Mortgage Payment Formula
Understand the fixed-rate mortgage principal-and-interest payment formula and the variables behind the monthly payment.
Payment = P × r(1+r)^n ÷ ((1+r)^n − 1)What the formula means.
The standard amortizing-payment formula spreads a loan balance across equal monthly principal-and-interest payments using the monthly interest rate and total number of payments.
The formula estimates principal and interest only.
Taxes, insurance, HOA fees and mortgage insurance may change the total monthly housing payment.
At a zero interest rate, payment simplifies to principal divided by number of payments.
Variables.
PAmount financed after the down payment.
rAnnual nominal rate divided by 12.
nLoan term in years multiplied by 12.
Worked example.
- r = 0.065 ÷ 12
- n = 30 × 12 = 360
- Apply P × r(1+r)^n ÷ ((1+r)^n − 1)
Common mistakes.
- Using the annual rate directly as the monthly rate.
- Forgetting to subtract the down payment from home price.
- Calling principal-and-interest payment the complete cost of owning the home.
Quick questions.
Does this formula include property taxes?
No. It calculates the amortizing principal-and-interest payment.
Why does the monthly rate use annual rate divided by 12?
The formula models monthly payment periods, so the nominal annual rate is converted to a monthly periodic rate.