For a fully amortizing, fixed-rate mortgage with monthly payments, calculate scheduled principal and interest (P&I) with M = L × i(1+i)n ÷ ((1+i)n − 1). M is the monthly P&I payment, L is the original loan principal, i is the annual note rate divided by 12, and n is the term in years multiplied by 12. To compare rates fairly, keep the loan amount and term unchanged, then recalculate the payment for each rate.
This result is not necessarily the amount leaving your bank account. Property taxes, homeowners insurance, mortgage insurance and other escrowed charges can raise the total housing payment. The calculation also uses the contract note rate, not APR, which reflects broader borrowing costs.
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The mortgage payment formula and what each symbol means
The standard formula assumes a level-payment, fully amortizing loan: the same scheduled P&I payment is made every month until the balance reaches zero at the end of the stated term.
M = L × i(1+i)n ÷ ((1+i)n − 1)
| Symbol | Meaning | How to express it |
|---|---|---|
| M | Scheduled monthly principal-and-interest payment | Currency amount |
| L | Starting loan principal | Currency amount borrowed |
| i | Periodic interest rate | Annual note rate as a decimal, divided by 12 for monthly payments |
| n | Total number of payments | Loan term in years × 12 |
For example, a 6% annual note rate becomes 0.06 ÷ 12 = 0.005 per month, and a 30-year term becomes 30 × 12 = 360 monthly payments. Keep the rate and payment period in matching units. If payments are monthly, use a monthly rate and a monthly payment count.
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What if the interest rate is zero?
When i is zero, the standard expression would divide by zero. Use the simpler result instead: M = L ÷ n. A $120,000 loan with 240 monthly payments and no interest would therefore have a $500 monthly P&I payment.
Use the note rate, not APR
The contract note rate is the interest rate used to calculate scheduled interest. APR incorporates certain fees and other borrowing costs, so it is not an interchangeable input for this formula. If you substitute APR for the note rate, the payment comparison will not describe the loan’s contractual amortization.
How to calculate a monthly mortgage payment step by step
- Write down the original principal. Use the amount financed, not the home’s purchase price. If you make a down payment, the financed principal is the purchase price minus that down payment, subject to the loan’s final terms.
- Identify the annual note rate. Enter it as a percentage first, then convert it to a decimal. A 4% rate is 0.04.
- Convert the rate to a monthly decimal. Divide the annual decimal rate by 12. At 4%,
i = 0.04 ÷ 12 = 0.003333333.... - Convert the term to a payment count. Multiply years by 12. Thirty years gives
n = 360; 15 years givesn = 180. - Apply the formula. Calculate
(1+i)n, multiply the numerator, and divide by the denominator. A spreadsheet or mortgage calculator avoids mistakes in the exponent. - Round only the displayed payment. Keep additional decimal places during the calculation, then round the final currency figure to cents or whole dollars. Rounding intermediate values can create a small discrepancy over hundreds of payments.
Worked example: $100,000 for 30 years at 4%
Use L = $100,000, i = 0.04 ÷ 12, and n = 360. The resulting payment is about $477.42 per month for principal and interest, normally displayed as $477.
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Consumer Financial Protection Bureau, How do mortgage lenders calculate monthly payments?, last reviewed December 11, 2024
The CFPB figure is a rounded P&I example. It does not include property taxes, homeowners insurance, mortgage insurance or other charges.
How much the payment changes at different interest rates
To isolate the effect of the rate, hold every other assumption constant. The following illustration uses a $100,000 principal, a 30-year term, 360 monthly payments and a fixed rate. The scenarios are mathematical assumptions, not quotes or predictions of approval.
