The basic formula for mortgage payment
Your monthly mortgage payment is calculated using three numbers: 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]
Where M is your monthly payment, P is the principal (the amount you borrowed), r is your monthly interest rate (annual rate divided by 12), and n is the total number of payments (years × 12). This is called an amortizing loan calculation, and it's the standard method lenders use.
You don't need to do this by hand. A mortgage calculator—available free on most lender websites, Bankrate, or the Consumer Financial Protection Bureau's website—will compute this instantly once you enter the loan amount, interest rate, and loan term.
Key Takeaways
- Your monthly payment depends on three things: how much you borrowed, your interest rate, and how many years you have to pay it back.
- A 30-year mortgage at 7% interest on a $300,000 loan produces a different monthly payment than a 15-year mortgage at the same rate, because the payments are spread over fewer months.
- Your actual monthly bill will be higher than the principal-and-interest payment because it includes property taxes, homeowners insurance, and possibly mortgage insurance.
- Changing any one of the three inputs—borrowing less, getting a lower rate, or extending the term—changes your monthly payment in a predictable way.
What goes into the three inputs
The loan amount is the principal—what you actually borrowed after your down payment. If you bought a $400,000 house and put down $80,000, your loan amount is $320,000. This is the P in the formula.
The interest rate is what the lender charges you to borrow the money, expressed as an annual percentage. A 7% rate means you pay 7% of the outstanding balance per year. The formula converts this to a monthly rate by dividing by 12. At 7% annual, your monthly rate is 0.07 ÷ 12 = 0.00583 (or about 0.583% per month). This is the r in the formula.
The loan term is how many years you have to repay the loan. A 30-year mortgage has 360 monthly payments (30 × 12). A 15-year mortgage has 180 payments. This is the n in the formula. Shorter terms mean higher monthly payments but less total interest paid over the life of the loan.
How loan term changes your payment
Stretching the loan over more years lowers your monthly payment but increases the total interest you pay. Shortening the term does the opposite: higher monthly payment, less total interest.
On a $300,000 loan at 7% interest, a 30-year term produces a lower monthly payment than a 15-year term. The trade-off is that over 30 years you pay significantly more in interest. A mortgage calculator will show you both the monthly payment and the total interest cost for any combination of term and rate, so you can see the full picture before deciding.
Some borrowers choose a 20-year or 25-year term as a middle ground. The longer the term, the more interest you pay overall, but the lower your monthly obligation.
How interest rate changes your payment
A higher interest rate increases your monthly payment. A lower rate decreases it. Even a difference of 0.5% can change your monthly payment by $100 or more on a large loan.
Your interest rate depends on market conditions, your credit score, your down payment size, and the type of loan (conventional, FHA, VA, USDA). Borrowers with higher credit scores typically receive lower rates. A larger down payment can also help you secure a better rate.
If you're shopping for a mortgage, getting rate quotes from multiple lenders is standard practice. Each lender will quote you a rate based on your financial profile. Comparing these rates side by side—using a mortgage calculator to see the monthly payment difference—helps you understand the real cost of each offer.
What's included in your actual monthly bill
The formula above calculates principal and interest only. Your actual mortgage payment bill includes other costs bundled together in what's called a PITI payment: Principal, Interest, Taxes, and Insurance.
Property taxes vary by location and are paid to your county or municipality. Homeowners insurance protects your house and is required by lenders. If you put down less than 20%, you'll also pay private mortgage insurance (PMI), which protects the lender if you default. Some loans also include HOA fees if you live in a community with a homeowners association.
Your lender typically collects all these costs in one monthly payment and holds the tax and insurance portions in an escrow account, paying those bills on your behalf when they're due. This means your actual bill is often $200 to $500 higher than the principal-and-interest calculation alone.
Using a calculator versus doing it by hand
The mortgage payment formula is complex enough that doing it by hand is impractical for most people. A calculator handles the exponents and decimals instantly and accurately.
Free calculators are available from Bankrate, NerdWallet, the Consumer Financial Protection Bureau, and most mortgage lenders' websites. You enter the loan amount, interest rate, and term, and the calculator shows your monthly payment and total interest cost. Many also let you adjust for property taxes, insurance, and PMI to see your full monthly bill.
If you want to understand how the formula works without calculating by hand, a spreadsheet program like Excel or Google Sheets has a PMT function that does the calculation for you. Type =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 is useful if you want to test many scenarios quickly.
How changes to your loan affect the payment
Once you understand the three inputs, you can predict how changes affect your payment. Borrowing $50,000 less lowers your payment proportionally. Locking in a rate 0.5% lower reduces your payment by a measurable amount. Extending the term from 30 to 40 years (if available) spreads payments over more months and lowers each one.
Some borrowers use this to compare scenarios: "What if I put down 15% instead of 10%?" or "What if rates drop to 6.5%?" A calculator lets you run these comparisons in seconds, showing you the financial impact of each choice before you commit.
Frequently Asked Questions
Does my credit score affect the mortgage payment calculation?
Your credit score doesn't change the formula itself, but it affects the interest rate you're offered. A higher credit score typically qualifies you for a lower rate, which lowers your monthly payment. The lender sets your rate based on your creditworthiness, then the formula calculates your payment from that rate.
What's the difference between a fixed-rate and adjustable-rate mortgage payment?
A fixed-rate mortgage has the same interest rate and monthly payment for the entire loan term. An adjustable-rate mortgage (ARM) starts with a lower rate for a set period (often 3, 5, 7, or 10 years), then adjusts periodically based on market conditions. Your payment stays the same during the fixed period, then changes when the rate adjusts. The initial payment calculation is the same; the difference is what happens later.
Can I pay off my mortgage faster by paying extra each month?
Yes. Extra payments go directly toward principal, reducing the amount owed and the interest you pay over time. You can make extra payments without penalty on most mortgages. A calculator can show you how much faster you'd pay off the loan if you added $100 or $200 to each payment, and how much interest you'd save.
Why does my actual bill differ from the calculator's principal-and-interest number?
The calculator's basic result shows only principal and interest. Your actual bill includes property taxes, homeowners insurance, and possibly PMI or HOA fees. These vary by location and loan type, so the calculator can't include them unless you enter those amounts separately. Many calculators have an option to add these costs and show your full monthly bill.
What happens to my payment if I refinance?
Refinancing means taking out a new loan to pay off the old one. Your new payment is calculated using the same formula, but with a new interest rate, possibly a new loan amount, and possibly a new term. If you refinance to a lower rate, your payment typically drops. If you extend the term, your payment drops further but you pay more interest overall.