David Read An Ad Offering 8 3 4 % 8 \frac{3}{4} \% 8 4 3 % Simple Interest On Accounts Over $ 500 \$500 $500 Left For A Minimum Of 5 Years. He Has $ 500 \$500 $500 And Thinks This Sounds Like A Great Deal. How Much Money Will He Earn In The 5 Years?

Mar 12, 2025 by ADMIN 252 views

**Understanding Simple Interest and Its Application**

Simple interest is a type of interest calculated only on the initial principal amount, without taking into account the interest accrued over time. It is a straightforward and easy-to-understand concept, making it a popular choice for various financial applications. In this article, we will delve into the world of simple interest and explore how it can be applied to real-life scenarios, such as the one presented in the problem.

The Problem: Calculating Simple Interest

David has $\$500$ and comes across an advertisement offering $8 \frac{3}{4} \%$ simple interest on accounts over $\$500$ left for a minimum of 5 years. The question is, how much money will he earn in the 5 years?

Breaking Down the Problem

To solve this problem, we need to understand the concept of simple interest and its formula. The formula for simple interest is:

${ I = P \times r \times t }$

Where:

$I$ is the interest earned
$P$ is the principal amount (initial amount of money)
$r$ is the interest rate (in decimal form)
$t$ is the time period (in years)

Converting the Interest Rate to Decimal Form

The interest rate is given as $8 \frac{3}{4} \%$ . To convert this to decimal form, we need to convert the fraction to a decimal. We can do this by dividing the numerator by the denominator:

${ 8 \frac{3}{4} = 8 + \frac{3}{4} = 8 + 0.75 = 8.75\% }$

To convert this to decimal form, we divide by 100:

${ 8.75\% = \frac{8.75}{100} = 0.0875 }$

Applying the Formula

Now that we have the interest rate in decimal form, we can apply the formula for simple interest:

${ I = P \times r \times t }$

Substituting the values, we get:

${ I = 500 \times 0.0875 \times 5 }$

Calculating the Interest

To calculate the interest, we multiply the principal amount, interest rate, and time period:

${ I = 500 \times 0.0875 \times 5 }$ ${ I = 218.75 }$

Conclusion

In this article, we explored the concept of simple interest and its application to a real-life scenario. We broke down the problem, converted the interest rate to decimal form, and applied the formula for simple interest. The result is that David will earn $\$218.75$ in interest over the 5-year period.

Real-World Applications

Simple interest has numerous real-world applications, including:

Banking and Finance: Simple interest is used to calculate interest on loans, credit cards, and savings accounts.
Investments: Simple interest is used to calculate returns on investments, such as bonds and certificates of deposit (CDs).
Personal Finance: Simple interest is used to calculate interest on personal loans, credit cards, and savings accounts.

Common Mistakes to Avoid

When working with simple interest, it's essential to avoid common mistakes, such as:

Not converting the interest rate to decimal form: Failing to convert the interest rate to decimal form can lead to incorrect calculations.
Not applying the formula correctly: Failing to apply the formula correctly can lead to incorrect calculations.
Not considering compounding interest: Failing to consider compounding interest can lead to incorrect calculations.

Conclusion

Simple interest is a fundamental concept in mathematics and finance, and it's essential to understand it to make informed decisions about your finances. In this article, we'll answer some frequently asked questions about simple interest to help you better understand this concept.

Q: What is simple interest?

A: Simple interest is a type of interest calculated only on the initial principal amount, without taking into account the interest accrued over time.

Q: How is simple interest calculated?

A: Simple interest is calculated using the formula:

${ I = P \times r \times t }$

Where:

$I$ is the interest earned
$P$ is the principal amount (initial amount of money)
$r$ is the interest rate (in decimal form)
$t$ is the time period (in years)

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

A: Simple interest is calculated only on the initial principal amount, while compound interest is calculated on both the principal amount and the accrued interest.

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

A: To convert a percentage to decimal form, divide the percentage by 100. For example, to convert 8.75% to decimal form, divide 8.75 by 100:

${ 8.75\% = \frac{8.75}{100} = 0.0875 }$

Q: What is the interest rate in the problem?

A: The interest rate in the problem is $8 \frac{3}{4} \%$ , which is equivalent to 8.75% in decimal form.

Q: How do I calculate the interest earned?

A: To calculate the interest earned, multiply the principal amount, interest rate, and time period:

${ I = P \times r \times t }$

Substituting the values, we get:

${ I = 500 \times 0.0875 \times 5 }$

Q: What is the interest earned in the problem?

A: The interest earned in the problem is $\$218.75$ .

Q: Can I use simple interest to calculate interest on a loan or credit card?

A: Yes, simple interest can be used to calculate interest on a loan or credit card. However, it's essential to consider compounding interest, which is the interest earned on both the principal amount and the accrued interest.

Q: What are some common mistakes to avoid when working with simple interest?

A: Some common mistakes to avoid when working with simple interest include:

Not converting the interest rate to decimal form
Not applying the formula correctly
Not considering compounding interest

Q: How can I use simple interest in real-life scenarios?

A: Simple interest can be used in various real-life scenarios, including:

Banking and Finance: Simple interest is used to calculate interest on loans, credit cards, and savings accounts.
Investments: Simple interest is used to calculate returns on investments, such as bonds and certificates of deposit (CDs).
Personal Finance: Simple interest is used to calculate interest on personal loans, credit cards, and savings accounts.

Conclusion

In conclusion, simple interest is a fundamental concept in mathematics and finance, and it's essential to understand it to make informed decisions about your finances. By answering these frequently asked questions, we hope to have provided you with a better understanding of simple interest and its application.