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|---|---|---|---|---|
| 3% | $421.60 | −$55.82 per month | $151,776 | $51,776 |
| 4% | $477.42 | Baseline | $171,871 | $71,871 |
| 5% | $536.82 | +$59.40 per month | $193,255 | $93,255 |
| 6% | $599.55 | +$122.13 per month | $215,838 | $115,838 |
| 7% | $665.30 | +$187.88 per month | $239,508 | $139,508 |
Totals are the scheduled payment multiplied by 360, calculated before display rounding. They exclude taxes, insurance, upfront points, closing costs, mortgage insurance and any extra payments. A lower monthly payment is not automatically a cheaper loan if the lower payment comes with a longer term, higher fees or a different rate structure.
What the table shows
Against the 4% baseline, moving to 5% raises the scheduled payment by about $59.40 each month and adds roughly $21,384 in scheduled interest over 30 years. Moving to 6% raises the payment by about $122.13 monthly and adds about $43,967 in interest. At 7%, the payment is about $187.88 higher each month and scheduled interest is about $67,637 higher than at 4%. These are not separate fees; they arise from applying a different rate to the same principal for the same 360-payment schedule.
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The comparison also works in the other direction. At 3%, the payment is about $55.82 below the 4% payment and scheduled interest is approximately $20,095 lower. Showing both the monthly difference and the lifetime interest difference prevents a small monthly change from obscuring a large long-term effect.
Compare rate scenarios without changing the question
- Keep the principal identical. Changing the down payment changes both the payment and the amount of interest.
- Keep the term and payment frequency identical. A 15-year payment cannot be compared directly with a 30-year payment as a pure rate comparison.
- Label each rate as an assumption or an actual lender offer. The formula describes the payment if that rate applies; it does not determine whether a lender will offer or approve it.
- Compare monthly P&I, scheduled P&I over the term and total interest together. Looking at only one of those figures can hide the cost of a different term or fee structure.
What the formula includes—and what it leaves out
The result is principal and interest only. Your servicer may collect additional amounts with the payment, often through an escrow account. The Consumer Financial Protection Bureau notes that a full monthly housing payment is often higher than P&I; its guidance on budgeting for a home is available at Decide how much you want to spend on a home.
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- Property taxes: The annual tax bill divided into monthly installments for budgeting or escrow.
- Homeowners insurance: The premium may be collected monthly even though the policy renews annually.
- Mortgage insurance: Depending on the loan and equity, an insurer’s premium may be added to the payment.
- Other escrowed charges: Some loans collect additional property-related amounts. The exact items depend on the loan documents and location.
Estimate these costs separately from the formula. A payment calculator that reports only P&I should not be mistaken for a complete affordability estimate.
Building a total monthly housing estimate
Start with the calculated P&I figure, then make a separate monthly estimate for each recurring housing cost. Dividing an annual tax or insurance bill by 12 gives a budgeting amount; the servicer’s actual escrow collection can follow its own schedule. Keep the components visible rather than folding an assumed tax or insurance amount into the loan principal. That way, a change in taxes or premiums does not look like a change in the interest rate.
For a rate comparison, use the same tax, insurance and mortgage-insurance assumptions for every scenario if the purpose is to isolate interest. For a real purchase budget, replace those assumptions with the amounts associated with the specific property and loan documents. The P&I formula cannot determine those property-based costs.
How amortization changes the payment over time
On a typical fixed-rate mortgage, the scheduled combined P&I payment remains level, but the split between interest and principal changes. At the beginning, the outstanding balance is largest, so the interest calculation consumes more of each payment. As the balance declines, the interest portion falls and more of the same payment reduces principal.
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For a $100,000 balance at 4%, the first month’s interest is approximately $333.33 (4% ÷ 12 × $100,000). Subtracting that from the roughly $477.42 scheduled P&I leaves about $144.09 to reduce principal. The balance then falls to approximately $99,855.91. In the second month, interest is about $332.85, so roughly $144.57 of the payment reduces principal. The amounts continue to shift even though the scheduled payment remains about $477.42.
An amortization schedule lists each payment’s interest, principal and remaining balance. It is useful for checking a lender’s figures, seeing when principal reduction accelerates and estimating the effect of an extra payment. It does not add taxes or insurance unless those items are separately modeled.
