Use this simple, accurate mortgage payment calculator to quickly estimate your monthly principal and interest payment. Understanding this figure is the first step toward smart homeownership planning.
How to Calculate Mortgage Payment
How to Calculate Mortgage Payment Formula
The standard formula for calculating a fixed-rate monthly mortgage payment is based on an amortization schedule. It solves for the monthly payment amount, M, using the principal, interest rate, and number of payments.
M = P [ i(1 + i)ᴺ / ((1 + i)ᴺ - 1) ]
Formula Source: Investopedia, CFPB
Variables Explained
- M: The total monthly mortgage payment (Principal and Interest). This is the result we solve for.
- P: The original principal amount or the balance of the loan.
- i: The monthly interest rate. This is the Annual Interest Rate divided by 12 (and converted to a decimal).
- N: The total number of payments (or total months in the term). Calculated as Loan Term (Years) multiplied by 12.
Related Calculators
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- Mortgage Affordability Calculator
- Amortization Schedule Generator
What is the Monthly Mortgage Payment?
The monthly mortgage payment (specifically, the P&I portion) is the fixed amount you pay the lender each month to service your debt. This payment is crucial because it determines a large part of your monthly housing expense. In the early years of the loan, a larger portion of the payment goes toward interest. As the loan matures, the principal portion increases.
It’s important to note that the result from this calculator only includes Principal and Interest (P&I). A borrower’s true monthly payment, often called PITI, may also include property taxes, homeowner’s insurance, and sometimes Private Mortgage Insurance (PMI), which are often held in an escrow account by the lender.
How to Calculate Mortgage Payment (Example)
Let’s calculate the monthly payment for a $200,000 loan at 4.0% interest over 15 years.
- Find the Monthly Interest Rate (i): Divide the annual rate by 1200: $4.0 \div 1200 = 0.003333333$.
- Find the Total Number of Payments (N): Multiply the term in years by 12: $15 \text{ years} \times 12 = 180 \text{ payments}$.
- Calculate the Amortization Factor: Use the formula’s core component: $\frac{i(1+i)^N}{(1+i)^N – 1}$. This complex factor will be approximately $0.00739686$.
- Calculate the Payment (M): Multiply the Principal (P) by the factor: $\$200,000 \times 0.00739686 = \$1,479.37$.
Frequently Asked Questions (FAQ)
The interest rate has the most significant impact. A small increase in the rate, even 0.5%, can raise your payment substantially, especially on a 30-year term, because you pay more interest over the life of the loan.
What is the difference between P&I and PITI?P&I is the Principal and Interest component—the amount needed to pay down the loan. PITI stands for Principal, Interest, Taxes, and Insurance. PITI is your full monthly housing payment when taxes and insurance are escrowed.
Is this calculator only for fixed-rate mortgages?Yes, this standard amortization formula is designed for fixed-rate loans where the interest rate remains constant throughout the term. Adjustable-rate mortgages (ARMs) have variable payments that change after an initial period.
Can I use this for Canadian or UK mortgages?The formula’s fundamental logic is the same, but you must adjust the rate conversion. This calculator assumes monthly compounding (the standard in the US), whereas other countries may use semi-annual or other compounding periods. Be sure to convert the annual rate to the monthly rate correctly based on your loan structure.