Mortgage Payment Calculator

Quickly calculate the monthly payment amount based on the amount borrowed, interest rate and time.

Period

Years:

Months:

Borrowed Amount

Amount:

Interest Rate

Annual Interest Rate (percentage):

Monthly Payment:

Monthly Mortgage Payment Formula

A mortgage payment is calculated to be the number of equal monthly payments that will pay off an amount owed in the time required. This would be a straighfoward division ( money owed / number of months ) if it wasn't for interest payments which are increasing the amount owed each month whilst the payments are reducing the amount owed.

To calculate the payments taking into account interest first we need the total number of periods we are interested in. For this calculator we calculate monthly ( your bank likely calculates daily ) so need the total number of months. We also need the annual interest rate expressed as a decimal value and converted to a monthly value.

$Total Monthly periods = P = Number of full years * 12 + Number of remaining months$

$Monthly interest rate (decimal) = m = (\frac{Annual interest rate (percentage)}{100}) / 12$

From these values we can calculate the compound interest rate factor.

Compound interest rate factor = n = (1 + m)^{P}

And using that and the total amount borrowed can work out the monthly payment amount.

Monthly payment = Total borrowed amount \times (\frac{m \times n}{n - 1})

Example

For a mortgage rate of 4% over 25 years for a borrowed amount of 250,000 the payment would be:

$P = 25 \times 12 + 0 = 300$

$m = (\frac{4}{100}) / 12 = 0.0033$

n = (1 + 0.0033)^{300} = 2.6869

Monthly payment = 250000 \times (\frac{0.0033 \times 2.6869}{2.6869 - 1}) = 1,314.06

Please note the calculator gives a value of 1,319.59 as it is using higher precision figures and not rounding them for the example.

Background

A mortgage is a loan used to purchase a home, consisting of principal ( the borrowed amount ) and interest ( the borrowing cost ). This process is also known as mortgae amortisation, the process of gradually writing off the cost of an asset such as a house.

Terms typically range from 15 to 30 years, with monthly payments which can be esitmated using this Mortgage Payment Calculator based on loan amount, interest rate, and term.

"Mortgage rates" and "mortgage interest rates" denote the interest charged on loans, varying based on economic factors. Even minor rate fluctuations can impact payments and overall costs significantly.