Loans & Mortgages
Monthly payment on an amortising loan
The payment that clears the principal exactly over n payments, with interest charged monthly on the outstanding balance. Negative exponents are allowed directly in the expression.
The Formula
M = P x r / (1 - (1+r)^-n)
The payment that clears the principal exactly over n payments, with interest charged monthly on the outstanding balance. Negative exponents are allowed directly in the expression.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| P | Principal | currency | The amount borrowed. |
| r | Monthly rate | percent | Annual rate divided by twelve. |
| n | Payments | months | Months in the term. |
| M | Monthly payment | currency | The fixed payment each month. |
What Each Symbol Means
Pcurrency
Principal
The amount borrowed.
rpercent
Monthly rate
Annual rate divided by twelve.
nmonths
Payments
Months in the term.
Mcurrency
Monthly payment
The fixed payment each month.
See It Worked With Real Numbers
A formula on its own does not tell you which number goes where. The how to compare loan offers 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 Compare Loan Offers, filed under Finance. Every number the guide produces comes from substituting into this one line.