Mortgage Calculator

A mortgage is a financial instrument that enables individuals to purchase real estate, such as homes or commercial properties, by borrowing money from a lending institution. It's a complex financial arrangement that involves a loan secured by the property itself, which serves as collateral. This article will provide a detailed explanation of what a mortgage is and how to calculate its various aspects.

What Is a Mortgage?

A mortgage is a legal agreement between a borrower and a lender, typically a bank or mortgage company. In this agreement, the lender provides funds to the borrower to purchase a property, and in return, the borrower agrees to repay the loan over a specified period, often decades.

Key Mortgage Terms

Before delving into calculations, it's important to understand some key mortgage terms:

  • Principal: The initial loan amount.
  • Interest Rate: The cost of borrowing money, usually expressed as an annual percentage.
  • Loan Term: The duration over which the mortgage is to be repaid.
  • Monthly Payment: The fixed amount paid by the borrower each month.
  • Amortization: The process of paying off a mortgage over time through regular payments.

Mortgage Calculation

Monthly Payment Calculation

The most critical aspect of mortgage calculation is determining the monthly payment. This calculation is based on the following formula:

Monthly Payment (M) = P [r(1 + r)^n] / [(1 + r)^n – 1]


  • M is the monthly payment
  • P is the principal loan amount
  • r is the monthly interest rate (annual rate divided by 12)
  • n is the number of monthly payments (loan term in years multiplied by 12)

Example Calculation

Let's calculate the monthly payment for a mortgage of $250,000 with a 4% annual interest rate and a 30-year loan term.

M = $250,000 [0.04/12 (1 + 0.04/12)^(3012)] / [(1 + 0.04/12)^(3012) - 1]

M ≈ $1,193.54

The monthly payment for this mortgage would be approximately $1,193.54.

Total Payment and Interest

Over the life of the mortgage, you'll also want to know the total amount paid and the total interest paid. These can be calculated as follows:

Total Payment = M * n

Total Interest = Total Payment - P

For our example:

Total Payment ≈ $1,193.54 30 12 ≈ $429,674.40

Total Interest ≈ $429,674.40 - $250,000 ≈ $179,674.40