How to Calculate a Mortgage Payment Using the Formula

The Formula Every Borrower Should Know

The standard fixed-rate mortgage payment uses the present value of an annuity formula. It looks like this:

M = P × [r(1 + r)^n] / [(1 + r)^n - 1]

Break down each variable once and the formula becomes mechanical:

• M = Monthly payment
• P = Principal loan amount (the amount borrowed, not the home price)
• r = Monthly interest rate (your annual rate divided by 12)
• n = Total number of monthly payments (loan term in years multiplied by 12)

A 30-year fixed mortgage at 7.00% annual rate produces an r of 0.005833 and an n of 360. Those two numbers feed every calculation below.

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Worked Example 1: $400,000 Loan at 7.00% Over 30 Years

This is a common scenario for a primary residence purchase in most major US metros.

Inputs:

• P = $400,000
• Annual rate = 7.00%, so r = 7.00 / 100 / 12 = 0.005833
• n = 30 × 12 = 360

Step 1. Calculate (1 + r)^n: (1.005833)^360 = 8.1165

Step 2. Multiply r by that result: 0.005833 × 8.1165 = 0.047346

Step 3. Subtract 1 from the same result: 8.1165 - 1 = 7.1165

Step 4. Divide step 2 by step 3: 0.047346 / 7.1165 = 0.006653

Step 5. Multiply by P: $400,000 × 0.006653 = $2,661.21 per month

Over 360 payments, total repayment equals $957,835.60. The interest component alone is $557,835.60, which is 139.5% of the original loan balance. That figure does not appear on most lender disclosure sheets without explicit request.

What the First Payment Actually Buys

Month 1 breakdown on this loan:

• Interest: $400,000 × 0.005833 = $2,333.20
• Principal: $2,661.21 - $2,333.20 = $328.01

87.7% of the first payment services interest. The balance after payment 1 is $399,671.99. Borrowers who focus only on the monthly number without examining this split routinely underestimate how slowly equity builds in the early years.

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Worked Example 2: $625,000 Loan at 6.75% Over 15 Years

A 15-year term at a lower rate dramatically changes the cost profile. Lenders typically price 15-year fixed mortgages 0.50 to 0.75 percentage points below 30-year rates. This example uses a realistic spread.

Inputs:

• P = $625,000
• Annual rate = 6.75%, so r = 6.75 / 100 / 12 = 0.005625
• n = 15 × 12 = 180

Step 1. (1 + r)^n: (1.005625)^180 = 2.7372

Step 2. r × result: 0.005625 × 2.7372 = 0.015397

Step 3. Result minus 1: 2.7372 - 1 = 1.7372

Step 4. Divide: 0.015397 / 1.7372 = 0.008864

Step 5. Multiply by P: $625,000 × 0.008864 = $5,540.26 per month

Total repayment: $997,246.80. Total interest paid: $372,246.80.

Compare that to the same $625,000 borrowed at 7.00% over 30 years. The 30-year payment calculates to $4,158.43 per month, with total interest of $872,034.80. The 15-year borrower pays $1,381.83 more each month but saves $499,788 in interest over the life of the loan.

The monthly payment gap is real. So is the long-term cost differential. Neither number is negotiable once you sign.

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How Rate Differences Translate to Dollar Costs

Many buyers treat a 0.25% rate difference as negligible. The math does not support that.

On a $500,000 loan over 30 years:

Each 0.25% increment adds roughly $83 to $86 per month and between $29,000 and $31,000 over the full term. Shopping two lenders and finding a 0.50% rate improvement on a $500,000 loan is worth approximately $60,141 in total interest. That gap justifies spending several hours on rate comparisons before locking.

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The Role of the Amortization Schedule

The formula calculates your fixed payment. The amortization schedule shows how that payment splits between principal and interest each month, and how the split evolves.

On the $400,000 / 7.00% / 30-year example:

• Month 1: $328.01 principal, $2,333.20 interest
• Month 60: $454.61 principal, $2,206.60 interest
• Month 120: $629.83 principal, $2,031.38 interest
• Month 180: $872.97 principal, $1,788.24 interest
• Month 240: $1,209.52 principal, $1,451.69 interest
• Month 300: $1,675.88 principal, $985.33 interest
• Month 360: $2,645.63 principal, $15.43 interest

The crossover point, where principal exceeds interest in the monthly payment, arrives at month 219 on this loan. That is 18.25 years into a 30-year mortgage. Refinancing before that point resets the amortization schedule and can reset the interest-to-principal ratio toward the front-heavy early months.

Borrowers who refinance every five to seven years to chase lower rates often pay more lifetime interest than those who hold their original loan, even when each refinance reduces the rate. Run the total interest numbers across both scenarios before treating a refinance as automatic savings.

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Inputs That Change the Output

The formula itself is fixed. These variables are where you have leverage before signing:

Loan Amount (P)

A larger down payment reduces P directly. On a $550,000 purchase, putting down 20% ($110,000) versus 10% ($55,000) reduces the loan by $55,000. At 7.00% over 30 years, that reduces monthly payments by $365.90 and saves $131,724 in interest. Larger down payments also eliminate private mortgage insurance, which typically adds 0.50% to 1.85% of the loan amount annually.

Interest Rate (r)

Already covered above. Rate is the variable with the highest dollar sensitivity per basis point.

Loan Term (n)

Shorter terms carry lower rates and lower total interest at the cost of higher monthly payments. The 15-year vs. 30-year comparison in Worked Example 2 illustrates this precisely.

Amortization Type

This formula applies to fully amortizing fixed-rate loans. Adjustable-rate mortgages, interest-only periods, and balloon structures use modified versions. If your loan has any of these features, the fixed-rate formula applies only to the initial period or not at all.

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Verify Before You Sign

Lenders generate payment quotes through software. Input errors, rate locks applied to the wrong product, or fee structures embedded in an APR rather than the note rate can all produce a quoted payment that differs from what the formula produces.

Run the formula with the exact rate on your Loan Estimate. Compare that output to the quoted monthly payment in Section 1 of the Estimate. The figures should match within rounding error. If they do not, ask the lender to reconcile the difference in writing before proceeding.

The formula takes four numbers. The calculation takes under two minutes. The cost of skipping it can be measured in tens of thousands of dollars.

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Run Your Exact Numbers

The worked examples above use round inputs to illustrate the mechanics. Your actual loan will have a specific principal, a rate quoted to three decimal places, and potentially a term that differs from 15 or 30 years.

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The CalcMoney mortgage calculator accepts your exact inputs and returns your monthly payment, total interest paid, and a full amortization schedule by month. It runs the same formula shown here with no rounding at intermediate steps. Use it to verify any lender quote, model different down payment scenarios, or compare the 15-year and 30-year cost profiles side by side with your actual numbers.