Monthly Repayment Calculator Loan

Loan Payment Formula:

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

Monthly Payment (PMT):

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1. What is the Loan Payment Formula?

The loan payment formula calculates the fixed monthly payment required to fully repay a loan over its term, including both principal and interest. This is known as the PMT (payment) formula in financial mathematics.

2. How Does the Calculator Work?

The calculator uses the standard loan payment 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, in decimal)
\( n \) — Total number of payments (loan term in years × 12)
\( PMT \) — Monthly payment amount (USD)

Explanation: The formula accounts for compound interest over the life of the loan, calculating a fixed payment that will pay off both principal and interest by the end of the term.

3. Importance of Loan Payment Calculation

Details: Understanding your monthly payment helps with budgeting, comparing loan offers, and making informed financial decisions about large purchases like homes or cars.

4. Using the Calculator

Tips: Enter the principal amount in USD, annual interest rate as a percentage (e.g., 5.25 for 5.25%), and loan term in years. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: Does this include taxes and insurance?
A: No, this calculates only principal and interest. For a complete mortgage payment, you would need to add property taxes, insurance, and possibly PMI.

Q2: How does a larger down payment affect the payment?
A: A larger down payment reduces the principal amount (P), which directly reduces your monthly payment.

Q3: What's the difference between APR and interest rate?
A: The interest rate is the cost of borrowing, while APR includes additional fees and costs, giving a more complete picture of loan cost.

Q4: How can I pay less interest overall?
A: You can pay less total interest by choosing a shorter loan term or making additional principal payments when possible.

Q5: Why does my actual payment differ slightly?
A: Lenders may use slightly different rounding methods or payment schedules (e.g., biweekly vs monthly).