After 6 Months, $ 5 , 000 \$5,000 $5 , 000 Deposited In A Savings Account With Simple Interest Had Earned $ 225 \$225 $225 In Interest. What Was The Interest Rate?Use The Formula I = P R T I = Prt I = P R T , Where I I I Is The Interest Earned, P P P Is

Introduction

Simple interest is a type of interest calculated only on the initial principal amount, without considering the interest accrued over time. It is a straightforward and easy-to-understand concept, making it a fundamental aspect of finance and mathematics. In this article, we will delve into the world of simple interest and explore how to calculate interest rates using the formula $i = prt$, where $i$ is the interest earned, $p$ is the principal amount, $r$ is the interest rate, and $t$ is the time period.

What is Simple Interest?

Simple interest is a type of interest that is calculated only on the initial principal amount. It is calculated as a percentage of the principal amount and is not affected by the interest accrued over time. The formula for simple interest is:

$$i = prt$$

Where:

• $i$ is the interest earned
• $p$ is the principal amount
• $r$ is the interest rate
• $t$ is the time period

Calculating Interest Rates

To calculate the interest rate, we need to rearrange the formula to isolate the interest rate $r$. We can do this by dividing both sides of the equation by $pt$:

$$r = \frac{i}{pt}$$

Now, let's apply this formula to the given problem. We are told that $\$5,000$ was deposited in a savings account with simple interest and earned $\$225$ in interest over a period of 6 months.

Solving for the Interest Rate

We can plug in the values given in the problem into the formula:

$$r = \frac{225}{5000 \times 0.5}$$

Where $0.5$ is the time period in years (6 months is equivalent to 0.5 years).

Simplifying the equation, we get:

$$r = \frac{225}{2500}$$

$$r = 0.09$$

To convert this to a percentage, we multiply by 100:

$$r = 9\%$$

Therefore, the interest rate is 9%.

Conclusion

In this article, we explored the concept of simple interest and how to calculate interest rates using the formula $i = prt$. We applied this formula to a real-world problem and calculated the interest rate for a savings account with simple interest. The interest rate was found to be 9%. This demonstrates the importance of understanding simple interest and how to calculate interest rates in finance and mathematics.

Real-World Applications

Simple interest has numerous real-world applications, including:

• Savings accounts: Simple interest is often used to calculate interest on savings accounts.
• Loans: Simple interest is used to calculate interest on loans, such as personal loans and mortgages.
• Investments: Simple interest is used to calculate interest on investments, such as bonds and certificates of deposit (CDs).

Common Mistakes to Avoid

When calculating interest rates, it's essential to avoid common mistakes, including:

• Forgetting to convert time periods: Make sure to convert time periods from months or years to the correct unit of time.
• Rounding errors: Be careful when rounding numbers to avoid errors in calculations.
• Not considering compounding interest: Simple interest assumes that interest is not compounded over time. If interest is compounded, use the formula for compound interest instead.

Final Thoughts

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Frequently Asked Questions

Q: What is simple interest?

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

Q: How is simple interest calculated?

A: Simple interest is calculated using the formula $i = prt$, where $i$ is the interest earned, $p$ is the principal amount, $r$ is the interest rate, and $t$ is the time period.

Q: What is the formula for simple interest?

A: The formula for simple interest is:

$$i = prt$$

Q: How do I calculate the interest rate?

A: To calculate the interest rate, you can rearrange the formula to isolate the interest rate $r$. You can do this by dividing both sides of the equation by $pt$:

$$r = \frac{i}{pt}$$

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 calculate compound interest?

A: Compound interest is calculated using the formula:

$$A = P(1 + r)^t$$

Where:

• $A$ is the future value of the investment
• $P$ is the principal amount
• $r$ is the interest rate
• $t$ is the time period

Q: What is the time period in years?

A: The time period in years is the number of years the money is invested or borrowed for.

Q: How do I convert months to years?

A: To convert months to years, you can divide the number of months by 12.

Q: What is the interest rate in decimal form?

A: The interest rate in decimal form is the interest rate as a decimal, rather than a percentage.

Q: How do I convert the interest rate from decimal form to percentage form?

A: To convert the interest rate from decimal form to percentage form, you can multiply the decimal form by 100.

Q: What is the principal amount?

A: The principal amount is the initial amount of money invested or borrowed.

Q: How do I calculate the interest earned?

A: To calculate the interest earned, you can use the formula:

$$i = prt$$

Where:

• $i$ is the interest earned
• $p$ is the principal amount
• $r$ is the interest rate
• $t$ is the time period

Q: What is the interest rate in percentage form?

A: The interest rate in percentage form is the interest rate as a percentage, rather than a decimal.

Q: How do I calculate the interest rate in percentage form?

