A monthly mortgage payment is not a number a lender invents. For a fixed-rate loan, the principal-and-interest portion comes from a single, well-known formula. Once you understand it, you can predict how any change — a higher rate, a bigger down payment, a shorter term — will move your payment before you ever talk to a lender.
The three inputs that set your payment
Three numbers determine the principal-and-interest portion of a fixed-rate mortgage payment:
- Loan amount (principal) — the home price minus your down payment.
- Interest rate — the annual cost of borrowing, expressed as a percentage.
- Loan term — the number of years you have to repay, most commonly 15 or 30 in the U.S.
Everything else in your monthly payment — taxes, insurance, PMI, HOA — is added on top of this principal-and-interest figure. So the formula below is the foundation; the extras are layered above it.
The mortgage payment formula
For a fixed-rate loan, the monthly principal-and-interest payment is:
Where:
- M = monthly principal-and-interest payment
- P = loan amount (principal)
- r = monthly interest rate = annual rate ÷ 12 (so 6.5% becomes 0.065 ÷ 12 ≈ 0.005417)
- n = total number of payments = years × 12 (so a 30-year loan has 360 payments)
The formula works because each payment must cover the interest on the remaining balance and chip away at the principal, ending at exactly zero after the final payment. Spreading repayment evenly across hundreds of payments is what produces this particular expression.
A worked example
Suppose you buy a $350,000 home with a 20% down payment ($70,000), financing the remaining $280,000 at a 6.5% annual rate over 30 years.
- P = $280,000
- r = 0.065 ÷ 12 ≈ 0.005417
- n = 30 × 12 = 360
Plugging these into the formula gives a monthly principal-and-interest payment of about $1,769.79. Over 360 payments that is roughly $637,125 in total — meaning about $357,125 of it is interest on top of the $280,000 you borrowed.
What happens when each input changes
The formula makes the trade-offs predictable. Using the same $280,000 loan over 30 years, here is how the monthly payment moves with the rate:
| Interest rate | Monthly P&I |
|---|---|
| 5.5% | $1,589.81 |
| 6.0% | $1,678.74 |
| 6.5% | $1,769.79 |
| 7.0% | $1,862.85 |
| 7.5% | $1,957.80 |
A one-percentage-point change in rate moves the payment by roughly $90–$95 a month on this loan — and far more over the life of the loan, because that difference compounds across 360 payments.
How the calculator uses your inputs
Our mortgage calculator applies this exact formula to the loan amount, rate, and term you enter, then adds property taxes, insurance, PMI (when applicable), and HOA dues to show the full estimated monthly housing cost. The amortization schedule uses the same math, payment by payment, to split each month into principal and interest.
Try the Mortgage Calculator