You have agreed to pay off an $8,000 car loan with 24 monthly payments of $400 each. Use the simple interest formula to determine the interest rate that you are being charged.

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Loan Interest Rate Calculation Example**

---

**Problem Statement:**

You have agreed to pay off an $8,000 car loan with 24 monthly payments of $400 each. Use the simple interest formula to determine the interest rate that you are being charged.

---

**Detailed Explanation:**

To determine the interest rate using the simple interest formula, follow these steps:

1. **Identify the Known Values:**
   - **Principal (P):** $8,000
   - **Total Number of Payments:** 24
   - **Monthly Payment (M):** $400

2. **Calculate the Total Payment Amount:**
   \[
   \text{Total Payment} = \text{Monthly Payment} \times \text{Number of Payments}
   \]
   \[
   \text{Total Payment} = \$400 \times 24 = \$9,600
   \]

3. **Determine the Total Interest Paid:**
   \[
   \text{Total Interest} = \text{Total Payment} - \text{Principal}
   \]
   \[
   \text{Total Interest} = \$9,600 - \$8,000 = \$1,600
   \]

4. **Use the Simple Interest Formula:**
   The simple interest formula is given by:
   \[
   I = P \times r \times t
   \]
   where:
   - \(I\) is the total interest paid,
   - \(P\) is the principal amount,
   - \(r\) is the annual interest rate,
   - \(t\) is the time period in years.

5. **Plug in the Known Values and Solve for \(r\):**
   Convert the number of payments into years:
   \[
   t = \frac{24}{12} = 2 \text{ years}
   \]
   Now, use the formula:
   \[
   1,600 = 8,000 \times r \times 2
   \]
   \[
   1,600 = 16,000r
   \]
   \[
   r = \frac{1,600}{16,000}
   \]
   \[
   r = 0.10
   \]

6. **Convert the Rate into a Percentage:**
   \[
   r = 0.10 \times 100 = 10\%
   \]
Transcribed Image Text:**Loan Interest Rate Calculation Example** --- **Problem Statement:** You have agreed to pay off an $8,000 car loan with 24 monthly payments of $400 each. Use the simple interest formula to determine the interest rate that you are being charged. --- **Detailed Explanation:** To determine the interest rate using the simple interest formula, follow these steps: 1. **Identify the Known Values:** - **Principal (P):** $8,000 - **Total Number of Payments:** 24 - **Monthly Payment (M):** $400 2. **Calculate the Total Payment Amount:** \[ \text{Total Payment} = \text{Monthly Payment} \times \text{Number of Payments} \] \[ \text{Total Payment} = \$400 \times 24 = \$9,600 \] 3. **Determine the Total Interest Paid:** \[ \text{Total Interest} = \text{Total Payment} - \text{Principal} \] \[ \text{Total Interest} = \$9,600 - \$8,000 = \$1,600 \] 4. **Use the Simple Interest Formula:** The simple interest formula is given by: \[ I = P \times r \times t \] where: - \(I\) is the total interest paid, - \(P\) is the principal amount, - \(r\) is the annual interest rate, - \(t\) is the time period in years. 5. **Plug in the Known Values and Solve for \(r\):** Convert the number of payments into years: \[ t = \frac{24}{12} = 2 \text{ years} \] Now, use the formula: \[ 1,600 = 8,000 \times r \times 2 \] \[ 1,600 = 16,000r \] \[ r = \frac{1,600}{16,000} \] \[ r = 0.10 \] 6. **Convert the Rate into a Percentage:** \[ r = 0.10 \times 100 = 10\% \]
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