Mortgage Loan Amortization Calculator

Mortgage Payment Formula:

\[ PMT = P \times \frac{r \times (1 + r)^n}{(1 + r)^n - 1} \]

Monthly Payment (PMT):

Total Interest:

Total Cost:

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1. What is the Mortgage Payment Formula?

The mortgage payment formula calculates the fixed monthly payment required to fully amortize a loan over its term. It accounts for the principal amount, interest rate, and loan duration to determine consistent payments.

2. How Does the Calculator Work?

The calculator uses the PMT formula:

\[ PMT = P \times \frac{r \times (1 + r)^n}{(1 + r)^n - 1} \]

Where:

\( P \) — Principal loan amount (USD)
\( r \) — Monthly interest rate (annual rate ÷ 12)
\( n \) — Total number of payments (term in years × 12)

Explanation: The formula calculates the fixed payment that covers both interest and principal each month, with the interest portion decreasing and principal portion increasing over time.

3. Importance of Amortization

Details: Understanding amortization helps borrowers see how much of each payment goes toward interest vs. principal, the total interest cost, and the remaining balance at any point in the loan term.

4. Using the Calculator

Tips: Enter the loan amount in USD, annual interest rate as a percentage (e.g., 3.5 for 3.5%), and loan term in years. The calculator will show the monthly payment, total interest, and complete amortization schedule.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between interest rate and APR?
A: The interest rate is the cost of borrowing the principal, while APR includes additional fees and costs, representing the true annual cost of the loan.

Q2: How can I pay less interest overall?
A: Make additional principal payments, choose a shorter loan term, or secure a lower interest rate to reduce total interest costs.

Q3: Why does most of my early payment go toward interest?
A: With amortized loans, interest is calculated on the outstanding balance, which is highest at the beginning of the loan term.

Q4: What happens if I make extra payments?
A: Extra payments directly reduce principal, which decreases future interest and may shorten the loan term.

Q5: How does loan term affect payments?
A: Shorter terms mean higher monthly payments but less total interest. Longer terms have lower payments but more total interest.