The basic formula: principal, rate, and time
Your monthly mortgage payment comes from three numbers: the loan amount (called the principal), the annual interest rate, and how many months you have to repay it. The standard formula used by lenders, banks, and mortgage calculators is called the amortization formula. It tells you exactly what you owe each month.
The formula looks like this: M = P × [r(1 + r)^n] / [(1 + r)^n − 1]. In plain terms: your monthly payment (M) equals your loan amount (P) multiplied by a fraction that accounts for your interest rate (r) and the total number of months you're paying (n). The interest rate you use in this formula is your annual rate divided by 12, because you're calculating a monthly payment.
This formula assumes you're making equal payments every month for the full term of the loan. It also assumes the interest rate stays the same—which is true for fixed-rate mortgages but not for adjustable-rate mortgages, where the rate changes after an initial period.
Key Takeaways
- Your monthly payment depends on three things: how much you borrowed, your annual interest rate divided by 12, and the total number of months in your loan term.
- A higher interest rate raises your monthly payment and the total amount you pay over the life of the loan, sometimes by tens of thousands of dollars.
- You can calculate your payment by hand using the amortization formula, but a mortgage calculator or spreadsheet saves time and reduces math errors.
- The same formula works for any loan term—15 years, 30 years, or anything in between—as long as the interest rate is fixed.
Breaking down each part of the formula
Start with your loan amount. If you're borrowing $300,000, that's your P. If you put down 20 percent and the home costs $375,000, your loan is $300,000, not $375,000.
Next, convert your annual interest rate to a monthly rate. If your rate is 6.5 percent per year, divide by 12: 6.5 ÷ 12 = 0.542 percent per month. In decimal form (which the formula needs), that's 0.065 ÷ 12 = 0.00542. This is your r.
Then count your total months. A 30-year mortgage is 30 × 12 = 360 months. A 15-year mortgage is 15 × 12 = 180 months. This is your n. The longer the term, the lower your monthly payment but the more interest you pay overall.
Once you have P, r, and n, the formula calculates how much of each payment goes to interest (more at the start, less at the end) and how much goes to principal (less at the start, more at the end). The result is your fixed monthly payment.
A worked example with real numbers
Let's say you borrow $300,000 at 6.5 percent for 30 years. Here's how it works:
P = 300,000 r = 0.065 ÷ 12 = 0.00542 n = 30 × 12 = 360
Plug these into the formula:
M = 300,000 × [0.00542(1 + 0.00542)^360] / [(1 + 0.00542)^360 − 1]
Working through the exponent: (1.00542)^360 = 6.898
M = 300,000 × [0.00542 × 6.898] / [6.898 − 1] M = 300,000 × [0.0374] / [5.898] M = 300,000 × 0.00634 M = $1,901
Your monthly payment (principal and interest only) is about $1,901. This does not include property taxes, homeowners insurance, or HOA fees, which are often added to your mortgage bill.
How interest rate changes affect your payment
A small change in interest rate creates a large change in what you pay. Using the same $300,000 loan over 30 years:
| Interest Rate | Monthly Payment | Total Paid Over 30 Years |
|---|---|---|
| 5.5% | $1,703 | $613,080 |
| 6.0% | $1,799 | $647,640 |
| 6.5% | $1,901 | $684,360 |
| 7.0% | $1,996 | $718,560 |
| 7.5% | $2,098 | $755,280 |
Moving from 6.5 percent to 7.5 percent adds $197 to your monthly payment. Over 30 years, that's an extra $70,920 in total payments. This is why shopping for the best interest rate matters—even a 0.5 percent difference is worth hundreds of thousands of dollars over the life of the loan.
Using a spreadsheet or calculator instead of doing it by hand
The amortization formula is accurate, but the math is tedious and straightforward to mess up. Most people use a mortgage calculator or a spreadsheet function instead.
In Excel or Google Sheets, use the PMT function: =PMT(rate, nper, pv). For the example above, you'd type =PMT(0.065/12, 360, -300000). The negative sign on the loan amount is required by the function; it tells the spreadsheet you're borrowing money, not receiving it. The result is your monthly payment.
Online mortgage calculators (found on lender websites, real estate sites, and financial websites) let you enter your loan amount, rate, and term without any math. They often show you a breakdown of how much goes to principal versus interest each month, and how your balance shrinks over time. This breakdown is called an amortization schedule.
A calculator is faster and removes the risk of arithmetic errors. Use it to compare different rates, loan terms, or down payment amounts to see how each choice affects your payment.
What the formula does not include
The amortization formula calculates principal and interest only. Your actual monthly mortgage bill usually includes other costs:
- Property taxes — paid to your county or municipality, varies by location and home value
- Homeowners insurance — required by lenders, varies by insurer and risk factors
- HOA fees — if your home is in a planned community, usually $100 to $500 per month
- PMI (private mortgage insurance) — required if you put down less than 20 percent, typically 0.5 to 1.5 percent of the loan amount per year
Your lender may bundle these into a single monthly payment called PITI (principal, interest, taxes, insurance). When you're comparing mortgages or budgeting, ask your lender for the full payment amount, not just the principal and interest.
Fixed-rate versus adjustable-rate mortgages
The formula above works perfectly for fixed-rate mortgages, where your interest rate never changes. Your payment stays the same for the entire 15, 20, or 30 years.
With an adjustable-rate mortgage (ARM), the interest rate is fixed for an initial period—often 3, 5, 7, or 10 years—then adjusts annually or semi-annually based on market conditions. During the fixed period, you use the formula as shown. After the rate adjusts, you recalculate using the new rate and the remaining balance and months. Your payment will change, sometimes significantly.
ARMs often start with a lower rate than fixed mortgages, which lowers your initial payment. But when the rate adjusts upward, your payment can jump hundreds of dollars per month. If you're considering an ARM, use the formula to calculate what your payment would be at a higher rate (lenders will tell you the maximum possible rate) to make sure you can afford it.
Frequently Asked Questions
Does the formula work the same way for 15-year and 30-year mortgages?
Yes. The only difference is the value of n (the number of months). A 15-year mortgage has 180 months instead of 360. Your monthly payment will be higher because you're repaying the loan faster, but you'll pay much less interest overall. For a $300,000 loan at 6.5 percent, a 15-year mortgage costs about $2,380 per month versus $1,901 for 30 years—but you save roughly $200,000 in total interest.
What if my interest rate is variable or changes during the loan?
The formula assumes a fixed rate for the entire term. If your rate changes, recalculate using the new rate, the remaining loan balance, and the remaining months. Your lender will do this automatically when an ARM adjusts. You can also recalculate yourself to see what your new payment will be.
Why does my actual payment differ from what the formula gives me?
The formula calculates principal and interest only. Your actual bill includes property taxes, insurance, HOA fees, and possibly PMI. Add those to the formula result to get your true monthly cost. Also check that you're using the monthly interest rate (annual rate divided by 12), not the annual rate itself.
Can I use this formula to compare different loan amounts or down payments?
Yes. Change the P value (your loan amount) and recalculate. A larger down payment lowers P, which lowers your monthly payment. You can also compare what happens if you borrow $250,000 versus $300,000, or put down 10 percent versus 20 percent, to see how each choice affects what you pay each month.
What happens to my payment if I make extra principal payments?
The formula calculates your required payment based on the original loan amount and term. Extra principal payments reduce your balance faster, which shortens the loan and saves interest, but they don't change the formula itself. If you pay extra, your loan will be paid off before the original term ends. Your lender can show you an updated amortization schedule reflecting the extra payments.