A mortgage payment has to be the same every month, even though interest accrues on a shrinking balance. The amortization formula solves that puzzle.
The mortgage payment formula
M = P × r × (1+r)^n ÷ ((1+r)^n − 1)
- P — the loan principal (price minus down payment)
- r — the monthly interest rate (annual rate ÷ 12)
- n — the total number of payments (years × 12)
- M — the monthly payment (principal + interest only)
How to calculate it step by step
For a $300,000 loan at 6.5% for 30 years:
- Monthly rate: 6.5% ÷ 12 = 0.005417
- Number of payments: 30 × 12 = 360
- (1 + r)^n = (1.005417)^360 ≈ 6.992
- M = 300,000 × 0.005417 × 6.992 ÷ (6.992 − 1) ≈ $1,896/month
Over 360 payments that is about $682,500 total — meaning roughly $382,000 of interest. Early payments are mostly interest; near the end they are almost all principal.
What is not in the formula
Real monthly housing costs also include:
- Property taxes and insurance — often escrowed into the payment
- PMI — required if your down payment is under 20%
- HOA fees — where applicable
How term length changes the math
A 15-year term at 6% vs a 30-year at 6.5% on $300,000:
- 15 years → ≈ $2,531/month but only ≈ $155,600 total interest
- 30 years → ≈ $1,896/month but ≈ $382,000 total interest
Shorter terms cost more monthly and far less over the life of the loan.
Put it into practice
Model your own mortgage — payment, total interest and full amortization — with the free Loan & Mortgage Calculator.
