Your monthly mortgage payment is calculated using one formula: M = P[r(1+r)^n] / [(1+r)^n - 1]. That is it. Every lender in the country uses this same equation for a fixed-rate loan.
The number this formula produces is your principal and interest payment — the core of what you owe each month. According to the Federal Reserve, the average 30-year fixed mortgage rate in the US has ranged from 6% to 8% over 2023–2024, which means a $300,000 loan costs between $2,027 and $2,201 per month in principal and interest alone. Understanding the formula means you can check any lender's quote before you sign anything.
Use the free Mortgage Calculator at RoughTools to calculate your monthly mortgage payment instantly — or follow the step-by-step method below.
The Monthly Mortgage Payment Formula
The standard formula for a fixed-rate mortgage payment is:
M = P × [r(1+r)^n] / [(1+r)^n - 1]
Every variable has a specific meaning:
- M — your monthly payment (what you want to find)
- P — the principal, meaning the loan amount (purchase price minus your down payment)
- r — the monthly interest rate (annual rate divided by 12)
- n — the total number of monthly payments (loan term in years multiplied by 12)
Worked example from start to finish
Say you are buying a home priced at $347,500. You put down $69,500 (20%), leaving a loan amount of $278,000. Your lender quotes 6.75% annual interest on a 30-year fixed mortgage.
Step 1 — Convert the annual rate to monthly:
r = 6.75% ÷ 12 = 0.5625% = 0.005625
Step 2 — Calculate total number of payments:
n = 30 years × 12 months = 360
Step 3 — Calculate (1+r)^n:
(1 + 0.005625)^360 = (1.005625)^360 ≈ 7.6941
Step 4 — Plug into the formula:
M = 278,000 × [0.005625 × 7.6941] / [7.6941 - 1]
M = 278,000 × [0.043279] / [6.6941]
M = 278,000 × 0.006465
M ≈ $1,797.27
Your principal and interest payment is $1,797 per month. In practice, lenders round to the nearest dollar, so your statement will show exactly $1,797 or $1,798 depending on how they handle rounding.
This does not include property taxes, homeowners insurance, or PMI — those are added on top and vary by location and lender. The full payment including those is called PITI (Principal, Interest, Taxes, Insurance).
How to Calculate Monthly Mortgage Payment Step by Step
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Gather your four inputs. You need the home price, your down payment amount (or percentage), the annual interest rate your lender quoted, and the loan term in years. If you are refinancing, your loan amount replaces the home price minus down payment.
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Calculate your loan principal. Subtract your down payment from the purchase price. On a $425,000 home with 10% down ($42,500), your principal P is $382,500. This is the amount the formula works on — not the purchase price.
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Convert the annual rate to a monthly rate. Divide the annual interest rate by 12. A 7.25% annual rate becomes 7.25 ÷ 12 = 0.6042% per month, or 0.006042 in decimal form. Never skip this step — using the annual rate directly gives you a wildly wrong answer.
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Calculate total payments n. Multiply your loan term in years by 12. A 30-year loan = 360 payments. A 15-year loan = 180 payments. A 20-year loan = 240 payments.
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Apply the formula. Plug P, r, and n into M = P[r(1+r)^n] / [(1+r)^n - 1]. The trickiest part is computing (1+r)^n — use a scientific calculator or the free Mortgage Calculator to handle the exponent automatically.
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Verify the answer makes sense. A rough check: for a 30-year loan at 7%, your monthly payment is approximately $6.65 per $1,000 borrowed. On a $300,000 loan that gives $300 × $6.65 = $1,995 — close to the formula result. If your calculated number is dramatically different, you have likely entered the rate as a whole number (e.g., 7) instead of a decimal (0.07) or forgotten to divide by 12.
Pro tip: When comparing lenders, run the formula with each lender's quoted rate before your meeting. Even a 0.25% rate difference on a $350,000 loan saves or costs roughly $57 per month — that is $20,520 over 30 years.
What is Included in a Monthly Mortgage Payment?
The formula above gives you principal and interest only — but your actual monthly payment to the lender is usually higher. Here is what makes up a full mortgage payment:
| Component | What it is | Typical amount | |---|---|---| | Principal (P) | Repays the loan balance | Varies by loan | | Interest (I) | Cost of borrowing the money | Varies by rate | | Property taxes (T) | Collected in escrow by lender | $200–$800/mo | | Homeowners insurance (I) | Required by all lenders | $80–$200/mo | | PMI | Required if down payment < 20% | $50–$200/mo |
The full PITI payment — Principal, Interest, Taxes, Insurance — is what lenders use to calculate your debt-to-income ratio when qualifying you for the loan.
On the worked example above ($278,000 loan, $1,797 P&I payment), a buyer in a moderate-tax area might add $350/month in taxes and $120/month in insurance, making the full PITI payment approximately $2,267 per month.
This is why comparing mortgage quotes on principal and interest alone can be misleading. Two lenders quoting the same rate will have identical P&I payments — but escrow amounts differ if they estimate taxes and insurance differently.
How Does a 15-Year Mortgage Compare to a 30-Year?
The monthly payment on a 15-year mortgage is significantly higher, but the total interest you pay is dramatically lower.
Using the same $278,000 loan at 6.75%:
| | 30-Year Fixed | 15-Year Fixed | |---|---|---| | Monthly payment (P&I) | $1,797 | $2,459 | | Total paid over life of loan | $646,920 | $442,620 | | Total interest paid | $368,920 | $164,620 | | Interest savings | — | $204,300 |
The 15-year payment is $662 more per month. But you pay the loan off 15 years earlier and save over $200,000 in interest.
