How to Calculate Your Monthly Mortgage Payment by Hand
The basic formula: principal, interest rate, and loan term
Your monthly mortgage payment is determined by three numbers: the amount you borrowed (the principal), the interest rate your lender charges, and how many months you have to pay it back. The payment stays the same every month for a fixed-rate mortgage—that is the whole point of a fixed rate. The formula that produces this number is not simple arithmetic, but you can work through it step by step with a calculator, or use an online mortgage calculator to see the result instantly.
The reason the formula exists is that your lender wants the same payment every month, even though early payments are mostly interest and later payments are mostly principal. The formula spreads the interest across all the months so that the payment never changes. If you understand how the three inputs work, you can see why a smaller down payment, a higher interest rate, or a longer loan term all raise your monthly payment.
Key Takeaways
- Your monthly payment depends on three things: how much you borrowed, the interest rate, and the number of months you have to repay it.
- The formula that calculates the payment is complex, but online calculators do it instantly once you enter those three numbers.
- A lower down payment, a higher interest rate, or a longer loan term will all increase your monthly payment.
- Your actual monthly bill may be higher than the mortgage payment alone because it often includes property taxes, homeowners insurance, and mortgage insurance.
- You can see how each change affects your payment by running the numbers through a calculator before you commit to a loan.
What information you need to gather first
Before you calculate, write down three pieces of information from your loan estimate or mortgage offer. First, the loan amount—this is the principal, the money you are actually borrowing. If you are buying a $300,000 house and putting down $60,000, your loan amount is $240,000, not $300,000. Second, the interest rate, usually shown as a percentage like 6.5% or 7.2%. Third, the loan term in years—most commonly 30 years, but also 15, 20, or other lengths.
If you have a variable-rate mortgage (an ARM), the interest rate will change after an initial period, so this calculation only works for the fixed-rate portion. For an adjustable rate, you would calculate the payment for the first period, then recalculate when the rate changes.
The mathematical formula, step by step
The formula is called the amortization formula. It looks like this:
M = P × [r(1 + r)^n] / [(1 + r)^n − 1]
Here is what each letter means: M is your monthly payment. P is the principal (the loan amount). r is the monthly interest rate (the annual rate divided by 12). n is the total number of monthly payments (the years times 12).
To use this formula, you first convert your annual interest rate to a monthly rate. If your rate is 6.5% per year, divide by 12: 6.5 ÷ 12 = 0.542%. Then convert that to decimal form: 0.542 ÷ 100 = 0.00542. Next, calculate (1 + r)^n—that is, 1.00542 raised to the power of 360 (if it is a 30-year loan). Then plug all the numbers into the formula. The result is your monthly payment before taxes, insurance, and mortgage insurance.
This is why most people use a calculator instead of doing it by hand. The exponent step alone requires a scientific calculator or a computer.
Using an online calculator to see the result
Enter your loan amount, interest rate, and loan term into any mortgage calculator online, and it will show you the monthly payment in seconds. Many lenders provide calculators on their websites. You can also find them through a search for "mortgage payment calculator." The result will be the principal and interest payment only—the part that goes toward paying back the loan itself.
Most calculators also let you add property taxes, homeowners insurance, and mortgage insurance (if you put down less than 20%) to see your total monthly housing cost. This total is sometimes called your PITI payment: principal, interest, taxes, and insurance. Knowing this number matters because lenders use it to decide how much they will lend you.
How changes to each number affect your payment
Run the same loan through a calculator with different numbers to see the impact. If you borrow $240,000 at 6.5% for 30 years, your payment is roughly $1,520 per month. If you lower the rate to 6% (because you improved your credit or rates dropped), the payment drops to about $1,440. If you raise the rate to 7%, it rises to about $1,600. A half-point change in interest rate moves your payment by $40 to $80 per month.
Loan term also matters. The same $240,000 at 6.5% over 15 years costs about $2,000 per month—much higher, because you are paying it back in half the time. Over 20 years, it is about $1,700. Longer terms lower your monthly payment but cost you more in total interest over the life of the loan.
Down payment size affects the loan amount. A $300,000 house with a 20% down payment ($60,000) means you borrow $240,000. With a 10% down payment ($30,000), you borrow $270,000, and your payment rises. You also pay mortgage insurance on top of the payment if you put down less than 20%, which adds another $100 to $300 per month depending on the loan size and your credit score.
What your payment covers and what it does not
The number you calculate with the formula is principal and interest only. It does not include property taxes, homeowners insurance, or mortgage insurance. Your actual monthly bill from your lender will be higher because these costs are usually rolled into one payment.
Property taxes vary by location and are assessed by your county or municipality. Homeowners insurance is required by your lender and protects the house against fire, theft, and weather damage. Mortgage insurance (PMI) is required if you put down less than 20% and protects the lender if you default. All three of these are added to your principal and interest payment to create your total monthly housing cost.
Why lenders use this formula and what it means for you
The amortization formula ensures that your payment stays exactly the same every month for the entire loan term. Early in the loan, most of your payment goes toward interest; later, most goes toward principal. By month 360 of a 30-year loan, you are paying almost entirely principal. This is why paying extra principal early in the loan saves you a lot of interest over time.
Understanding how the formula works helps you see why a lower interest rate or a shorter loan term saves you money, even though the monthly payment might be higher. It also shows you why refinancing to a lower rate can cut years off your loan if you keep the same monthly payment instead of lowering it.
Frequently Asked Questions
Can I calculate my payment if I have an adjustable-rate mortgage?
Yes, but only for the fixed-rate period. Use the initial interest rate and calculate the payment for that period. When the rate adjusts, you will need to recalculate with the new rate. Your lender should tell you the adjustment date and how the new rate will be set.
Why is my actual monthly payment higher than the calculator shows?
The calculator is showing principal and interest only. Your lender adds property taxes, homeowners insurance, and possibly mortgage insurance to create your total monthly bill. Ask your lender for a breakdown of what each part costs.
Does paying extra principal reduce my monthly payment?
No. Your monthly payment stays the same. Extra principal payments reduce the total interest you pay and shorten the loan term, but they do not lower the required monthly payment. You make them in addition to your regular payment.
What if I want to pay off my mortgage early?
You can pay extra toward principal at any time without penalty on most fixed-rate mortgages. Check your loan documents to confirm there is no prepayment penalty. Paying extra principal cuts years off the loan and saves thousands in interest.
How do I know if my interest rate is good?
Interest rates change daily and depend on your credit score, down payment size, loan term, and the current market. Ask multiple lenders for quotes on the same loan terms and compare. Your credit score, debt-to-income ratio, and the size of your down payment all affect the rate you are offered.