | Interest rate per payment period | decimal | Annual rate divided by 12 for monthly payments. A 6.5% annual rate is 0.0054167 monthly. |
| n | Total number of payments | count | Monthly loans: years multiplied by 12. Thirty years is 360 payments. |
| M | Payment per period | currency | Principal and interest only; taxes, insurance and fees are not included. |
What Each Symbol Means
Pcurrency
Principal borrowed
The amount financed, after down payment and excluding any financed fees unless they were rolled in.
rdecimal
Interest rate per payment period
Annual rate divided by 12 for monthly payments. A 6.5% annual rate is 0.0054167 monthly.
ncount
Total number of payments
Monthly loans: years multiplied by 12. Thirty years is 360 payments.
Mcurrency
Payment per period
Principal and interest only; taxes, insurance and fees are not included.
See It Worked With Real Numbers
A formula on its own does not tell you which number goes where. The how to calculate loan 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 Loan Payment, filed under Finance. Every number the guide produces comes from substituting into this one line.