The basic formula for a monthly mortgage payment
Your monthly house payment is calculated using the loan amount, interest rate, and loan term. The standard formula is called the amortization formula, and it produces the same result whether you use a calculator, a spreadsheet, or a mortgage payment table.
The formula is: M = P [ r(1 + r)^n ] / [ (1 + r)^n – 1 ], where M is your monthly payment, P is the principal (the amount borrowed), r is the monthly interest rate (annual rate divided by 12), and n is the total number of payments (years multiplied by 12).
In practice, you do not need to do this math by hand. But understanding what goes into the calculation helps you see why a small change in interest rate or loan term shifts your payment significantly.
Key Takeaways
- Your monthly payment depends on three things: how much you borrowed, the interest rate, and how many months you have to pay it back.
- A mortgage payment calculator will give you the exact number in seconds, but the formula shows you why changing the rate or term changes your payment.
- Your actual monthly payment to the lender includes principal and interest, but your total housing payment to your bank may also include property taxes, insurance, and HOA fees.
- The same loan amount at a higher interest rate means a higher monthly payment and more total interest paid over the life of the loan.
- Shortening the loan term (paying it off faster) raises your monthly payment but cuts the total interest you pay significantly.
What each part of the formula means
The principal (P) is the amount you borrow. If you buy a house for $300,000 and put down $60,000, your principal is $240,000. This number stays the same throughout the calculation.
The interest rate (r) is what the lender charges you to borrow the money. A 6% annual rate becomes 0.06 divided by 12, or 0.005 per month. This monthly rate is what goes into the formula. A 7% rate becomes 0.07 ÷ 12, or about 0.00583 per month. That small difference compounds across 360 payments.
The loan term (n) is how many months you have to repay. A 30-year mortgage is 360 months. A 15-year mortgage is 180 months. The longer the term, the lower your monthly payment—but you pay more interest overall because the money is borrowed for longer.
Working through a concrete example
Say you borrow $240,000 at 6% annual interest over 30 years. Your monthly rate is 0.06 ÷ 12 = 0.005. Your number of payments is 30 × 12 = 360.
Plugging into the formula: M = 240,000 [ 0.005(1.005)^360 ] / [ (1.005)^360 – 1 ]. The (1.005)^360 part equals about 6.023. So M = 240,000 [ 0.005 × 6.023 ] / [ 6.023 – 1 ] = 240,000 [ 0.03012 ] / [ 5.023 ] = 240,000 × 0.005996 = $1,439.43.
Your monthly principal and interest payment is $1,439.43. If you take the same loan at 7% instead, the monthly payment rises to about $1,596. That extra 1% in interest costs you roughly $157 more per month, or $56,520 more over 30 years.
The difference between principal-and-interest and your total housing payment
The formula above gives you only the principal and interest portion of your payment. But when you send a check to your mortgage lender or make an automatic transfer, you may be paying more than that.
Your total monthly payment often includes property taxes, homeowners insurance, and mortgage insurance (if your down payment was less than 20%). Some lenders also collect HOA fees or condo fees. These are rolled into a single payment called PITI (principal, interest, taxes, insurance) or sometimes PITI plus HOA.
To find your true monthly cost, add these amounts to the principal-and-interest figure. Property taxes vary by location and home value. Insurance depends on the home's replacement cost and your location. Your lender can give you an estimate of taxes and insurance before you close, and that estimate should be part of your loan disclosure documents.
How interest rate changes affect your payment
Interest rate is the lever that moves your payment most visibly. A 0.5% increase on a $240,000 loan over 30 years raises your monthly payment by roughly $60 to $80. A 1% increase raises it by roughly $120 to $160.
This matters when you are shopping for rates. If one lender offers 6.25% and another offers 6.75%, the difference is real money every month. Over 30 years, that 0.5% difference adds up to tens of thousands of dollars in extra interest.
Your interest rate depends on your credit score, the size of your down payment, the loan type (conventional, FHA, VA, USDA), and the current market. Rates change daily. Locking in a rate with a lender holds that rate for a set period—usually 30, 45, or 60 days—while your loan is being processed.
How loan term affects your payment and total cost
Choosing between a 30-year and 15-year mortgage is a choice between a lower monthly payment and lower total interest. The 15-year mortgage has a higher monthly payment but you pay off the loan twice as fast and pay far less interest overall.
Using the same $240,000 at 6%: a 30-year term gives a $1,439 monthly payment. A 15-year term gives a $1,699 monthly payment—about $260 more per month. But over 15 years, you pay roughly $305,820 in total interest on the 30-year loan versus roughly $65,820 on the 15-year loan. You save about $240,000 in interest by paying $260 more per month.
Some people choose a 20-year term as a middle ground. The math works the same way: shorter term means higher monthly payment but significantly lower total interest. Longer term means lower monthly payment but you pay much more interest over time.
Using online calculators and spreadsheets
Most people use a mortgage calculator rather than working through the formula by hand. Free calculators are available from Bankrate, NerdWallet, the Consumer Financial Protection Bureau, and most major lenders. You enter the loan amount, interest rate, and term, and the calculator returns your monthly payment when ready.
You can also build a spreadsheet using the PMT function in Excel or Google Sheets. The syntax is =PMT(rate, nper, pv), where rate is your monthly interest rate, nper is the number of payments, and pv is the loan amount (entered as a negative number). This gives you the same result as the formula and lets you quickly test different rates or terms.
Calculators and spreadsheets also show you an amortization schedule—a month-by-month breakdown of how much of each payment goes to principal versus interest. Early in the loan, most of your payment is interest. Later, most goes to principal. This schedule is useful for understanding how much principal you have paid off at any point.
Frequently Asked Questions
Does my credit score affect my monthly payment?
Your credit score does not change the formula, but it affects the interest rate you are offered. A higher credit score typically qualifies you for a lower rate, which lowers your monthly payment. A lower score may mean a higher rate and a higher payment. The difference can be 0.5% to 2% depending on your score and the lender.
What if I want to pay extra toward principal each month?
The formula calculates your required payment. You can always pay more than that amount, and the extra goes directly to principal. Paying extra shortens your loan term and reduces the total interest you pay. Some lenders allow you to make extra payments without penalty; check your loan documents to confirm.
Does the down payment size change the monthly payment?
Yes, indirectly. The down payment reduces the principal you borrow. A larger down payment means a smaller loan amount, which means a lower monthly payment. A 20% down payment also usually means you avoid mortgage insurance, which further lowers your total monthly cost.
How do adjustable-rate mortgages affect the calculation?
An adjustable-rate mortgage (ARM) has an interest rate that changes after an initial fixed period. The formula applies to the fixed period. When the rate adjusts, your lender recalculates your payment using the new rate and the remaining loan balance and term. Your payment may go up or down depending on whether rates have risen or fallen.
Can I use this formula to compare loans from different lenders?
Yes. If two lenders offer different rates or terms, plug each into the formula or a calculator to see the monthly payment difference. Also compare the total interest paid over the life of the loan. A lower rate saves you money both monthly and over time, but the monthly difference is what affects your budget when ready.