How are mortgage payments calculated?

Understand how monthly payments are determined, and learn how to calculate them yourself

A mortgage is a simple interest loan. When you borrow money to buy a house you make regular monthly payments which include interest. Interest is money you pay the lender for the loan. This is how the lender makes money.

Your loan’s monthly payment is calculated based on the terms of the loan. The loan terms are

1. How much is borrowed (the "principal"),
2. How many months to pay the loan back (number of payments), and
3. The interest rate you pay.

The formula used to calculate the monthly payment is

pi(1+i)ⁿ / ((1+i)ⁿ – 1)

This formula may look scary, but don’t worry. You learn exactly how it works here. The letters in this formula have the following meanings. We will go into more detail with each letter.

• p is the principal, or beginning loan balance (how much you borrow).
• i is the interest rate per pay period.
• n is the number of payments made to pay off the loan (number of years * 12).

You can calculate the monthly payments for a home loan using this formula. If you have a calculator that has a power button (x^y) you can use it to calculate the payment amount. An easier way is to use the calculator on this awesome website.

Before you can calculate the payment the interest needs to be converted. The interest rate of, let’s say, 2.5% is annual interest (don't you wish!), or how much interest you pay for the loan in one year. We need to convert that into interest per pay period – in this case interest per month because monthly payments are made to the lender. The following steps convert annual interest to interest per pay period

1. Convert 2.5% to decimal form. 2.5% is 2.5 / 100, or .025 in decimal form.
2. Convert .025 to interest per pay period by dividing it by 12 (12 monthly payments per year). .025 / 12 = .00208333.

Mortgage Payment Example Code

Here is the exact code that this website uses to calculate the monthly payment. For you techies, this is server-side php code.

function get_payment($p, $i, $n) {
$int = $i/100/12;	// convert annual int to monthly
$pwr = pow(1 + $int, $n);	// calculate (1 + i)n
$pay = $p * $int * $pwr / ($pwr -1);	// the rest of the calculation
$pay = round($pay, 2);	// round to the nearest penny
return $pay;	// return the payment amount
}

A home loan example: you borrow $235,000 for 30 years (360 months) at a 2.5% annual interest rate.

• p is amount borrowed: $235,000
• i is the interest rate: 2.5% annual interest, or .00208333 monthly
• n is the # of payments: 360 (30 years)

Now take these three numbers, (p, i and n) and plug them into the formula. 235,000 * .00208333 * (1 + .00208333)³⁶⁰ / ((1 * .00208333)³⁶⁰ – 1)

Plug that into the payment calculator and you get $928.53. That is your monthly payment. If you pay that amount every month for 30 years (360 months), you will have paid off your mortgage.

However, this site's main puropose is to help you pay off your mortgage sooner. If you pay more than the required monthly payment, especially if you pay a lot more, you can pay off your mortgage much quicker and save a lot of money in interest. See the payment options page to learn how to do this.

Note: your house payment may include principal, interest, taxes and insurance, usually called PITI. You may also be paying PMI which adds to the payment. The calculation on this page only includes the first two; principal and interest. See the page on PITI and PMI to learn more.