# 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]

Where:

• 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