How to Calculate a Mortgage Payment

What is the formula for a monthly mortgage payment?

The formula for a fixed-rate monthly mortgage payment is M = P × r(1 + r)^n ÷ [(1 + r)^n − 1]. It is the standard amortization formula, the same one lenders and our mortgage calculator use, and it produces a payment that stays the same every month and brings the balance to exactly zero on the last payment.

• M is the monthly payment of principal and interest.
• P is the principal, the amount you borrow (home price minus down payment).
• r is the monthly interest rate: the annual rate as a decimal, divided by 12.
• n is the total number of monthly payments: years × 12.

How do you calculate a mortgage payment step by step?

Here is the formula worked by hand for a $400,000 home with 20% down, borrowed at a 6.5% fixed rate for 30 years.

• Find the loan amount: $400,000 − $80,000 down = P of $320,000.
• Convert the rate: 6.5% ÷ 100 ÷ 12 = r of 0.0054167.
• Count the payments: 30 × 12 = n of 360.
• Compute the growth factor: (1 + 0.0054167)^360 = 6.9918.
• Top of the fraction: 0.0054167 × 6.9918 = 0.037872. Bottom: 6.9918 − 1 = 5.9918.
• Divide and multiply: 0.037872 ÷ 5.9918 = 0.0063207, and $320,000 × 0.0063207 = $2,022.62.

Is there a simple mortgage formula?

The simplest shortcut is a payment-per-$100,000 factor: find the monthly payment for $100,000 at your rate and term, then scale it to your loan. At 6.5% for 30 years that factor is $632.07, so a $320,000 loan costs 3.2 × $632.07 = $2,022.62. The table below, computed with our payment calculator, covers common rates.

There is no accurate shortcut that avoids the exponent entirely. A flat rule such as a fixed percentage of the loan only holds near one specific rate, because the payment does not rise in a straight line with the rate. If you need a number you will rely on, use the full formula or the calculator.

How much of each mortgage payment goes to interest?

Each month's interest equals the remaining balance times the monthly rate; the rest of the payment reduces the principal. In the first month of our example, interest is $320,000 × 0.0054167 = $1,733.33, so only $289.28 of the $2,022.62 payment goes toward the loan balance.

As the balance falls, the interest portion shrinks and the principal portion grows. This schedule of shifting splits is called amortization. On this loan, the yearly principal paid does not overtake the yearly interest until year 20. The mortgage amortization calculator prints the full month-by-month schedule; here are selected years from it.

What else is included in a monthly mortgage payment?

Your actual monthly bill usually includes more than principal and interest. Most lenders collect property tax and homeowners insurance through an escrow account, and many loans add mortgage insurance and HOA dues. Together these are often called PITI: principal, interest, taxes and insurance.

Continuing the example with property tax of 1.2% of the price ($400 a month) and insurance of $1,500 a year ($125 a month), the mortgage calculator shows a total out-of-pocket cost of $2,547.62 a month: $2,022.62 for the loan plus $525 in escrow items.

Private mortgage insurance, or PMI, applies to most conventional loans with less than 20% down. It protects the lender, not you, and its cost depends on your credit score and down payment, so get the figure from your Loan Estimate rather than guessing.

How do rate, term and down payment change the payment?

The payment rises with the loan amount and the rate and falls as the term gets longer. The loan amount is the most direct lever: the payment scales in exact proportion, so borrowing 10% less cuts the payment by 10%.

Rate changes matter more than they look. Moving from 6.5% to 7.5% raises the payment per $100,000 from $632.07 to $699.21, which on a $320,000 loan is about $215 more a month and about $77,000 more interest over 30 years.

A shorter term raises the monthly payment but slashes total interest. At 6.5%, a 15-year loan costs $871.11 per $100,000 instead of $632.07, while total interest per $100,000 drops from $127,544 to $56,799. For the full trade-off, see our guide to the 15 vs. 30-year mortgage. To work backward from your income to a price, read how much house can I afford.

How do you calculate a mortgage payment in Excel or Google Sheets?

Use the built-in PMT function: =PMT(rate/12, years*12, -loan). For the example, =PMT(0.065/12, 360, -320000) returns 2,022.62. The minus sign in front of the loan makes the result positive. PMT uses the same formula shown above, so it will match the calculator to the cent.