How to Calculate a Mortgage Payment
A mortgage payment is calculated using a formula that spreads the total cost of a fixed-rate loan — including all interest — into equal monthly instalments over the loan term. While the payment amount stays the same every month, the split between principal repaid and interest paid changes significantly over time, a process called amortisation.
Last updated: March 31, 2026
The Formula
M = P × [r(1+r)^n] ÷ [(1+r)^n − 1]
Variable Definitions
| Symbol | Name | Description |
|---|---|---|
| M | Monthly Payment | The fixed amount you pay each month, covering both principal and interest |
| P | Loan Principal | The amount borrowed — the purchase price minus your down payment |
| r | Monthly Interest Rate | The annual interest rate divided by 12. For 6% annual rate: r = 0.06 ÷ 12 = 0.005 |
| n | Number of Payments | Loan term in years × 12. A 30-year mortgage has n = 360 payments |
Step-by-Step Example
You are buying a $400,000 home with a 20% down payment ($80,000) at a 6.75% annual fixed rate on a 30-year mortgage.
Given
Solution
- 1Calculate (1 + r)^n:
(1.005625)^360 ≈ 7.6874 - 2Calculate the numerator: r × (1+r)^n:
0.005625 × 7.6874 = 0.043242 - 3Calculate the denominator: (1+r)^n − 1:
7.6874 − 1 = 6.6874 - 4Divide numerator by denominator:
0.043242 ÷ 6.6874 = 0.006466 - 5Multiply by principal:
320,000 × 0.006466 = $2,069/month
Monthly mortgage payment is $2,069. Over 30 years you repay $320,000 principal plus $424,840 in interest, for a total of $744,840.
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Common Mistakes to Avoid
Using the annual rate directly instead of dividing by 12 first — this vastly overstates the monthly payment.
Forgetting that PMI (Private Mortgage Insurance), property taxes, and homeowner's insurance are separate costs added on top of the P&I payment calculated here.
Confusing the loan amount with the purchase price — the loan is purchase price minus your down payment.
Assuming a fixed payment means a fixed principal repayment — early payments are mostly interest; principal repayment accelerates toward the end of the term.