Mortgage Calculator

1. What is the Mortgage Calculator?

Definition: This calculator computes the monthly mortgage payment, total payment, total interest, and payoff period for a home loan based on the home value, down payment, loan term, interest rate, and optional extra monthly payments.

Purpose: It helps homebuyers estimate the cost of a mortgage, compare different loan scenarios, and understand the impact of extra payments on the loan term and interest costs, aiding in financial planning and budgeting.

2. How Does the Calculator Work?

The calculator uses the following formula for monthly mortgage payment, as shown in the image above:

\( P = \frac{L \cdot r \cdot (1 + r)^n}{(1 + r)^n - 1} \)

Where:

• \( P \): Monthly payment;
• \( L \): Loan amount (home value minus down payment);
• \( r \): Monthly interest rate (annual rate divided by 12);
• \( n \): Total number of monthly payments (loan term in years times 12).

Steps:

• Enter the home value.
• Enter the down payment.
• Enter the loan term in years.
• Enter the annual interest rate.
• Optionally, enter an extra monthly payment.
• Calculate the monthly payment using the formula.
• Compute total payment (monthly payment times number of payments).
• Compute total interest (total payment minus loan amount).
• If extra payments are included, iteratively calculate the reduced payoff period.
• Display results, formatted in scientific notation if the absolute value is less than 0.001, otherwise with 4 decimal places.

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