After making 25 payments of $481.18 on your original 5 year $26000 car loan at 4.2% compounded monthly you want to find the amount that remains. What is the amount of the remaining balance of your car loan? (Round balance to the nearest cent.)

The remaining balance of your car loan would be $

To calculate the remaining balance of your car loan, we will use the **amortization formula** for the remaining balance after making a certain number of payments.

### Given:
- **Loan amount (P):** $26,000
- **Annual interest rate (r):** 4.2% or 0.042
- **Number of monthly payments (N):** 5 years × 12 months/year = 60 payments
- **Monthly payment (M):** $481.18
- **Payments made:** 25 payments
- **Interest compounded monthly**

### Step 1: Monthly interest rate
The monthly interest rate is calculated by dividing the annual interest rate by 12:
\[
i = \frac{0.042}{12} = 0.0035
\]

### Step 2: Remaining balance formula
The remaining balance of a loan after making $n$ payments is given by:

\[
B_n = P(1 + i)^n - \frac{M \left( (1 + i)^n - 1 \right)}{i}
\]

Where:
- $ B_n $ = remaining balance after $n$ payments
- $ P $ = loan amount
- $ i $ = monthly interest rate
- $ n $ = number of payments already made
- $ M $ = monthly payment
- $ N $ = total number of payments

### Step 3: Calculate the remaining balance

Let's calculate the remaining balance after 25 payments:

\[
B_{25} = 26000(1 + 0.0035)^{60} - \frac{481.18 \times \left( (1 + 0.0035)^{25} - 1 \right)}{0.0035}
\]

I'll compute this for you now.The remaining balance of your car loan after making 25 payments is **$19,515.31**.

Would you like further explanation on any part of the calculation or process? Here are five related questions to expand on this:

1. How does the amortization schedule affect monthly payments over time?
2. What happens if the interest rate is increased during the loan period?
3. How can extra payments reduce the remaining balance?
4. What is the impact of compounding frequency on loan balance?
5. How would the balance differ for a shorter or longer loan term?

**Tip:** Making extra payments directly toward the principal can significantly reduce the overall interest paid and the loan term.

After making 25 payments of $481.18 on your original 5 year $26000 car loan at 4.2% compounded monthly you want to find the amount that remains. What is the amount of the remaining balance of your car loan? (Round balance to the nearest cent.)

Find the remaining balance on a $26,000 car loan with a 4.2% annual interest rate after 25 payments of $481.18. This problem covers the amortization formula, compound interest, and loan repayment calculations. Perfect for high school students (Grades 10-12).

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