Why fixed-rate, adjustable-rate and balloon loans need different treatment
Fixed-rate amortizing mortgages
The formula is designed for this case: one note rate, regular monthly payments and full repayment by the end of the term. The scheduled P&I payment stays level unless the loan is modified or an additional charge is collected outside P&I.
Adjustable-rate mortgages
An adjustable-rate mortgage (ARM) can have an initial payment calculated from its starting rate. When the rate adjusts, the payment is typically recalculated using the new rate and the remaining term, although the CFPB notes that this does not happen in every case. A single fixed-rate calculation therefore cannot forecast every future ARM payment. Review the loan’s adjustment dates, rate limits and payment terms before relying on a scenario.
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For an ARM, identify which period the calculation represents: the initial period or a later adjustment. If modeling a later payment, use the applicable new rate, the outstanding principal at that point and the remaining payment count when the loan terms call for a recalculation. Do not present the initial-rate result as a promise that the payment will remain unchanged.
Balloon loans
A balloon loan may calculate scheduled payments over a longer amortization period than the actual loan term. That structure can leave a large final balance due. Applying the ordinary fully amortizing formula and treating its monthly result as the complete cost would miss the balloon payment.
The CFPB explains the distinction between ordinary amortization and these repayment structures in How does paying down a mortgage work?, last reviewed May 28, 2024.
Using a calculator or spreadsheet
The CFPB describes mortgage calculators as tools that use the loan amount, term and interest rate to estimate monthly P&I. Enter the same three inputs for every rate scenario and verify that the calculator is set to monthly payments and the intended number of years.
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Spreadsheet method
Most spreadsheet programs provide a payment function. With a 4% annual rate in cell A1, a 30-year term in A2 and a $100,000 principal in A3, a generic monthly-payment expression is:
=PMT(A1/12,A2*12,-A3)The negative principal makes the payment display as a positive number. If your spreadsheet uses different cell locations, substitute those references. Confirm that the result agrees with the standard formula and that the rate is a decimal, not the number 4.
Manual calculation checks
- At a positive rate, the scheduled payment should exceed simple principal divided by the number of payments.
- With the same principal and term, a higher rate should produce a higher P&I payment.
- With the same rate and principal, a shorter term should produce a higher monthly payment but fewer total payments.
- At a zero rate, the result should equal principal divided by the payment count.
Common mistakes and how to correct them
Entering 4 instead of 0.04
A percentage must be converted to a decimal before dividing by 12. Entering 4 as the annual rate represents 400%, not 4%.
Dividing the rate but not the term
Monthly payments require both a monthly rate and a monthly count. Use annual rate ÷ 12 and years × 12. Mixing annual and monthly units produces a materially wrong result.
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Using the purchase price as the loan amount
The formula starts with principal borrowed. Subtract the down payment and account for any financed costs according to the actual loan documents.
Confusing P&I with the total payment
Add separate estimates for taxes, insurance and applicable mortgage insurance when assessing a monthly budget. Do not add them to the formula unless you are intentionally building a separate total-payment model.
Comparing rates while changing the term
A lower payment can result from stretching repayment over more years rather than from a better rate. Hold the term constant for a rate-only comparison, then make a separate comparison of term options.
Rounding too early
Keep the full rate and exponent during calculation. Round the final payment for presentation and note that multiplying a rounded monthly figure by the number of payments can differ slightly from the unrounded total.
Treating a scenario as an offer
A computed payment does not include a lender’s underwriting decision, credit-based pricing, fees or points unless you enter those items separately. Identify the rate’s source, date and assumptions whenever you share a result.
Independent reader supportYour contribution helps us test, update, and keep practical guides available for everyone.A practical workflow for evaluating a mortgage payment
- Define the loan: Record principal, term, payment frequency and whether the rate is fixed, adjustable or part of a balloon structure.
