Mortgage Calculator

Formula & Methodology

A fixed-rate mortgage follows the standard amortization formula used by lenders worldwide:

M = P × r(1+r)ⁿ ÷ ((1+r)ⁿ − 1)

Here M is the monthly payment, P is the principal (the amount borrowed), r is the monthly interest rate — the annual rate divided by 12 — and n is the total number of monthly payments (the term in years multiplied by 12).

Each month the lender charges interest on whatever balance remains, and the rest of your payment reduces that balance. Early in the loan the balance is large, so most of each payment is interest; later the split flips and most of it becomes equity. This calculator applies that same math month by month. When you add an extra payment, the entire extra amount goes straight to principal, so the balance falls faster and less interest accrues — which is why even modest extra payments shorten a mortgage so dramatically.

What the headline number does not include. The P&I figure above covers principal and interest only. Property taxes, homeowners insurance, private mortgage insurance (PMI), and HOA fees are separate and can add hundreds of dollars to a real monthly housing bill. Enter them under Advanced options and the calculator adds them as a second line — Total monthly payment (PITI) — without touching the underlying amortization math.

Total monthly payment (PITI) = P&I + property tax + home insurance + PMI + HOA. Two details matter. Property tax is levied on the home price, not on the loan, so the calculator recovers the price as loan ÷ (1 − down payment %); if you leave the down payment blank it uses the loan amount as the price, which understates rather than overstates the tax bill. Home insurance is entered as an annual premium and divided by 12. PMI and HOA are monthly figures and are added exactly as entered.

Worked example. A $300,000 loan at 6.5% for 30 years produces a monthly payment of about $1,896 and total interest of roughly $382,000 — more than the loan itself. Seeing that number up front, before you sign anything, is exactly the point of this tool.

Common Mistakes When Estimating a Mortgage

1. Confusing the interest rate with the APR. The interest rate is the cost of borrowing the principal. The APR includes lender fees and discount points, so it is always higher. Enter the interest rate here for the payment, but compare loan offers on APR.
2. Treating principal and interest as the whole payment. Lenders usually collect property taxes and homeowners insurance in escrow, and loans with under 20% down add PMI. Budget for PITI — principal, interest, taxes, and insurance — not just the figure above. Fill in Advanced options on this page to see how far P&I and PITI actually diverge: on a $300,000 loan at 6.5% with a 1.1% tax rate and $1,500 a year of insurance, P&I is about $1,896 while the full payment is about $2,365.
3. Choosing a loan by the lowest monthly payment. Stretching a loan from 15 to 30 years lowers the payment but can more than double the interest you pay. Always compare the total cost column, not just the monthly number.
4. Entering the home price instead of the loan amount. If you buy a $375,000 home with 20% down, the loan amount is $300,000, not $375,000. A wrong starting number makes every result wrong.

Frequently Asked Questions

Does this mortgage calculator include taxes, insurance, and PMI?

Yes — if you fill in Advanced options. The headline number is principal and interest (P&I). Add a property tax rate, home insurance, PMI, or HOA fee and the results gain a Total monthly payment (PITI) block with a line-by-line breakdown. Property tax is applied to the home price, which the calculator recovers as loan ÷ (1 − down payment %); home insurance is the annual premium ÷ 12. Leave Advanced options empty and you get P&I only.

How is a monthly mortgage payment calculated?

With the standard amortization formula: M = P × r(1+r)^n / ((1+r)^n − 1), where P is the loan amount, r is the monthly interest rate (annual rate ÷ 12), and n is the number of monthly payments (years × 12). Example: a $300,000 loan at 6.5% for 30 years gives r = 0.005417 and n = 360, so the monthly payment is about $1,896 and total interest is roughly $382,000.

What is the difference between the interest rate and the APR?

The interest rate is the cost of borrowing the principal alone. The APR (annual percentage rate) includes the interest rate plus lender fees and discount points, spread over the loan term, so it is always equal to or higher than the interest rate. Use the interest rate to compute your monthly payment, and the APR when comparing loan offers.

Is a 15-year or 30-year mortgage better?

It depends on cash flow. On a $300,000 loan at 6.5%, a 30-year term costs about $1,896 per month and roughly $382,000 in total interest, while a 15-year term costs about $2,613 per month but only around $170,000 in interest — a saving of over $200,000. Choose the shorter term if the higher payment fits comfortably in your budget; otherwise the 30-year term with optional extra payments offers more flexibility.

What is an amortization schedule and why does it matter?

An amortization schedule is a month-by-month table showing how every payment splits into interest and principal, and how your balance falls over time. It matters because it exposes the true cost of your loan: in the early years most of each payment goes to interest, so extra payments made early have the biggest effect on both total interest and your payoff date. Expand any year in the table above to see this shift for your own loan.

Related Scenarios

The tool above handles any loan you enter. These pages work through specific situations in detail, each with its own worked numbers.

References

• Consumer Financial Protection Bureau — Owning a Home: the official U.S. guide to shopping for a mortgage, comparing loan offers, and understanding closing costs.
• Investopedia — Amortization: a clear explanation of how loan balances are paid down over time and why early payments are mostly interest.
• Federal Housing Finance Agency (FHFA): the U.S. regulator overseeing Fannie Mae, Freddie Mac, and conforming loan limits — the rules that shape most American mortgages.

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