Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
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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:**
\[
r = 0.10 \times 100 = 10\%
\]](https://content.bartleby.com/qna-images/question/f8311114-a7cb-49e3-b44e-1e05de4bc29a/088f2651-2029-4cae-addd-54ef40a2d770/gw9qj0p.png)
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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