The formula lenders use to calculate your monthly payment
Your monthly mortgage payment is calculated using a fixed formula that accounts for three things: the loan amount, the interest rate, and the number of months you have to repay it. The formula is:
M = P [ r(1 + r)^n ] / [ (1 + r)^n – 1 ]
In this formula, M is your monthly payment, P is the principal (the amount you borrowed), r is your monthly interest rate (your annual rate divided by 12), and n is the total number of payments (years multiplied by 12). This formula produces the same payment every month for a fixed-rate mortgage—the payment never changes, even though the portion going toward interest versus principal shifts over time.
The formula assumes you make a payment every month without missing any, and that you do not make extra payments. If you do make extra payments or skip a month, your lender recalculates based on your actual balance.
Key Takeaways
- The mortgage payment formula divides the loan into equal monthly chunks, with each payment covering both interest and principal.
- Your monthly interest rate is your annual rate divided by 12, and the number of payments is your loan term in years times 12.
- The formula produces the same payment every month on a fixed-rate mortgage, but the split between interest and principal changes as you pay down the loan.
- A small change in interest rate or loan term produces a large change in your monthly payment, which is why comparing offers matters.
Breaking down each part of the formula
The principal (P) is straightforward: it is the amount you borrowed. If you put 20 percent down on a $300,000 house, your principal is $240,000. If you borrowed the full amount, your principal is $300,000.
The monthly interest rate (r) is where many people stumble. If your lender quotes you a 6.5 percent annual rate, you divide 6.5 by 100 to get 0.065, then divide that by 12 to get 0.00542 (rounded). That 0.00542 is what goes into the formula as r. A 7 percent rate becomes 0.07 ÷ 12 = 0.00583. The difference looks small, but it compounds across 360 payments.
The number of payments (n) is your loan term in years times 12. A 30-year mortgage is 360 payments. A 15-year mortgage is 180 payments. A 20-year mortgage is 240 payments. Shorter terms mean fewer payments but higher monthly amounts, because the principal is divided across fewer months.
Why the formula has exponents and fractions
The exponents in the formula—the (1 + r)^n parts—account for compound interest. Each month, you owe interest not just on the original loan, but on the interest that has already accrued. The formula calculates a payment amount that, when made every month, will pay off the entire loan plus all the interest by the end of the term.
The fraction at the end ensures that the payment is the same every month. Without it, you would pay a different amount each month. The formula solves for the single payment that balances out over the life of the loan.
If you work through the formula by hand for a $300,000 loan at 6.5 percent over 30 years, you get a monthly payment of approximately $1,896. That same loan at 7 percent costs about $1,996 per month—$100 more. Over 30 years, that $100 difference adds up to $36,000 in extra payments.
How to use the formula with a calculator or spreadsheet
You do not have to solve the formula by hand. A basic calculator with an exponent button (usually marked ^ or x^y) can do it, or you can use a spreadsheet like Excel or Google Sheets.
In Excel, the function is =PMT(rate, nper, pv). The rate is your monthly interest rate (annual rate divided by 12), nper is the number of payments, and pv is the principal as a negative number. For a $300,000 loan at 6.5 percent over 30 years, you would enter =PMT(0.065/12, 360, -300000) and the spreadsheet returns 1895.69.
Most mortgage lenders provide an amortization schedule—a month-by-month breakdown showing how much of each payment goes to interest and how much goes to principal. You can request this from your lender, or generate one yourself using the same spreadsheet function repeated down a column for each month.
What changes your monthly payment
Three variables move your payment: the principal borrowed, the interest rate, and the loan term. Borrowing more money raises your payment. A higher interest rate raises your payment. A longer term lowers your payment, but you pay more interest overall.
A $300,000 loan at 6.5 percent costs $1,896 per month over 30 years, but only $2,107 per month over 15 years. The 15-year payment is $211 higher each month, but you pay roughly $180,000 less in total interest because the loan is paid off in half the time.
Property taxes, homeowners insurance, and HOA fees are not part of the mortgage payment formula itself. Lenders often bundle these into an escrow account and collect them along with your mortgage payment, but the formula only calculates principal and interest.
How interest and principal split changes over time
Early in your loan, most of your payment goes toward interest. Late in your loan, most goes toward principal. This is because interest is calculated on your remaining balance each month, and that balance is highest at the start.
On a $300,000 loan at 6.5 percent over 30 years, your first payment of $1,896 includes about $1,625 in interest and only $271 in principal. By payment 180 (halfway through), interest and principal are nearly equal. By payment 360 (the last payment), almost all $1,896 goes to principal and almost nothing to interest.
This is why paying extra toward principal early in the loan saves you the most money. An extra $100 per month in the first year reduces your total interest by thousands, because that $100 stops accruing interest for the remaining 29 years.
Adjustable-rate mortgages and the formula
The formula above applies to fixed-rate mortgages, where the interest rate never changes. With an adjustable-rate mortgage (ARM), the rate is fixed for an initial period (often 3, 5, 7, or 10 years), then adjusts annually or semi-annually based on a market index.
When the rate adjusts, your lender recalculates your payment using the same formula, but with the new interest rate and the remaining balance as the new principal. If rates rise, your payment rises. If rates fall, your payment falls. The remaining term does not change unless you refinance.
ARMs are riskier than fixed-rate mortgages because your payment can increase significantly when the rate adjusts. Some ARMs have rate caps that limit how much the rate can rise per adjustment period or over the life of the loan.
Frequently Asked Questions
Does the formula change if I make extra payments?
The formula itself does not change, but your lender recalculates your remaining balance and adjusts your payoff date. Extra payments reduce your principal faster, which means less interest accrues in future months. Your regular monthly payment stays the same unless you refinance or your ARM rate adjusts.
What if I want to know my payment before I apply for a mortgage?
Use the PMT function in a spreadsheet, or search for a mortgage calculator online. Enter the loan amount you expect to borrow, the interest rate you have been quoted, and your desired loan term. The calculator applies the formula and shows you the monthly payment in seconds.
Why do different lenders quote different monthly payments for the same loan?
The formula is the same, but the inputs differ. One lender might quote 6.5 percent, another 6.75 percent. One might charge points (upfront fees that buy down your rate), which changes the effective rate. Always compare the interest rate and any fees side by side to see the true cost.
Can I use the formula to calculate payments on other loans?
Yes. The formula works for any amortizing loan—car loans, personal loans, student loans—as long as the interest rate is fixed and you make equal monthly payments. The only difference is the principal amount, rate, and term.
What happens to my payment if I refinance?
Refinancing means taking out a new loan to pay off the old one. Your lender uses the formula again with your new interest rate, your remaining balance as the new principal, and your new term. Your payment can go up or down depending on whether your new rate is higher or lower, and whether you extend or shorten the term.