The basic formula: principal, interest rate, and loan term
A mortgage payment is calculated using three numbers: the amount you borrowed (principal), the annual interest rate, and how many months you have to pay it back. The formula tells you what your monthly payment will be before taxes, insurance, or homeowners association fees get added on.
The standard formula is called the amortization formula. It looks like this:
M = P × [r(1 + r)^n] / [(1 + r)^n − 1]
Where M is your monthly payment, P is the principal (the loan amount), r is the monthly interest rate (annual rate divided by 12), and n is the total number of monthly payments.
You do not need to memorize or calculate this by hand. Mortgage calculators, spreadsheets, and lenders all use this formula behind the scenes. But understanding what each piece does helps you see why a higher interest rate or longer loan term changes your payment.
Key Takeaways
- The mortgage payment formula uses your loan amount, monthly interest rate, and total number of payments to calculate what you owe each month.
- A higher interest rate increases your monthly payment; a longer loan term decreases it but increases total interest paid over the life of the loan.
- The formula assumes you make the same payment every month and that the interest rate does not change (fixed-rate mortgages only).
- Mortgage calculators and spreadsheet functions like Excel's PMT function do the math for you; you only need to enter the three numbers.
- Your actual monthly payment also includes property taxes, homeowners insurance, and possibly PMI, which the formula does not cover.
Breaking down each part of the formula
Principal (P) is the amount of money the lender gave you. If you borrowed $300,000, that is your P. The formula assumes you will pay back the entire principal over the life of the loan.
Annual interest rate is what the lender charges you to borrow the money, expressed as a percentage per year. If your rate is 6.5%, you convert that to a monthly rate by dividing by 12: 6.5% ÷ 12 = 0.542% per month, or 0.00542 as a decimal. This is the r in the formula.
Loan term is how many years you have to pay back the loan—usually 15, 20, or 30 years. You convert this to months by multiplying by 12. A 30-year mortgage is 360 monthly payments. This is the n in the formula.
The formula multiplies and divides these three pieces to arrive at a payment amount that, if paid every month for the full term, will pay off both the principal and all the interest owed.
Why the formula produces different payments for different terms
A 30-year mortgage spreads the same loan across more payments than a 15-year mortgage. That means each individual payment is smaller. But you pay interest for twice as long, so the total interest over the life of the loan is much higher.
For example, a $300,000 loan at 6.5% costs roughly $686 per month over 30 years, but about $2,380 per month over 15 years. The 15-year payment is higher, but you pay far less total interest because the loan is paid off sooner.
The formula accounts for this automatically. When you increase n (the number of payments), the payment M goes down. When you decrease n, the payment goes up. The interest rate r affects the payment in the same direction: a higher rate means a higher payment, and a lower rate means a lower payment.
Using a spreadsheet to calculate the payment yourself
Excel, Google Sheets, and most other spreadsheets have a built-in function called PMT that does the formula work for you. The syntax is:
=PMT(rate, nper, pv)
Where rate is your monthly interest rate (annual rate divided by 12), nper is the number of payments, and pv is the loan amount (entered as a negative number).
For a $300,000 loan at 6.5% annual interest over 30 years, you would enter:
=PMT(0.065/12, 360, -300000)
The result is approximately $1,896. That is your principal and interest payment only—it does not include property taxes, insurance, or PMI.
If you want to see how the payment changes with a different rate or term, you can change those numbers and the spreadsheet recalculates instantly. This is useful for comparing loan offers or deciding between a 15-year and 30-year term.
What the formula does not include
The mortgage payment formula calculates only principal and interest. Your actual monthly payment to the lender is usually higher because it also includes:
- Property taxes, which vary by location and home value.
- Homeowners insurance, required by the lender.
- PMI (private mortgage insurance), required if you put down less than 20%.
- HOA fees, if your property is in a homeowners association.
Lenders often bundle these into a single payment called PITI (principal, interest, taxes, insurance). The formula gives you only the PI part. To estimate your full payment, you need to add the other costs based on your specific property and location.
Fixed-rate versus adjustable-rate mortgages
The formula assumes a fixed interest rate—meaning the rate stays the same for the entire loan term. With a fixed rate, your principal and interest payment never changes, even though the amount of each payment that goes toward principal versus interest shifts over time.
An adjustable-rate mortgage (ARM) has an interest rate that changes after an initial fixed period, usually 3, 5, 7, or 10 years. Once the rate adjusts, your monthly payment recalculates using the new rate. The formula still applies, but you would use it again with the new rate and the remaining balance and term.
For an ARM, you can use the formula to calculate your payment during the fixed-rate period, but you cannot predict your payment after the rate adjusts without knowing what the new rate will be.
How amortization schedules show the formula in action
An amortization schedule is a month-by-month breakdown of your mortgage payment. It shows how much of each payment goes toward principal and how much goes toward interest, plus your remaining balance after each payment.
Early in the loan, most of your payment goes toward interest. As time passes, more of each payment goes toward principal. But the total payment amount stays the same (on a fixed-rate mortgage) because the formula was designed to account for this shift.
You can generate an amortization schedule using a spreadsheet, a mortgage calculator, or your lender's website. Seeing the schedule helps you understand why paying extra toward principal early in the loan saves so much interest over time.
Frequently Asked Questions
Can I use the formula to calculate my payment if I have an adjustable-rate mortgage?
Yes, but only for the period when your rate is fixed. Once your rate adjusts, the formula still works, but you need to plug in the new interest rate, the remaining loan balance, and the remaining number of payments. Your lender will tell you the new rate and recalculate your payment for you.
Why does my actual monthly payment differ from what the formula gives me?
The formula calculates principal and interest only. Your actual payment includes property taxes, homeowners insurance, PMI, and possibly HOA fees. Add those costs to the formula result to get your full monthly payment.
Does the formula change if I make extra payments toward principal?
No. The formula calculates your required monthly payment. If you pay extra, you reduce the remaining balance and shorten the loan term, but the formula itself does not change. Your lender will apply the extra payment directly to principal.
What happens to the formula if interest rates drop and I refinance?
Refinancing is like taking out a new loan. The formula applies to your new loan using the new interest rate, the new loan amount (which may be less if you have paid down the original), and a new term. Your new payment will be lower if the new rate is lower, assuming the term stays the same.
Is there a simpler way to estimate my payment without using the formula?
Yes. A mortgage calculator on a lender's website or a financial site does the formula work for you. You enter the loan amount, interest rate, and term, and it shows your payment instantly. This is faster and less error-prone than calculating by hand or building a spreadsheet.