Mortgage Payment Formula
Calculate monthly mortgage payments from principal, interest rate, and loan term.
Includes total interest paid.
The Formula
The mortgage payment formula calculates the fixed monthly payment for a fully amortizing loan. Each payment covers both interest and principal, with the interest portion decreasing over time.
Variables
| Symbol | Meaning |
|---|---|
| M | Monthly payment |
| P | Principal (loan amount) |
| r | Monthly interest rate (annual rate / 12) |
| n | Total number of payments (years × 12) |
Example 1
$300,000 mortgage at 6.5% annual rate for 30 years
r = 0.065 / 12 = 0.005417, n = 30 × 12 = 360
M = 300,000 × [0.005417 × (1.005417)³⁶⁰] / [(1.005417)³⁶⁰ - 1]
M = 300,000 × [0.005417 × 6.9916] / [6.9916 - 1]
= $1,896.20 per month (total paid: $682,632 — that is $382,632 in interest)
Example 2
Same $300,000 at 6.5% but for 15 years
r = 0.005417, n = 15 × 12 = 180
M = 300,000 × [0.005417 × (1.005417)¹⁸⁰] / [(1.005417)¹⁸⁰ - 1]
= $2,613.32 per month (total paid: $470,398 — saves $212,234 in interest vs 30-year)
When to Use It
Use the mortgage formula when:
- Estimating monthly payments before buying a home
- Comparing different loan terms (15 vs 30 years)
- Calculating how much total interest you will pay
- Determining the maximum loan you can afford based on a target payment