The 15-year option also typically comes with a lower interest rate — lenders charge 0.5% to 0.75% less because the shorter term reduces their risk. Recalculate with 6.125% on the 15-year and the monthly payment drops to $2,368 while the interest savings grow even larger.
The right choice depends on your cash flow. A buyer who is tight on monthly expenses benefits from the lower 30-year payment. A buyer with stable income who prioritizes building equity fast should lean toward the 15-year. Use the loan payoff calculator to model both scenarios side by side.
How Much Does a 1% Interest Rate Difference Actually Cost?
A 1% rate increase costs far more than most buyers expect. On a 30-year fixed mortgage, every 1% increase in interest rate raises your monthly payment by roughly $56 per $100,000 borrowed.
On a $350,000 loan:
| Rate | Monthly P&I | Total interest over 30 years | |---|---|---| | 5.75% | $2,042 | $385,048 | | 6.75% | $2,270 | $467,200 | | 7.75% | $2,506 | $552,160 |
The difference between 5.75% and 7.75% is $464 per month and $167,112 in total interest. That is why mortgage shopping matters so much. According to the Consumer Financial Protection Bureau (CFPB), borrowers who get at least three mortgage quotes save an average of $1,500 over the first five years compared to those who accept the first offer.
Even improving your credit score from 680 to 740 before applying can reduce your quoted rate by 0.5% or more — worth tens of thousands of dollars over the life of the loan.
Common Mistakes When Calculating Mortgage Payments
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Using the annual rate instead of the monthly rate. The formula requires r to be the monthly rate (annual ÷ 12). Plugging in 6.75 instead of 0.005625 produces a payment of tens of thousands of dollars — obviously wrong. Always divide by 12 first.
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Forgetting that principal is not the purchase price. Your P in the formula is the loan amount after your down payment. On a $400,000 home with 5% down, P is $380,000 — not $400,000. Using the full purchase price overstates your payment.
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Treating the formula result as your total payment. The formula gives you principal and interest only. Property taxes, insurance, and PMI are additional. First-time buyers frequently budget based on the P&I number and are surprised by the full PITI payment.
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Comparing lenders on monthly payment alone. Two quotes at 6.75% will have the same monthly payment — but one might charge $8,000 in origination fees and the other $1,500. Always compare the APR (Annual Percentage Rate), which folds fees into the rate for an apples-to-apples comparison.
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Not recalculating after every rate change. Many buyers get pre-approved at one rate and lock in weeks later when rates have moved. A 0.375% increase between pre-approval and closing can add $80–$100/month. Recalculate any time your quoted rate changes.
Frequently Asked Questions
How do I calculate my monthly mortgage payment by hand? Use the formula M = P[r(1+r)^n] / [(1+r)^n - 1], where P is your loan amount, r is the monthly interest rate (annual rate ÷ 12), and n is the total payments (years × 12). For a $300,000 loan at 7% over 30 years: r = 0.005833, n = 360, giving a monthly payment of $1,996. The hardest part is computing (1.005833)^360 — a scientific calculator handles this in seconds.
What if I make extra principal payments each month? Extra payments go directly toward reducing your loan balance, which shrinks the interest charged in subsequent months. A $200 extra payment each month on a $300,000 loan at 7% cuts the 30-year term to roughly 24 years and saves approximately $93,000 in interest. The loan payoff calculator lets you model any extra payment amount.
What is the difference between interest rate and APR on a mortgage? The interest rate is what you pay to borrow the principal, used in the monthly payment formula. APR (Annual Percentage Rate) includes the interest rate plus lender fees (origination, points, mortgage insurance) expressed as a yearly rate. The APR is always equal to or higher than the interest rate. When comparing mortgage offers, compare APRs — not just rates — because two loans at 6.75% with different fee structures have different APRs and different true costs.
How much do I need to earn to afford a $400,000 mortgage? Using the 28% rule, your gross monthly income should be at least 3.57 times your monthly mortgage payment. On a $400,000 loan at 7% over 30 years, the P&I payment is approximately $2,661. Add $400/month for taxes and insurance and the full payment is around $3,061. Divide by 0.28: you need at least $10,932/month gross income — about $131,000/year — to stay within the 28% guideline. Use the home affordability calculator for a full picture including your existing debts.
When should I use the mortgage formula vs just using a calculator? Use the formula when you want to verify a lender's quote, understand how your payment is built, or run a quick scenario that is not pre-loaded in a calculator. Use the Mortgage Calculator for everything else — it handles the exponent arithmetic, adds taxes and insurance, shows an amortization schedule, and runs multiple scenarios in seconds. Both approaches give the same P&I number.
These calculations are estimates for planning purposes. Actual payments depend on your lender, credit profile, local tax rates, and insurance costs. Consult a licensed mortgage professional before making borrowing decisions.
Use the Free Mortgage Calculator
The Free Mortgage Calculator at RoughTools handles the entire principal and interest calculation automatically. Enter your home price, down payment, interest rate, and loan term — the tool instantly returns your monthly P&I payment, full PITI estimate, total interest paid over the life of the loan, and a month-by-month amortization schedule showing exactly how much of each payment reduces your balance vs pays interest. No account needed, no data stored, completely free.
You might also need:
- Loan Calculator — for personal loans and auto loans
- Down Payment Calculator — find your minimum down payment by loan type
- Home Affordability Calculator — how much house your income supports
- Salary Calculator — convert hourly or annual income for affordability calculations