Lenny purchases a car and finances it with a $7,000 amortized loan. The interest rate is 12% and the loan will be totally repaid over the next six years. Lenny owes one payment per year. Construct an amortization table.

To construct an amortization table for Lenny's loan, we need to break down each payment across the six years. Here's a step-by-step process for calculating and constructing the amortization table:

1. **Loan Details**:
   - Loan Amount $ P = 7000 $
   - Annual Interest Rate $ r = 12\% = 0.12 $
   - Loan Term $ n = 6 $ years
   - One payment per year

2. **Step 1: Calculate the annual payment using the amortization formula**:

\[
A = \frac{P \times r \times (1 + r)^n}{(1 + r)^n - 1}
\]
Where:
- $ A $ is the annual payment,
- $ P $ is the principal loan amount,
- $ r $ is the annual interest rate,
- $ n $ is the number of periods (years).

Let’s calculate $ A $.

The annual payment $ A $ is approximately \$1,702.58.

### Step 2: Construct the Amortization Table
The amortization table will break down each year's payment into:
- Interest paid
- Principal repaid
- Remaining balance

For each year:
- **Interest** = Remaining Balance * Interest Rate
- **Principal Payment** = Annual Payment - Interest
- **Remaining Balance** = Previous Balance - Principal Payment

Let’s build the full amortization table.

It seems like I can’t do more advanced data analysis right now. Please try again later.

If you'd like, I can guide you through the steps of constructing the amortization table manually or try to resolve it later. Let me know what you'd prefer!

Here are five related questions:
1. How does changing the interest rate affect the loan payments?
2. What would happen if Lenny decided to repay the loan in fewer than six years?
3. How would the amortization table differ for a loan with monthly payments?
4. Can the same formula be applied to loans with different compounding periods (e.g., semi-annual)?
5. How would a balloon payment affect the loan schedule?

**Tip**: Understanding the breakdown between interest and principal over time helps reveal how the majority of early payments go toward interest!

Explore how to construct an amortization table for a $7,000 car loan at 12% interest over six years. Learn key concepts like amortization, compound interest, and how each payment is broken down into interest and principal. This step-by-step guide is perfect for students in Grades 10-12.

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