Mortgage Calculator
Calculate monthly mortgage payments, total interest, and total cost of a loan.
Mortgage Parameters
Advanced Options
Estimated Monthly Payment
Principal amount:
Loan Balance Over Time
Annual Amortization Schedule
| 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:
Identify the Loan Parameters
- 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)
Set up the Amortization Formula
Calculate the Core Payment
(1+i)^n, then multiply the numerator, subtract 1 in the denominator, and divide.
For your specific inputs, the calculated Principal & Interest payment is .
Add Escrow and Additional Costs
Final Total Payment = P&I + Taxes + Insurance + PMI + HOA
Result:
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:
Formula Used
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.
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.
4. Apply the Payment Formula
M = $300,000 × [0.005417 × 6.9916] / [6.9916 − 1] = $300,000 × 0.03788 / 5.9916 = $1,896.20.
How to Calculate Mortgage Step-by-Step
Understanding the underlying solution workflow helps build mathematical intuition:
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
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.