Finance

Mortgage Calculator

Calculate monthly mortgage payments, total interest, and total cost of a loan.

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Last updated: June 2026

Mortgage Parameters

Home Price Slider
Min: 5,000 Max: 2,000,000

Advanced Options

Estimated Monthly Payment

Principal amount:

Principal & Interest
Property Taxes
Homeowners Insurance
PMI (Private Mortgage Ins.)
HOA Fees

Loan Balance Over Time

Annual Amortization Schedule

Total Interest Paid:
Year Beg. Balance Interest Paid Principal Paid Remaining Balance

Step-by-Step Manual Calculation Guide

While our Mortgage Calculator provides instant results and charts, understanding how to compute your monthly payments manually is vital for deep comprehension. Follow this chronological methodology using the standard Amortization formula:

1

Identify the Loan Parameters

Identify and note down the given values for your mortgage:
  • Principal (P): The total loan amount (Home Price minus Down Payment). (e.g., )
  • Annual Interest Rate (r): The yearly interest rate as a decimal. (e.g., % = )
  • Number of Months (n): The total number of monthly payments. (e.g., years = months)
2

Set up the Amortization Formula

Convert the annual interest rate to a monthly rate by dividing by 12. Then, plug your values into the standard mortgage formula:
M = P \left[ \frac{i(1 + i)^n}{(1 + i)^n - 1} \right]
Where M is the monthly principal & interest payment, and i is the monthly interest rate.
3

Calculate the Core Payment

Perform the arithmetic operations following PEMDAS. First calculate the exponent (1+i)^n, then multiply the numerator, subtract 1 in the denominator, and divide.

For your specific inputs, the calculated Principal & Interest payment is .
4

Add Escrow and Additional Costs

Your total monthly payment usually includes more than just Principal and Interest. Add any applicable Property Taxes, Homeowners Insurance, PMI, and HOA fees.

Final Total Payment = P&I + Taxes + Insurance + PMI + HOA
Result:
BasicMathTools STEM Editorial Team Verified
Reviewed by Applied Math & Finance Specialists Editorial Policy
Updated: July 2026 Fact-Checked

What Is the Mortgage Calculator?

The Mortgage Calculator computes your monthly payment, total interest cost, and amortization schedule for fixed-rate home loans. Whether you're buying your first home, refinancing, or comparing lender offers, this tool breaks down exactly how much of each payment goes toward principal vs. interest over the life of the loan.

Mortgages are amortized loans, meaning each monthly payment covers both interest on the outstanding balance and a portion of the principal. In the early years, most of your payment goes to interest. Over time, the interest share shrinks and the principal share grows — a phenomenon known as the amortization curve.

The Monthly Payment Formula

M = P × [r(1+r)^n] / [(1+r)^n - 1]
where P = loan principal, r = monthly interest rate (annual rate / 12), and n = total number of monthly payments (years × 12).

How to Use the Mortgage Calculator

Using this calculator is straightforward. Enter your known values into the fields below, and the solver will compute the result immediately. Here is what each input represents:

Loan Amount ($) Example input: 300000
Annual Interest Rate (%) Example input: 5.5
Loan Term (Years) Example input: 30

Formula Used

M = P \frac{r(1+r)^n}{(1+r)^n - 1}
Worked Example

Worked Example: Monthly Payment on a $300,000 Home Loan

Problem: You take out a $300,000 mortgage at 6.5% annual interest for 30 years (360 monthly payments). What is your monthly payment?

1. Convert to Monthly Rate

Annual rate 6.5% = 0.065. Monthly rate r = 0.065 / 12 = 0.005417.

r = \frac{0.065}{12} = 0.005417

2. Calculate Total Payments

30 years × 12 months = 360 total payments.

3. Compute the Growth Factor

(1 + 0.005417)^360 = (1.005417)^360 ≈ 6.9916.

(1.005417)^{360} \approx 6.9916

4. Apply the Payment Formula

M = $300,000 × [0.005417 × 6.9916] / [6.9916 − 1] = $300,000 × 0.03788 / 5.9916 = $1,896.20.

