Amortization Formula
Calculate monthly loan payments for mortgages, car loans, and other installment loans.
See exactly what you will pay.
The Formula
M = P × [r(1+r)ⁿ] / [(1+r)ⁿ - 1]
This formula calculates the fixed monthly payment for a loan. Each payment covers both interest and principal, gradually paying off the entire balance.
Variables
| Symbol | Meaning |
|---|---|
| M | Monthly payment amount |
| P | Principal — the loan amount |
| r | Monthly interest rate (annual rate ÷ 12) |
| n | Total number of payments (years × 12) |
Example 1
$300,000 mortgage at 6% annual interest for 30 years
r = 0.06/12 = 0.005, n = 30 × 12 = 360
M = 300,000 × [0.005(1.005)³⁶⁰] / [(1.005)³⁶⁰ - 1]
M = 300,000 × [0.005 × 6.0226] / [6.0226 - 1]
M = 300,000 × 0.03011 / 5.0226
M ≈ $1,799 per month (total paid: $647,515)
Example 2
$25,000 car loan at 5% for 5 years
r = 0.05/12 = 0.004167, n = 60
M = 25,000 × [0.004167(1.004167)⁶⁰] / [(1.004167)⁶⁰ - 1]
M ≈ $472 per month (total paid: $28,306)
When to Use It
Use the amortization formula when:
- Calculating monthly mortgage or car loan payments
- Comparing different loan terms and interest rates
- Creating loan amortization schedules
- Understanding how much of each payment goes to interest vs principal