The monthly mortgage payment comes from the amortization formula M = P × r(1 + r)^n ÷ ((1 + r)^n − 1). P is the loan amount, r the monthly rate (annual ÷ 12), n the payment count. On $400,000 at 6.5% over 30 years, the payment is $2,528.27 a month; total interest is $510,177.95.
You need only three numbers from your loan offer and a calculator. This guide works through the formula piece by piece, does the arithmetic by hand for a real example, and shows how the rate and the term change your payment.
What Is the Monthly Mortgage Payment Formula?
Every fixed-rate US mortgage uses the same formula, which finds the single fixed monthly payment that pays off the whole balance, interest included, by the final month:
M = P × r(1 + r)^n ÷ ((1 + r)^n − 1)
Each letter means something concrete:
- M is the monthly payment you are solving for — the fixed principal-and-interest amount you pay every month.
- P is the principal, the amount you borrow. On a $400,000 loan, P is 400,000.
- r is the monthly interest rate: the annual rate as a decimal, divided by 12. At 6.5%, r = 0.065 ÷ 12 = 0.005417.
- n is the total number of payments. A 30-year mortgage means n = 30 × 12 = 360 payments.
A free mortgage calculator runs the same formula instantly — but working it out once by hand shows you exactly where the number comes from, and why a small change in rate or term moves it so much. (At 0% the formula divides by zero, so the payment is simply P ÷ n: $1,111.11 a month on a $400,000 loan over 360 months.)
Why Is the Payment the Same Every Month?
The payment stays fixed, but what it pays for does not. Each month the lender first charges interest on the balance you still owe; whatever is left reduces the principal. Early on, most of the payment is interest; as the balance shrinks, more of each payment goes to principal.
This is amortization: the formula finds the one payment that covers each month’s interest while chipping the balance down to exactly zero on the final payment. On a 30-year mortgage the split starts out extremely lopsided — in month 1 of our example, $2,166.67 of the $2,528.27 payment is interest and only $361.61 reduces the balance. Our guide to how to pay off your mortgage early shows how extra payments attack that imbalance.
Worked Example: A $400,000 Loan at 6.5% Over 30 Years
Take a $400,000 home loan at 6.5% over 30 years (360 payments), step by step.
Step 1: Find the monthly rate.
r = 0.065 ÷ 12 = 0.005417, or about 0.5417% a month.
Step 2: Count the payments.
n = 30 × 12 = 360 payments.
Step 3: Raise (1 + r) to the power of n.
(1 + 0.005417)^360 = 6.991798 — the compounding factor, capturing how interest builds up over 360 months.
Step 4: Work out the top of the fraction.
r × (1 + r)^n = 0.005417 × 6.991798 = 0.037872.
Step 5: Work out the bottom of the fraction.
(1 + r)^n − 1 = 6.991798 − 1 = 5.991798.
Step 6: Divide and multiply by the principal.
M = 400,000 × 0.037872 ÷ 5.991798 = $2,528.27 a month.
The exact payment is $2,528.2717, so $2,528.27 is what your statement would show.
Step 7: Find the total interest.
Total paid = $2,528.27 × 360 = $910,177.95 (using the unrounded payment), so total interest = $910,177.95 − $400,000 = $510,177.95. Borrowing $400,000 for thirty years at 6.5% costs more in interest than the amount borrowed — the number that matters most when you compare offers.
What Does Each Payment Actually Pay? The Amortization Schedule
Here is how the $2,528.27 payment splits over the life of the loan:
| Month | Interest | Principal | Remaining balance |
|---|---|---|---|
| 1 | $2,166.67 | $361.61 | $399,638.39 |
| 12 | $2,144.53 | $383.74 | $395,529.10 |
| 60 (year 5) | $2,030.93 | $497.34 | $374,443.91 |
| 120 (year 10) | $1,840.54 | $687.73 | $339,104.51 |
| 180 (year 15) | $1,577.27 | $951.01 | $290,236.56 |
| 240 (year 20) | $1,213.20 | $1,315.07 | $222,661.13 |
| 300 (year 25) | $709.77 | $1,818.50 | $129,216.65 |
| 360 (year 30) | $13.62 | $2,514.65 | $0.00 |
Two facts jump out. After five years you have repaid only $25,556.09 of the $400,000. And the principal portion does not overtake the interest portion until month 233, more than 19 years in — in year 1 you pay $25,868.36 in interest and only $4,470.90 in principal. That slow start is why extra payments early on are so powerful.
How Does the Interest Rate Change the Payment?
