1. What is the Loan Balance Equation?

The loan balance equation calculates the remaining amount owed on a loan after a certain number of payments. It accounts for both the compounding interest and the payments made against the principal.

2. How Does the Calculator Work?

The calculator uses the loan balance equation:

Where:

• \( PV \) — Initial loan amount (principal)
• \( r \) — Monthly interest rate (annual rate ÷ 12)
• \( k \) — Number of payments already made
• \( PMT \) — Monthly payment amount

Explanation: The first term calculates what the original principal would have grown to with interest, while the second term calculates the future value of all payments made.

3. Importance of Loan Balance Calculation

Details: Knowing your remaining balance helps with financial planning, refinancing decisions, and understanding how much equity you've built in an asset.

4. Using the Calculator

Tips: Enter the original loan amount, annual interest rate, monthly payment amount, and number of payments already made. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: Why does my balance sometimes increase?
A: If your payments are smaller than the accrued interest, your balance can grow (negative amortization).

Q2: How accurate is this calculation?
A: It's mathematically precise for fixed-rate loans with consistent payments. It may differ slightly from lender statements due to rounding or payment date variations.

Q3: Can I use this for credit cards?
A: Yes, if you know your average monthly payment and the card's APR, though credit cards often have variable rates.

Q4: What if I make extra payments?
A: The calculation assumes consistent payments. For variable payments, you'd need a more complex amortization schedule.

Q5: How can I pay off my loan faster?
A: Increasing your monthly payment, even slightly, can significantly reduce your payoff time and total interest paid.