Home Loan Calculator

Home Loan Calculator

A home loan calculator helps you estimate your monthly mortgage payments by using a mathematical formula. The key variables in this calculation are the principal loan amount, the interest rate, and the loan term. Here’s how you can calculate your monthly mortgage payment:

Formula:

M=P×r×(1+r)n(1+r)n−1M = \frac{P \times r \times (1 + r)^n}{(1 + r)^n – 1}M=(1+r)n−1P×r×(1+r)n​

Where:

• $M$ = Monthly mortgage payment
• $P$ = Principal loan amount (the amount borrowed)
• $r$ = Monthly interest rate (annual interest rate divided by 12)
• $n$ = Total number of payments (loan term in years multiplied by 12)

Steps:

1. Determine the Monthly Interest Rate: Divide the annual interest rate by 12. For instance, if the annual rate is 4%, the monthly rate is $4\%÷12=0.333\%$ or $0.00333$ in decimal form.
2. Calculate the Total Number of Payments: Multiply the number of years by 12. For a 30-year mortgage, it’s $30\times 12=360$ payments.
3. Apply the Formula: Insert these values into the formula. For example, with a $300,000 loan, a 4% annual interest rate, and a 30-year term:
   • Principal ($P$) = $300,000
   • Monthly Interest Rate ($r$) = 0.00333
   • Number of Payments ($n$) = 360

   The formula becomes:

   1. M=(1+0.00333)360−1300,000×0.00333×(1+0.00333)360​

      Calculating this provides your monthly payment.

   This calculation helps you understand your financial commitment and plan your budget accordingly. For ease, many online calculators automate this process, letting you quickly input your details and get an immediate result.