Carter bought a new car and financed $⁢17,000 to make the purchase. He financed the car for 72 months with an APR of 6.5%. Assuming he made monthly payments, determine the total interest Carter paid over the life of the loan. Round your answer to the nearest cent, if necessary.

To determine the total interest Carter paid, we can use the formula for monthly payments on an amortized loan, then calculate the total interest. The formula for the monthly payment on a loan is:

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

where:
- $ M $ is the monthly payment,
- $ P $ is the loan principal (amount financed),
- $ r $ is the monthly interest rate,
- $ n $ is the total number of payments.

### Step 1: Identify the values
1. $ P = 17,000 $ (the loan amount),
2. APR is 6.5%, so the monthly interest rate $ r = \frac{6.5\%}{12} = \frac{0.065}{12} \approx 0.0054167 $,
3. $ n = 72 $ months.

### Step 2: Calculate the monthly payment $ M $
\[
M = \frac{17,000 \times 0.0054167 \times (1 + 0.0054167)^{72}}{(1 + 0.0054167)^{72} - 1}
\]

Calculating this yields:

1. $ (1 + 0.0054167)^{72} \approx 1.432364 $,
2. Numerator: $ 17,000 \times 0.0054167 \times 1.432364 \approx 131.9317 $,
3. Denominator: $ 1.432364 - 1 = 0.432364 $,
4. Monthly payment $ M \approx \frac{131.9317}{0.432364} \approx 305.24 $.

So, Carter's monthly payment is approximately $ 305.24 $.

### Step 3: Calculate the total interest
1. Total amount paid over the life of the loan = $ M \times n = 305.24 \times 72 \approx 21,977.28 $,
2. Total interest paid = Total amount paid - Principal = $ 21,977.28 - 17,000 = 4,977.28 $.

### Final Answer:
The total interest Carter paid over the life of the loan is approximately **$4,977.28**.

Would you like more details on any of these steps? 

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**Related Questions:**

1. How does increasing the loan term affect the total interest paid?
2. What would the interest be if the APR were lowered to 5%?
3. How would a down payment reduce the total interest paid?
4. How does the monthly payment change if the loan term is reduced to 60 months?
5. What are the effects of compounding interest on a loan?

**Tip:** Always aim to make extra payments when possible on a loan, as this can significantly reduce the total interest paid over time.

Carter bought a new car and financed $17,000 to make the purchase. He financed the car for 72 months with an APR of 6.5%. Assuming he made monthly payments, determine the total interest Carter paid over the life of the loan. Round your answer to the nearest cent, if necessary.

Determine the total interest paid on a $17,000 car loan with a 6.5% APR over 72 months. Learn how to use the amortization formula to find monthly payments and total interest for a comprehensive understanding of car loan financing. Ideal for students in Grades 10-12.

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