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. what is the number?

To construct an amortization table for Lenny's car loan, we'll calculate the annual payment required to fully repay the $7,000 loan over 6 years with an interest rate of 12%. 

### Step 1: Calculate the Annual Payment

To find the annual payment for an amortized loan, we use the formula for the annual payment $ P $ of an amortizing loan:

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

where:

- $ PV = 7000 $ is the present value or principal amount of the loan.
- $ r = \frac{12}{100} = 0.12 $ is the annual interest rate.
- $ n = 6 $ is the total number of payments (one per year for six years).

Let's calculate the annual payment $ P $ first.The annual payment $ P $ required to fully repay the loan is approximately **$1,702.58**.

### Step 2: Construct the Amortization Table

Now, let's construct the amortization table to show the breakdown of each payment into interest and principal components, as well as the remaining balance after each payment.

An amortization table typically includes:

1. **Year**: The payment year.
2. **Payment**: The total payment made each year (which is constant).
3. **Interest**: The interest portion of the payment for that year.
4. **Principal**: The principal portion of the payment for that year.
5. **Remaining Balance**: The outstanding loan balance after the payment.

Let's compute these values for each year.It seems like I can’t do more advanced data analysis right now. Please try again later. However, I can guide you through the process of constructing the amortization table manually if you’d like!

### Here's how you can proceed:

1. **Calculate Interest for Each Year**:
   - The interest for each year is calculated as the remaining balance multiplied by the interest rate (12%).
   
2. **Calculate Principal Repayment**:
   - Subtract the interest from the total payment to find out how much of the payment goes towards repaying the principal.

3. **Update the Remaining Balance**:
   - Subtract the principal repayment from the remaining balance to get the new balance for the next year.

4. **Repeat for Each Year**:
   - Repeat the above steps for each of the 6 years.

Would you like a detailed example for each year or have any other questions? 

Here are 5 related questions to explore:
1. What is an amortized loan, and how does it differ from a non-amortized loan?
2. How does the interest rate affect the total interest paid over the loan term?
3. What happens to the loan if the interest rate changes during the repayment period?
4. How can extra payments affect the amortization schedule?
5. What is the impact of loan duration on the size of each payment?

**Tip:** Amortization tables are helpful for understanding how much of your payment goes toward interest versus principal at any point in time.

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. What is the number?

Construct an amortization table for a $7,000 car loan financed over 6 years with an annual interest rate of 12%. Learn how to break down each annual payment into interest, principal, and remaining balance. Suitable for advanced high school or college-level students.

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