Loans & Mortgages
Principal and interest
The standard amortisation formula on the amount borrowed.
The Formula
P&I = Loan x r / (1 - (1 + r)^-n)
The standard amortisation formula on the amount borrowed.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| L | Loan amount | currency | Home price minus the down payment. |
| r | Monthly rate | rate | Annual rate divided by twelve. |
| n | Payments | count | Term in years multiplied by twelve. |
What Each Symbol Means
Lcurrency
Loan amount
Home price minus the down payment.
rrate
Monthly rate
Annual rate divided by twelve.
ncount
Payments
Term in years multiplied 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 a mortgage 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 Mortgage Payment, filed under Finance. Every number the guide produces comes from substituting into this one line.