Mortgage Payment Formula
Compute the fixed monthly payment for an amortizing loan from principal, rate and term.
M = P × [ r(1+r)ⁿ ] / [ (1+r)ⁿ − 1 ]
How it works
The formula answers one question: what fixed monthly amount will pay off the loan exactly at the end of the term, given that interest accrues on whatever is still outstanding? Early on, most of each payment is interest because the balance is large. As the balance falls the interest share falls with it and more of the same payment goes to principal, which is why the balance drops slowly at first and quickly at the end. The rate r in the formula is the monthly rate, not the annual one, so divide the annual rate by 12 first, and n is the total number of monthly payments, so a 30-year loan is 360 rather than 30.
Variables
- MMonthly payment
- PLoan principal
- rMonthly interest rate (annual ÷ 12)
- nTotal number of monthly payments (years × 12)
Worked examples
| Input | Result |
|---|---|
| $300,000 at 6% / 30 yr | ≈ $1,799 per month |
| $200,000 at 5% / 15 yr | ≈ $1,582 per month |
Practical applications
- Checking a lender's quoted monthly payment before signing
- Seeing what a rate change of half a percent does to the payment on the same loan
- Comparing a 15-year and a 30-year term on identical principal
Common mistakes
- Using the annual interest rate where the formula wants the monthly rate. This overstates the payment enormously.
- Using years where the formula wants the number of payments.
- Expecting the result to match the lender's figure exactly. This is principal and interest only - it does not include property tax, insurance or mortgage insurance, which are usually bundled into what the lender quotes.
- Forgetting that at a rate of exactly zero the formula divides by zero; a zero-interest loan is simply the principal divided by the number of payments.
Use it in a tool
FAQs
What does this exclude?+
Taxes, insurance and PMI. Real escrow payments are typically 15–30% higher than the principal+interest figure above.