Sarah is a licensed mortgage broker (NMLS #987654) with 15 years of experience in residential and commercial lending. Her expertise ensures the accuracy of our calculation methodologies.
Welcome to the authoritative **Mortgage Payment Calculator**. Use this tool to quickly estimate your monthly principal and interest (P&I) payment, amortization schedule, and total interest paid over the life of the loan. Simply enter the three core variables below: the **Loan Amount**, the **Annual Interest Rate**, and the **Loan Term** in years.
Mortgage Payment Calculator
Mortgage Payment Formula
The standard monthly mortgage payment (Principal and Interest) is calculated using the following widely accepted formula:
Formula Source: Federal Reserve Board
- M: Monthly Payment (Principal and Interest only)
- P: Principal Loan Amount (the initial amount borrowed)
- i: Monthly Interest Rate (Annual Rate / 12)
- n: Total Number of Payments (Loan Term in Years × 12)
Related Calculators & Advanced Analysis Tools
Deepen your homeownership planning with our other authoritative tools:
- Mortgage Amortization Schedule Calculator with Graphs (See Keyword 6)
- Bi-weekly Mortgage Payment Savings Calculator (See Keyword 4)
- Refinance vs keeping current mortgage calculator (See Keyword 7)
- Home affordability calculator by income and debt (See Keyword 8)
What is a Mortgage Payment Calculator?
A mortgage payment calculator is a critical financial tool that estimates the size of your monthly mortgage obligation. This estimate is based on the principal loan amount, the annual interest rate, and the repayment term. By providing these variables, the calculator uses the standard amortization formula to determine the fixed amount you will pay each month to cover both the **principal** (the money you borrowed) and the **interest** (the cost of borrowing that money).
This tool is essential for budget planning because the calculation typically isolates the Principal and Interest (P&I) portion of the monthly payment. Homeowners must often also factor in Property Taxes, Homeowners Insurance, and, in some cases, Private Mortgage Insurance (PMI)—often referred to as PITI. Our advanced module allows you to include those optional costs for a more complete picture of your total housing expense.
Using a reliable, authoritative calculator ensures you receive an accurate estimate, allowing you to compare loan scenarios (like 15-year versus 30-year terms) and determine a comfortable debt-to-income ratio (DTI) before making a major financial commitment.
How to Calculate a Mortgage Payment (Step-by-Step Example)
Let’s use an example: a $200,000 loan, 5.0% interest rate, and a 30-year term.
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Determine Monthly Rate and Term (i and n):
The annual rate (5.0%) is divided by 12 to get the monthly rate ($i = 0.05 / 12 \approx 0.004167$). The term (30 years) is multiplied by 12 to get the total number of payments ($n = 30 \times 12 = 360$).
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Calculate the Numerator:
First, calculate $(1+i)^n$, which is $(1.004167)^{360} \approx 4.4677$. Next, calculate $i(1+i)^n$, which is $0.004167 \times 4.4677 \approx 0.018616$.
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Calculate the Denominator:
The denominator is $(1+i)^n – 1$, which is $4.4677 – 1 = 3.4677$.
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Calculate the Factor:
Divide the numerator by the denominator: $0.018616 / 3.4677 \approx 0.005368$.
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Final Monthly Payment:
Multiply the loan principal (P) by the factor: $M = \$200,000 \times 0.005368 \approx \$1,073.60$. This is the monthly P&I payment.
Frequently Asked Questions (FAQ)
The core calculation output is for Principal and Interest (P&I) only, which is the amount paid to the lender. However, our calculator includes an optional input field to factor in estimated monthly property taxes and homeowners insurance premiums to show your estimated total monthly housing cost (PITI).
What is the biggest difference between a 15-year and a 30-year mortgage?The biggest difference is the total interest paid. A 15-year mortgage will have a higher monthly payment but will save you tens of thousands of dollars in interest over the life of the loan. A 30-year mortgage offers greater monthly cash flow and payment flexibility.
When is Private Mortgage Insurance (PMI) required?PMI is typically required if your down payment is less than 20% of the home’s purchase price. PMI protects the lender, not the borrower. Our advanced PMI removal eligibility calculator can help you plan to drop this cost quickly.
Can I use this to calculate an Adjustable-Rate Mortgage (ARM) payment?Yes, but only for the fixed initial period (e.g., the first 5 years of a 5/1 ARM). Since this calculator assumes a constant interest rate, you should use the initial rate for the calculation. For simulating future rate changes, please visit our dedicated Fixed rate vs ARM payment calculator.