Abdul plans to purchase a new sports car. The dealer requires a 10% down payment on the $31,000 vehicle. Abdul will finance the rest of the cost with a fixed-rate amortized auto loan at 8.5% annual interest with monthly payments over 5 years.

Complete the parts below. Do not round any intermediate computations. Round your final answers to the nearest cent if necessary. 

Let's walk through the steps Abdul will need to take to complete the purchase of his new sports car.

### Part 1: Calculate the Down Payment
The down payment is 10% of the car's price.

\[
\text{Down payment} = 0.10 \times 31,000 = 3,100
\]

### Part 2: Calculate the Loan Amount
Abdul will finance the remaining cost of the vehicle after the down payment.

\[
\text{Loan amount} = \text{Car price} - \text{Down payment} = 31,000 - 3,100 = 27,900
\]

### Part 3: Monthly Payment Calculation
Now, we need to calculate Abdul's monthly payment for the loan. The formula for calculating the monthly payment on a loan is:

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

Where:
- $ M $ = monthly payment
- $ P $ = loan amount ($27,900)
- $ r $ = monthly interest rate (annual rate divided by 12)
- $ n $ = total number of payments (number of months in the loan)

#### Step 1: Convert the annual interest rate to a monthly interest rate
\[
r = \frac{8.5\%}{12} = \frac{0.085}{12} = 0.0070833
\]

#### Step 2: Calculate the number of payments
Since the loan is for 5 years with monthly payments:
\[
n = 5 \times 12 = 60 \text{ months}
\]

#### Step 3: Plug in the values
Now we can calculate the monthly payment.

\[
M = \frac{27,900 \cdot 0.0070833 \cdot (1 + 0.0070833)^{60}}{(1 + 0.0070833)^{60} - 1}
\]

Let me calculate this for you.Abdul's monthly payment for the loan will be approximately **$572.41**.

### Part 4: Total Amount Paid Over the Life of the Loan
The total amount paid over the life of the loan is the monthly payment multiplied by the number of months.

\[
\text{Total amount paid} = M \times n = 572.41 \times 60
\]

Let me calculate that for you.The total amount Abdul will pay over the life of the loan is approximately **$34,344.67**.

### Part 5: Total Interest Paid
To find the total interest Abdul will pay, subtract the original loan amount from the total amount paid:

\[
\text{Total interest paid} = \text{Total amount paid} - \text{Loan amount} = 34,344.67 - 27,900
\]

Let me calculate this.Abdul will pay approximately **$6,444.67** in interest over the life of the loan.

### Summary:
1. **Down payment:** $3,100
2. **Loan amount:** $27,900
3. **Monthly payment:** $572.41
4. **Total amount paid over 5 years:** $34,344.67
5. **Total interest paid:** $6,444.67

Would you like any details or have questions about these calculations?

Here are five related questions:
1. What if the down payment was 15%? How would it affect the loan amount?
2. How would Abdul’s monthly payment change if the interest rate was 7% instead of 8.5%?
3. What is the total amount paid for the car, including both down payment and loan payments?
4. How much would Abdul save if he paid off the loan in 4 years instead of 5?
5. What is the balance of the loan after Abdul makes 30 payments?

**Tip:** When choosing a loan, always compare total interest paid, not just the monthly payment.

Abdul plans to purchase a new sports car. The dealer requires a 10% down payment on the $31,000 vehicle. Abdul will finance the rest of the cost with a fixed-rate amortized auto loan at 8.5% annual interest with monthly payments over 5 years.

Learn how to calculate the down payment, loan amount, monthly payments, total paid, and interest for Abdul's new car purchase. This problem covers percentage calculations, loan amortization, and interest formulas. Suitable for Grades 10-12.

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