Blake bought a new car and financed $11,000 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 Blake paid over the life of the loan. Round your answer to the nearest cent, if necessary.

To determine the total interest Blake paid over the life of the loan, we can use the formula for calculating the monthly payment on an amortized loan, and then calculate the total interest by comparing the total payments to the original loan amount.

### Step 1: Identify the values
- Loan amount ($ P $) = \$11,000
- Annual interest rate ($ r $) = 6.5% = 0.065
- Loan term ($ t $) = 72 months
- Monthly interest rate = $ \frac{r}{12} = \frac{0.065}{12} = 0.0054167 $ (rounded to six decimal places)

### Step 2: Use the amortization formula
The monthly payment $ M $ is calculated using the formula:

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

where:
- $ M $ is the monthly payment,
- $ P $ is the loan amount,
- $ r $ is the monthly interest rate, and
- $ n $ is the total number of payments (72 months).

Substituting the values:

\[
M = 11,000 \times \frac{0.0054167(1 + 0.0054167)^{72}}{(1 + 0.0054167)^{72} - 1}
\]

### Step 3: Calculate total interest
Once we have the monthly payment, we can find the total interest by subtracting the original loan amount from the total of all the monthly payments over the 72 months.

Let me calculate this for you.Blake's monthly payment is approximately \$184.91. Over the 72 months, he will pay a total of \$2,313.46 in interest.

Would you like more details or have any questions?

Here are five related questions:
1. How does the interest rate affect the total interest paid?
2. What would the total interest be if the loan term were 60 months instead of 72 months?
3. What happens to the monthly payment if Blake made a higher down payment?
4. How would the total interest change if the interest rate was 5% instead of 6.5%?
5. How can Blake save on interest over the life of the loan?

**Tip:** Paying extra on your loan each month can significantly reduce the total interest paid.

Learn how to calculate the total interest Blake paid on his $11,000 car loan with a 6.5% APR over 72 months. This problem covers key concepts in loan amortization, including interest calculation and monthly payment formulas, and is suitable for students in Grades 9-12.

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