Loans
Monthly payment on a fixed-rate loan
P is the amount borrowed, r the monthly rate and n the number of monthly payments. The denominator is the present-value factor of an annuity, which is why the same formula covers every fixed-rate loan.
The Formula
M = P x r / (1 - (1 + r)^-n)
P is the amount borrowed, r the monthly rate and n the number of monthly payments. The denominator is the present-value factor of an annuity, which is why the same formula covers every fixed-rate loan.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| P | Principal borrowed | currency | Amount borrowed after any down payment. |
| r | Monthly rate | rate | Annual nominal rate divided by 12. |
| n | Number of payments | count | Term in years multiplied by 12. |
| M | Monthly payment | currency | The fixed payment covering interest and principal. |
What Each Symbol Means
Pcurrency
Principal borrowed
Amount borrowed after any down payment.
rrate
Monthly rate
Annual nominal rate divided by 12.
ncount
Number of payments
Term in years multiplied by 12.
Mcurrency
Monthly payment
The fixed payment covering interest and principal.
See It Worked With Real Numbers
A formula on its own does not tell you which number goes where. The how to calculate an amortization schedule 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 An Amortization Schedule, filed under Finance. Every number the guide produces comes from substituting into this one line.