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.