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.
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
![**Loan Interest Rate Calculation Example**
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**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.
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**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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