To determine the total interest Blake paid over the life of the loan, we need to follow these steps:

Step 1: Identify the loan details

• Principal amount (loan amount): $P = 19,000$
• Interest rate (annual rate, APR): $r = 6.5\% = 0.065$
• Loan term: $t = 72$ months (6 years)
• Monthly interest rate: $\frac{r}{12} = \frac{0.065}{12} \approx 0.005417$

Step 2: Use the formula for monthly payment calculation

The formula for calculating the monthly payment $M$ for a loan is:

$M = \frac{P \cdot \frac{r}{12}}{1 - (1 + \frac{r}{12})^{-n}}$ where:

• $P$ is the principal loan amount
• $r$ is the annual interest rate (as a decimal)
• $n$ is the total number of monthly payments (72 months)

Plugging in the numbers:

$M = \frac{19,000 \cdot 0.005417}{1 - (1 + 0.005417)^{-72}}$

Let's calculate the monthly payment $M$.

Step 3: Calculate the monthly payment

Using the formula:

$M = \frac{19,000 \cdot 0.005417}{1 - (1.005417)^{-72}}$

Now, solving this:

$M \approx \frac{19,000 \cdot 0.005417}{1 - 0.6986} = \frac{19,000 \cdot 0.005417}{0.3014}$

$M \approx \frac{102.93}{0.3014} \approx 341.96$

The monthly payment is approximately $341.96.

Step 4: Determine the total amount paid over the life of the loan

The total amount paid over the loan term is:

$\text{Total paid} = M \times n = 341.96 \times 72 = 24,635.52$

Step 5: Calculate the total interest paid

The total interest paid is the total amount paid minus the principal:

$\text{Interest paid} = \text{Total paid} - P = 24,635.52 - 19,000 = 5,635.52$

Final Answer:

The total interest Blake paid over the life of the loan is $5,635.52.

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Would you like further explanation on any of the steps? Or do you have any additional questions?

Here are some follow-up questions to deepen your understanding:

1. How would the monthly payment change if the loan term was shorter or longer?
2. What would happen if Blake had a higher or lower APR?
3. How do you calculate the monthly payment for a car loan with a down payment included?
4. How can you use an online loan calculator to verify the monthly payment and interest?
5. What is the impact of refinancing on the total interest paid over the life of the loan?

Tip: If you want to pay less interest over time, consider making extra payments toward the principal to reduce the loan balance faster.