A: To calculate the interest rate in percentage form, you can multiply the decimal form by 100.

Q: What is the time period in months?

A: The time period in months is the number of months the money is invested or borrowed for.

Q: How do I convert years to months?

A: To convert years to months, you can multiply the number of years by 12.

Q: What is the interest earned in decimal form?

A: The interest earned in decimal form is the interest earned as a decimal, rather than a percentage.

Q: How do I calculate the interest earned in decimal form?

A: To calculate the interest earned in decimal form, you can use the formula:

$$i = prt$$

Where:

• $i$ is the interest earned
• $p$ is the principal amount
• $r$ is the interest rate
• $t$ is the time period

Q: What is the interest rate in decimal form?

A: The interest rate in decimal form is the interest rate as a decimal, rather than a percentage.

Q: How do I calculate the interest rate in decimal form?

A: To calculate the interest rate in decimal form, you can divide the interest rate in percentage form by 100.

Q: What is the principal amount in decimal form?

A: The principal amount in decimal form is the principal amount as a decimal, rather than a percentage.

Q: How do I calculate the principal amount in decimal form?

A: To calculate the principal amount in decimal form, you can divide the principal amount in percentage form by 100.

Q: What is the time period in decimal form?

A: The time period in decimal form is the time period as a decimal, rather than a percentage.

Q: How do I calculate the time period in decimal form?

A: To calculate the time period in decimal form, you can divide the time period in percentage form by 100.

Q: What is the interest earned in percentage form?

A: The interest earned in percentage form is the interest earned as a percentage, rather than a decimal.

Q: How do I calculate the interest earned in percentage form?

A: To calculate the interest earned in percentage form, you can multiply the interest earned in decimal form by 100.

Q: What is the interest rate in percentage form?

A: The interest rate in percentage form is the interest rate as a percentage, rather than a decimal.

Q: How do I calculate the interest rate in percentage form?

A: To calculate the interest rate in percentage form, you can multiply the interest rate in decimal form by 100.

Q: What is the principal amount in percentage form?

A: The principal amount in percentage form is the principal amount as a percentage, rather than a decimal.

Q: How do I calculate the principal amount in percentage form?

A: To calculate the principal amount in percentage form, you can multiply the principal amount in decimal form by 100.

Q: What is the time period in percentage form?

A: The time period in percentage form is the time period as a percentage, rather than a decimal.

Q: How do I calculate the time period in percentage form?

A: To calculate the time period in percentage form, you can multiply the time period in decimal form by 100.

Q: What is the interest earned in decimal form?

A: The interest earned in decimal form is the interest earned as a decimal, rather than a percentage.

Q: How do I calculate the interest earned in decimal form?

A: To calculate the interest earned in decimal form, you can use the formula:

$$i = prt$$

Where:

• $i$ is the interest earned
• $p$ is the principal amount
• $r$ is the interest rate
• $t$ is the time period

Q: What is the interest rate in decimal form?

A: The interest rate in decimal form is the interest rate as a decimal, rather than a percentage.

Q: How do I calculate the interest rate in decimal form?

A: To calculate the interest rate in decimal form, you can divide the interest rate in percentage form by 100.

Q: What is the principal amount in decimal form?

A: The principal amount in decimal form is the principal amount as a decimal, rather than a percentage.

Q: How do I calculate the principal amount in decimal form?

A: To calculate the principal amount in decimal form, you can divide the principal amount in percentage form by 100.

Q: What is the time period in decimal form?

A: The time period in decimal form is the time period as a decimal, rather than a percentage.

Q: How do I calculate the time period in decimal form?

A: To calculate the time period in decimal form, you can divide the time period in percentage form by 100.

Q: What is the interest earned in percentage form?

A: The interest earned in percentage form is the interest earned as a percentage, rather than a decimal.

Q: How do I calculate the interest earned in percentage form?

A: To calculate the interest earned in percentage form, you can multiply the interest earned in decimal form by 100.

Q: What is the interest rate in percentage form?

A: The interest rate in percentage form is the interest rate as a percentage, rather than a decimal.

Q: How do I calculate the interest rate in percentage form?

A: To calculate the interest rate in percentage form, you can multiply the interest rate in decimal form by 100.

Q: What is the principal amount in percentage form?

A: The principal amount in percentage form is the principal amount as a percentage, rather than a decimal.

Q: How do I calculate the principal amount in percentage form?

A: To calculate the principal amount in percentage form, you can multiply the principal amount in decimal form by 100.

Q: What is the time period in percentage form?

A: The time period in percentage form is the time period as a percentage, rather than a decimal.

Q: How do I calculate the time period in percentage form?

A: To calculate the time period in percentage form, you can multiply the time period in decimal form by 100.

Q: What is the interest earned in decimal form?

A: