Use this simple, accurate mortgage calculator to quickly estimate your monthly principal and interest (P&I) payments.
Mortgage Payment Calculator
Estimated Monthly Payment (P&I)
Detailed Calculation Steps
Mortgage Payment Calculator Formula
The standard formula for calculating a fixed-rate monthly mortgage payment is:
M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1 ]
Where:
- M = Monthly payment
- P = Principal loan amount (initial balance)
- i = Monthly interest rate (Annual Rate / 12)
- n = Total number of payments (Term in Years × 12)
Formula Source: Investopedia – Mortgage Payment, Bankrate – Mortgage Calculator
Variables
The calculation uses three primary variables, all explained here:
- Loan Amount (P): The principal sum borrowed. This is the amount you are financing after subtracting any down payment from the home price.
- Annual Interest Rate (R): The yearly rate of interest expressed as a percentage. The calculator converts this to a monthly rate for the formula.
- Loan Term (N): The length of the loan, usually expressed in years (e.g., 15, 20, or 30 years).
Related Calculators
You may find these other financial tools helpful:
- Home Affordability Calculator
- Refinance Savings Calculator
- Amortization Schedule Generator
- Debt-to-Income Ratio Calculator
What is a Mortgage Payment Calculator?
A mortgage payment calculator is a critical tool that estimates the required monthly payment for a loan, covering the principal and interest (P&I). It uses the loan amount, the annual interest rate, and the loan term to project the fixed monthly expense.
Understanding your P&I payment is the first step in budgeting for a home purchase, though it excludes other costs like property taxes, homeowner’s insurance, and private mortgage insurance (PMI), which are often bundled into the total monthly cost (PITI).
Using this calculator helps potential homeowners determine what they can comfortably afford and compare different loan scenarios (e.g., 15-year vs. 30-year mortgages, or different interest rates).
How to Calculate a Mortgage Payment (Example)
Let’s use an example: A $200,000 loan at 5% interest for 30 years.
- Determine Monthly Rate (i): Annual Rate (5% or 0.05) / 12 months = 0.0041667
- Determine Total Payments (n): Term (30 years) × 12 months = 360 payments
- Calculate (1 + i)^n: (1 + 0.0041667)^360 ≈ 4.46774
- Calculate Numerator: P * i * (1 + i)^n = 200,000 * 0.0041667 * 4.46774 ≈ 3,723.12
- Calculate Denominator: (1 + i)^n – 1 = 4.46774 – 1 = 3.46774
- Final Payment (M): Numerator / Denominator = 3,723.12 / 3.46774 ≈ $1,073.64
Frequently Asked Questions (FAQ)
A: No. This calculator estimates only the Principal and Interest (P&I) portion of your payment. You must manually add property taxes, homeowner’s insurance, and PMI (if applicable) to get your total housing cost (PITI).
A: A shorter term (like 15 years) significantly increases your monthly payment because you are repaying the principal over fewer months. However, you pay substantially less total interest over the life of the loan.
A: An amortization schedule is a table showing the periodic loan payments, specifying the amount of principal and interest included in each payment, until the loan is fully paid off.
A: Not exactly. The Annual Interest Rate is the rate used to calculate interest charges. The Annual Percentage Rate (APR) includes the interest rate plus certain other loan costs (like points and fees) to give you the total cost of borrowing.