The rate is the biggest lever on your payment. Holding the loan at $400,000 over 30 years and changing only the rate:
| Annual rate | Monthly payment | Total interest | Total paid |
|---|---|---|---|
| 5% | $2,147.29 | $373,023.14 | $773,023.14 |
| 6% | $2,398.20 | $463,352.76 | $863,352.76 |
| 6.5% | $2,528.27 | $510,177.95 | $910,177.95 |
| 7% | $2,661.21 | $558,035.59 | $958,035.59 |
| 7.5% | $2,796.86 | $606,868.89 | $1,006,868.89 |
| 8% | $2,935.06 | $656,620.99 | $1,056,620.99 |
Improving your rate from 7.5% to 6.5% saves $268.59 a month and $96,690.94 in total interest. Even half a point matters: 7% versus 6.5% is $132.94 a month and $47,857.64 over the loan’s life — why shopping lenders and improving your credit score before you apply can be worth tens of thousands.
How Does the Loan Term Change the Payment?
The term is the second lever, and it pulls in the opposite direction from what most people expect: a longer term means a smaller monthly payment but much more total interest. Same $400,000 loan at 6.5%:
| Term | Monthly payment | Total interest | Total paid |
|---|---|---|---|
| 15 years | $3,484.43 | $227,197.30 | $627,197.30 |
| 20 years | $2,982.29 | $315,750.21 | $715,750.21 |
| 30 years | $2,528.27 | $510,177.95 | $910,177.95 |
Stretching from 15 to 30 years cuts the payment by $956.16 a month — but costs an extra $282,980.65 in interest. The 20-year term sits in the middle: $454.02 a month more than the 30-year, saving $194,427.74 in interest. Our guide to the 15-year vs 30-year mortgage compares the two terms in full. Before you choose a term, check how much house can i afford — the 28/36 rule sizes the payment to your income first.
What the Formula Leaves Out: PITI
The formula gives principal and interest only. Your real monthly cost is PITI — principal, interest, taxes, and insurance — which adds:
- Property taxes. Often $300 to $800 a month depending on the home’s value and local tax rates, usually collected by the lender in escrow.
- Homeowners insurance. Typically $150 to $300 a month, also escrowed.
- Private mortgage insurance (PMI). If your down payment is under 20%, expect roughly 0.3% to 1.5% of the loan amount per year — on a $360,000 loan at 0.75%, that is $225 a month. Our guide to what is PMI works out the cost and when it goes away.
- HOA dues. Some homes add $100 to $500 a month in association fees, which lenders count in your housing cost.
A $2,528.27 principal-and-interest payment can easily become $3,300 to $3,600 a month once taxes, insurance, and PMI are added. Always compare offers on the full PITI number, not the formula number alone.
Common Mistakes When Calculating by Hand
Four errors show up again and again:
- Forgetting to divide the rate by 12. Using 0.065 instead of 0.005417 as r gives a payment of about $26,000 a month — ten times too high. The monthly rate is the single most common mistake.
- Using the rate as a whole number. The formula needs the decimal: 6.5% is 0.065, not 6.5.
- Counting years instead of months. A 30-year mortgage is n = 360, not n = 30. Using 30 gives a payment of about $14,482 a month.
- Mixing APR and interest rate. The formula uses the interest rate, not the APR: if your offer’s APR is 6.78% but the rate is 6.5%, the payment is calculated at 6.5%.
If your hand calculation looks wildly different from the lender’s quote, check those four first.
A Faster Way to Check Your Answer
Once you have done the formula by hand, you never need to do it again — Calcrio’s free mortgage calculator runs it in seconds, so you can test a dozen combinations of amount, rate, and term in the time one hand calculation takes.
FAQ: How to Calculate Monthly Mortgage Payments
How do I calculate my monthly mortgage payment?
Use the formula M = P × r(1 + r)^n ÷ ((1 + r)^n − 1), with r as the monthly rate (annual rate ÷ 12) and n as the total number of payments. For a $400,000 loan at 6.5% over 30 years, the payment is $2,528.27 a month.
What is the formula for a monthly mortgage payment?
The standard amortization formula is M = P × r(1 + r)^n ÷ ((1 + r)^n − 1). M is the monthly payment, P is the amount borrowed, r is the monthly interest rate, and n is the number of monthly payments.
How much is the monthly payment on a $400,000 mortgage?
At 6.5% over 30 years, the payment is $2,528.27 a month in principal and interest, with $510,177.95 in total interest. At 6% it drops to $2,398.20, and at 7% it rises to $2,661.21.
Why is most of my early mortgage payment interest?
Because interest is charged on the balance you still owe, and the balance is highest at the start. In month 1 of a $400,000 loan at 6.5%, $2,166.67 of the $2,528.27 payment is interest, and principal does not overtake interest until month 233.
Does the mortgage payment formula include taxes and insurance?
No. The formula covers principal and interest only. Property taxes, homeowners insurance, PMI, and HOA dues are added on top — the full PITI payment can be $800 or more above the formula number.
Can I calculate a mortgage payment without the formula?
Yes — a $400,000 loan at 0% over 360 months is simply $400,000 ÷ 360 = $1,111.11 a month, and any loan’s payment can be found with a free mortgage calculator. Learn the formula once, so you can spot a wrong quote.