Loan Balance Calculator: Understanding Your Remaining Debt

What is a Loan Balance?

A loan balance refers to the remaining amount of money that a borrower owes to a lender at any given point during the loan term. As you make payments on your loan, the balance decreases over time. Understanding your loan balance is crucial for managing your debt and planning your financial future.

The Loan Balance Formula

The formula used to calculate the remaining balance of a loan is:

\[B = L\frac{(1+r)^n - (1+r)^p}{(1+r)^n - 1}\]

Where:

• \(B\) = Remaining balance
• \(L\) = Original loan amount
• \(r\) = Monthly interest rate (annual rate divided by 12)
• \(n\) = Total number of monthly payments
• \(p\) = Number of payments made

Step-by-Step Calculation Process

1. Calculate the monthly interest rate: \[r = \frac{\text{Annual Interest Rate}}{12}\]
2. Apply the formula to calculate the remaining balance.
3. Calculate the monthly payment using the standard loan payment formula.
4. Calculate total payment: \[\text{Total Payment} = \text{Monthly Payment} \times \text{Total Number of Payments}\]
5. Calculate total interest: \[\text{Total Interest} = \text{Total Payment} - \text{Original Loan Amount}\]

Example Calculation

Let's calculate the remaining balance for a $20,000 loan at 5% annual interest for 5 years, after making 24 payments:

1. \(r = \frac{5\%}{12} = 0.004167\)
2. \(B = 20000 \times \frac{(1+0.004167)^{60} - (1+0.004167)^{24}}{(1+0.004167)^{60}-1} = 12,811.22\)
3. Monthly Payment = $377.42
4. Total Payment = $377.42 × 60 = $22,645.20
5. Total Interest = $22,645.20 - $20,000 = $2,645.20

Visual Representation

The green portion represents the amount paid ($7,188.78), while the red portion shows the remaining balance ($12,811.22) after 24 payments.