Which Equation Demonstrates The Use Of A Simple Interest Formula, I = P × R × T I = P \times R \times T I = P × R × T , To Compute The Interest Earned On $70 At 3% For 12 Years?A. I = ( 70 ) × ( 0.12 ) × ( 3 I = (70) \times (0.12) \times (3 I = ( 70 ) × ( 0.12 ) × ( 3 ]B. $i = (70) \times (0.03) \times

Mar 7, 2025 by ADMIN 304 views

**Understanding Simple Interest Formulas: A Comprehensive Guide**

Introduction

Simple interest is a fundamental concept in finance and mathematics, used to calculate the interest earned on a principal amount over a specific period. The simple interest formula, $I = P \times r \times t$ , is a widely used equation to determine the interest earned. In this article, we will explore the use of the simple interest formula and identify the correct equation that demonstrates its application.

What is Simple Interest?

Simple interest is a type of interest that is calculated only on the principal amount, without considering the interest accrued over time. It is a straightforward and easy-to-understand concept, making it a popular choice for financial calculations. The simple interest formula, $I = P \times r \times t$ , is used to calculate the interest earned, where:

$I$ is the interest earned
$P$ is the principal amount
$r$ is the interest rate (expressed as a decimal)
$t$ is the time period (in years)

The Simple Interest Formula

The simple interest formula, $I = P \times r \times t$ , is a fundamental equation in finance and mathematics. It is used to calculate the interest earned on a principal amount over a specific period. The formula is straightforward and easy to apply, making it a popular choice for financial calculations.

Example: Computing Interest Earned

Let's consider an example to demonstrate the use of the simple interest formula. Suppose we want to calculate the interest earned on $70 at 3% for 12 years. We can use the simple interest formula to determine the interest earned.

Equation A: Incorrect Application

The first equation, $i = (70) \times (0.12) \times (3)$ , is an incorrect application of the simple interest formula. In this equation, the interest rate is expressed as a percentage (3%), but it is not converted to a decimal. Additionally, the time period is expressed as a decimal (0.12), which is incorrect.

Equation B: Correct Application

The second equation, $i = (70) \times (0.03) \times (12)$ , is the correct application of the simple interest formula. In this equation, the interest rate is converted to a decimal (0.03), and the time period is expressed as a whole number (12). This equation accurately represents the simple interest formula and can be used to calculate the interest earned.

Conclusion

In conclusion, the simple interest formula, $I = P \times r \times t$ , is a fundamental equation in finance and mathematics. It is used to calculate the interest earned on a principal amount over a specific period. The correct equation that demonstrates the use of the simple interest formula is $i = (70) \times (0.03) \times (12)$ . This equation accurately represents the simple interest formula and can be used to calculate the interest earned.

Additional Examples

To further illustrate the use of the simple interest formula, let's consider a few additional examples:

Suppose we want to calculate the interest earned on $100 at 5% for 10 years. We can use the simple interest formula to determine the interest earned: $i = (100) \times (0.05) \times (10) = $50.
Suppose we want to calculate the interest earned on $500 at 2% for 5 years. We can use the simple interest formula to determine the interest earned: $i = (500) \times (0.02) \times (5) = $50.

Real-World Applications

The simple interest formula has numerous real-world applications in finance, banking, and economics. It is used to calculate interest earned on loans, investments, and savings accounts. The formula is also used to determine the interest rate on bonds, stocks, and other financial instruments.

Common Mistakes

When applying the simple interest formula, it is essential to avoid common mistakes. Some common mistakes include:

Failing to convert the interest rate to a decimal
Expressing the time period as a decimal or percentage
Using the wrong formula or equation
Failing to consider compounding interest

Conclusion

Introduction

The simple interest formula, $I = P \times r \times t$ , is a fundamental concept in finance and mathematics. In our previous article, we explored the use of the simple interest formula and identified the correct equation that demonstrates its application. In this article, we will answer frequently asked questions about the simple interest formula.

Q: What is the simple interest formula?

A: The simple interest formula is $I = P \times r \times t$ , where:

$I$ is the interest earned
$P$ is the principal amount
$r$ is the interest rate (expressed as a decimal)
$t$ is the time period (in years)

Q: How do I calculate the interest earned using the simple interest formula?

A: To calculate the interest earned using the simple interest formula, you need to multiply the principal amount ( $P$ ) by the interest rate ( $r$ ) and the time period ( $t$ ). For example, if you want to calculate the interest earned on $100 at 5% for 10 years, you would use the formula: $I = (100) \times (0.05) \times (10) = $50.

Q: What is the difference between simple interest and compound interest?

A: Simple interest is calculated only on the principal amount, while compound interest is calculated on both the principal amount and the accrued interest. Compound interest is more complex and is used in more advanced financial calculations.

Q: Can I use the simple interest formula to calculate interest earned on a loan?

A: Yes, you can use the simple interest formula to calculate interest earned on a loan. However, you need to consider the loan's interest rate, principal amount, and time period to determine the interest earned.

Q: How do I convert a percentage to a decimal?

A: To convert a percentage to a decimal, you need to divide the percentage by 100. For example, if you want to convert 5% to a decimal, you would divide 5 by 100, which equals 0.05.

Q: What is the time period in the simple interest formula?

A: The time period in the simple interest formula is the number of years the money is invested or borrowed for. It is expressed as a whole number.

Q: Can I use the simple interest formula to calculate interest earned on a savings account?

A: Yes, you can use the simple interest formula to calculate interest earned on a savings account. However, you need to consider the account's interest rate, principal amount, and time period to determine the interest earned.

Q: What are some common mistakes to avoid when using the simple interest formula?

A: Some common mistakes to avoid when using the simple interest formula include:

Failing to convert the interest rate to a decimal
Expressing the time period as a decimal or percentage
Using the wrong formula or equation
Failing to consider compounding interest

Q: Can I use the simple interest formula to calculate interest earned on a bond?

A: Yes, you can use the simple interest formula to calculate interest earned on a bond. However, you need to consider the bond's interest rate, principal amount, and time period to determine the interest earned.

Conclusion

In conclusion, the simple interest formula, $I = P \times r \times t$ , is a fundamental concept in finance and mathematics. By understanding the simple interest formula and avoiding common mistakes, individuals can make informed financial decisions and achieve their financial goals. We hope this Q&A article has provided you with a better understanding of the simple interest formula and its applications.