- Calculate P&I: Convert the note rate and term to monthly units and apply the formula.
- Run rate scenarios: Keep principal and term fixed, then calculate each assumed rate.
- Build the complete housing budget: Add separately estimated taxes, insurance, mortgage insurance and other recurring housing costs.
- Review total interest: Multiply the unrounded payment by the scheduled payment count and subtract principal to estimate scheduled interest.
- Check the loan documents: For an actual offer, verify the note rate, term, payment schedule, adjustment provisions, balloon balance and fees rather than relying on a generic calculator.
Frequently asked questions
How do I calculate my monthly mortgage payment?
Convert the annual note rate to a monthly decimal, multiply the term in years by 12, and use M = L × i(1+i)n ÷ ((1+i)n − 1). The result is scheduled monthly principal and interest for a fully amortizing loan.
How much does my mortgage payment change if the interest rate changes?
Recalculate the payment for each rate while keeping principal, term and payment frequency constant. In the $100,000, 30-year illustration, the payment rises from $477.42 at 4% to $536.82 at 5%, an increase of about $59.40 per month.
Does a mortgage payment calculator include taxes and insurance?
Not necessarily. A calculator using the standard formula reports P&I. Property taxes, homeowners insurance, mortgage insurance and other escrowed charges must be estimated separately unless the calculator explicitly models them.
Should I enter APR or the interest rate?
Use the contract note rate. APR reflects certain fees and other borrowing costs and is not the rate used for the scheduled amortization calculation.
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What happens if the rate is 0%?
Use principal divided by the number of payments. For example, $120,000 spread over 240 payments is $500 per month because the usual expression is not defined when the periodic rate is zero.
Why does the payment stay the same while the interest portion changes?
On a typical fixed-rate amortizing loan, the combined P&I payment is level. Interest is calculated on the declining balance, so the interest share decreases and the principal share increases over time.
Can I use this formula for an ARM?
It can describe an ARM’s initial payment when the initial rate and terms fit the assumptions. It cannot by itself forecast every later payment because the rate and recalculation rules may change.
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Not as a complete repayment description. A balloon loan can use a longer amortization period than its actual term and leave a large final balance, which must be modeled separately.
Why do my rounded totals differ from the lender’s?
Keeping full precision until the final display avoids most differences. Multiplying a rounded monthly figure by the payment count can differ slightly from totals calculated with the unrounded payment, and the loan documents control the actual schedule.
The central distinction is simple: the formula answers “What is the scheduled principal-and-interest payment for these assumptions?” It does not answer “What will my complete housing cost be?” or “Will a lender approve me?” Keeping those questions separate makes rate comparisons accurate and useful.
Frequently Asked Questions
How do I calculate my monthly mortgage payment?
Convert the annual note rate to a monthly decimal, convert years to monthly payments, and apply the fully amortizing payment formula. The result is principal and interest only.
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Hold principal, term and payment frequency constant, then recalculate for each rate. For $100,000 over 30 years, payment is about $477.42 at 4% and $536.82 at 5%.
Does a mortgage calculator include taxes and insurance?
Only if those items are entered separately. The standard formula calculates P&I; taxes, homeowners insurance, mortgage insurance and other escrowed charges are additional.
Should I use APR in the mortgage payment formula?
No. Use the contract note rate. APR includes certain fees and borrowing costs and is not interchangeable with the rate used for amortization.
Can this formula calculate an ARM or balloon-loan payment?
It can model an ARM period when its applicable rate and remaining term are known, but it cannot forecast every adjustment. A balloon loan requires separate modeling of its final balance.
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For a fixed-rate, fully amortizing mortgage, convert the annual note rate to a monthly rate, convert the term to monthly payments, and apply the amortization formula. Compare rates with the same principal and term, review both monthly P&I and total interest, and add taxes, insurance and other housing costs separately. Treat the result as an assumption-based calculation—not a lender quote or complete affordability decision.
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