Mortgage payment formula
For a fixed-rate mortgage, lenders use an amortization formula to calculate an equal principal-and-interest payment each month.
- M is the monthly principal-and-interest payment.
- P is the loan principal: home price minus down payment.
- r is the monthly interest rate: annual rate divided by 12.
- n is the number of monthly payments: loan years multiplied by 12.
Mortgage payment example
Imagine a $400,000 home with an $80,000 down payment. The loan amount is $320,000. At a 6.5% annual interest rate on a 30-year term, the monthly principal-and-interest payment is about $2,023.
| Item | Amount |
|---|---|
| Home price | $400,000 |
| Down payment | $80,000 (20%) |
| Loan amount | $320,000 |
| Interest rate | 6.5% per year |
| Loan term | 30 years (360 payments) |
| Monthly principal and interest | About $2,023 |
This calculation is an estimate. Closing costs, lender fees and the exact payment schedule can change the numbers.
What is included in a mortgage payment?
The formula above covers only principal and interest. Your total monthly housing cost may also include:
- Property taxes, often collected monthly in an escrow account.
- Homeowners insurance, which protects the home against covered damage.
- Private mortgage insurance (PMI), commonly required when a conventional loan has less than 20% down.
- HOA fees, if the home belongs to a homeowners association.
When comparing homes, include these costs so you are looking at the full monthly commitment, not only the loan payment.
Three things that change your payment
1. The interest rate
Interest has a large effect over a long term. With the same $320,000 loan over 30 years, a higher rate means a higher monthly payment and more total interest. Getting several loan estimates can make the comparison clearer.
2. The down payment
A larger down payment means borrowing less. It reduces the monthly payment and can help a buyer avoid PMI when they reach the relevant loan-to-value threshold.
3. The loan term
A 15-year mortgage typically has a higher monthly payment than a 30-year mortgage because the balance is repaid faster. However, the shorter term usually leads to much less interest over the life of the loan.
Use a mortgage calculator
Doing the formula by hand is useful for understanding the result, but a calculator makes it easy to test different rates, down payments and loan terms in seconds.
Open the mortgage calculatorFrequently asked questions
How do I calculate a monthly mortgage payment?
Use the amortization formula M = P × [r(1+r)ⁿ] ÷ [(1+r)ⁿ − 1]. The loan amount, monthly interest rate and number of payments determine the result.
Does a larger down payment lower my mortgage payment?
Yes. It lowers the amount you borrow, so the principal-and-interest payment becomes smaller. It may also reduce or remove PMI on eligible loans.
Is a 15-year mortgage cheaper than a 30-year mortgage?
A 15-year mortgage usually costs less in total interest, but requires a higher monthly payment. A 30-year mortgage has lower monthly payments but generally costs more over the full term.
Is this financial advice?
No. This guide is for general educational estimates. A lender can provide the terms and full costs for a specific loan.