M = \$1,896.20 \text{ per month}
Final Result Monthly Payment = $1,896.20 | Total Amount Paid = $682,632 | Total Interest = $382,632 over 30 years.

How to Calculate Mortgage Step-by-Step

Understanding the underlying solution workflow helps build mathematical intuition:

1
Identify and note down the given values for: Loan Amount ($), Annual Interest Rate (%), Loan Term (Years).
2
Set up the primary formula: \(M = P \frac{r(1+r)^n}{(1+r)^n - 1}\). Substitute the identified values into their respective positions.
3
Perform the required logical or mathematical steps to calculate the final output.
4
Round the final calculated answer to the required decimal accuracy or significant figures.

Real-World Applications of Mortgage Calculator

Home Purchase Affordability Analysis

Determine the maximum home price you can afford based on your income, down payment, and target monthly budget before visiting lenders.

Refinancing Decision Support

Compare your current loan's remaining payments against a new loan at a lower rate to calculate breakeven point and total savings from refinancing.

Extra Payment Impact Modeling

See how making additional principal payments each month shortens the loan term and reduces total interest — even $100/month extra can save tens of thousands.

Common Pitfalls & Mistakes to Avoid

Forgetting Property Taxes, Insurance, and PMI

Your true monthly housing cost includes property taxes, homeowner's insurance, and private mortgage insurance (PMI) if your down payment is less than 20%. Budget for total PITI, not just principal and interest.

Comparing Rates Without Considering Points

Lenders may offer lower rates in exchange for upfront "points" (prepaid interest). A 6.0% rate with 2 points may cost more upfront than 6.25% with 0 points. Compare the APR, which includes points.

Ignoring the Amortization Front-Loading Effect

In the first years of a 30-year mortgage, roughly 70-80% of each payment goes to interest. This means refinancing early can be beneficial, but selling early means you've built little equity.

Key Terminology Glossary

Amortization The gradual repayment of a loan through fixed periodic payments that cover both interest and a portion of principal, with the principal share increasing over time.
Principal The original amount borrowed (the loan balance), excluding interest. Each monthly payment reduces the principal by a small amount.
Escrow An account held by the lender where a portion of your monthly payment is deposited to cover property taxes and insurance when they come due.
PMI (Private Mortgage Insurance) Insurance required by lenders when the borrower's down payment is less than 20%, protecting the lender against default. PMI typically costs 0.5%–1% of the loan annually.

Expert Tips for Mortgage Calculator

  • Factor in extra costs: Real-world monthly housing expenses usually include property taxes, home insurance, and potentially Private Mortgage Insurance (PMI).
  • Analyze amortization: Paying even a small extra principal amount each month early in the term can significantly reduce the overall interest paid and shorten the loan life.
  • Compare terms: A 15-year mortgage will have higher monthly payments but saves a massive amount of interest over the life of the loan compared to a 30-year option.

About the Mortgage Calculator

The Mortgage Calculator is maintained by Basic Math Tools, an educational platform committed to providing accurate STEM and financial computing tools. Every tool processes calculations transparently in your browser for privacy and speed.

If you have suggestions or request additional features, please review our Editorial Policy or contact our math team.

Frequently Asked Questions

How is the monthly mortgage calculated?
It is calculated using the standard amortization formula which accounts for principal, interest rate, and the life of the loan.
How does the Mortgage Calculator calculate results?
The calculator applies the standard mathematical formula (M = P \frac{r(1+r)^n}{(1+r)^n - 1}) used in finance. Enter your known values, and it computes the result using the same methods taught in textbooks, displaying each step for verification.
Is the Mortgage Calculator accurate enough for professional use?
The underlying math uses well-established formulas and high-precision arithmetic. For routine professional calculations, the results are reliable. For safety-critical or high-stakes applications, always verify results independently.
Do I need to create an account to use this calculator?
No. All tools on Basic Math Tools are completely free and require no registration. Calculations run entirely in your web browser — nothing is stored on our servers.
Can I access the Mortgage Calculator on my phone?
Yes. Every calculator is designed mobile-first and works on smartphones, tablets, and desktop computers. The interface adapts automatically to your screen size.