Converting the Interest Rate to a Decimal

Oct 13, 2025 by miodeya.com 147 views

Understanding the Problem

To calculate the interest earned on a principal amount, we can use the formula for simple interest: I = P * r * t, where I is the interest earned, P is the principal amount, r is the annual interest rate, and t is the time period in years. In this problem, we are given the principal amount P = $40,000, the annual interest rate r = 3 \frac{1}{2} % = 3.5%, and the time period t = 3 years.

Converting the Interest Rate to a Decimal

Before we can use the formula, we need to convert the interest rate from a percentage to a decimal. To do this, we divide the percentage by 100: 3.5% = 3.5 / 100 = 0.035.

Calculating the Interest Earned

Now that we have the interest rate in decimal form, we can plug in the values into the formula: I = P * r * t = $40,000 * 0.035 * 3.

Performing the Calculation

To calculate the interest earned, we multiply the principal amount by the interest rate and then by the time period: I = $40,000 * 0.035 * 3 = $4,200.

Understanding the Result

The result of the calculation is that the $40,000 principal amount earns $4,200 in interest over a period of 3 years at an annual interest rate of 3 \frac{1}{2} %.

Calculating the Total Amount

To find the total amount after 3 years, we add the interest earned to the principal amount: Total Amount = Principal Amount + Interest Earned = $40,000 + $4,200 = $44,200.

Conclusion

In conclusion, the $40,000 principal amount earns $4,200 in interest over a period of 3 years at an annual interest rate of 3 \frac{1}{2} %.

Real-World Applications

This problem has real-world applications in finance and banking. For example, a person who invests $40,000 in a savings account with a 3 \frac{1}{2} % annual interest rate can expect to earn $4,200 in interest over a period of 3 years.

Tips and Tricks

When calculating interest, make sure to convert the interest rate from a percentage to a decimal.
Use the formula I = P * r * t to calculate the interest earned.
Add the interest earned to the principal amount to find the total amount.

Common Mistakes

Failing to convert the interest rate from a percentage to a decimal.
Using the wrong formula to calculate the interest earned.
Forgetting to add the interest earned to the principal amount to find the total amount.

Frequently Asked Questions

Q: What is the interest earned on a principal amount of $40,000 at an annual interest rate of 3 \frac{1}{2} % over a period of 3 years? A: The interest earned is $4,200.
Q: What is the total amount after 3 years? A: The total amount is $44,200.

References

Q: What is the interest earned on a principal amount of $40,000 at an annual interest rate of 3 \frac{1}{2} % over a period of 3 years?

A: The interest earned is $4,200.

Q: What is the total amount after 3 years?

A: The total amount is $44,200, which is the sum of the principal amount ($40,000) and the interest earned ($4,200).

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

A: To calculate the interest earned, you can use the formula I = P * r * t, where I is the interest earned, P is the principal amount, r is the annual interest rate, and t is the time period in years.

Q: What is the annual interest rate in decimal form?

A: The annual interest rate in decimal form is 0.035, which is obtained by dividing the percentage by 100.

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

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

Q: What is the time period in years?

A: The time period in years is 3, which is the number of years over which the interest is earned.

Q: How do I calculate the total amount after 3 years?

A: To calculate the total amount after 3 years, you can add the interest earned to the principal amount.

Q: What is the principal amount?

A: The principal amount is $40,000, which is the initial amount invested.

Q: What is the interest rate?

A: The interest rate is 3 \frac{1}{2} %, which is the rate at which the interest is earned.

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

Q: What is the total amount after 3 years?

A: The total amount after 3 years is $44,200, which is the sum of the principal amount ($40,000) and the interest earned ($4,200).

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

Q: What is the annual interest rate in decimal form?

A: The annual interest rate in decimal form is 0.035, which is obtained by dividing the percentage by 100.

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

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

Q: What is the time period in years?

A: The time period in years is 3, which is the number of years over which the interest is earned.

Q: How do I calculate the total amount after 3 years?

A: To calculate the total amount after 3 years, you can add the interest earned to the principal amount.

Q: What is the principal amount?

A: The principal amount is $40,000, which is the initial amount invested.

Q: What is the interest rate?

A: The interest rate is 3 \frac{1}{2} %, which is the rate at which the interest is earned.

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

Q: What is the total amount after 3 years?

A: The total amount after 3 years is $44,200, which is the sum of the principal amount ($40,000) and the interest earned ($4,200).

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

Q: What is the annual interest rate in decimal form?

A: The annual interest rate in decimal form is 0.035, which is obtained by dividing the percentage by 100.

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

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

Q: What is the time period in years?

A: The time period in years is 3, which is the number of years over which the interest is earned.

Q: How do I calculate the total amount after 3 years?

A: To calculate the total amount after 3 years, you can add the interest earned to the principal amount.

Q: What is the principal amount?

A: The principal amount is $40,000, which is the initial amount invested.

Q: What is the interest rate?

A: The interest rate is 3 \frac{1}{2} %, which is the rate at which the interest is earned.

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

Q: What is the total amount after 3 years?

A: The total amount after 3 years is $44,200, which is the sum of the principal amount ($40,000) and the interest earned ($4,200).

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

Q: What is the annual interest rate in decimal form?

A: The annual interest rate in decimal form is 0.035, which is obtained by dividing the percentage by 100.

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

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

Q: What is the time period in years?

A: The time period in years is 3, which is the number of years over which the interest is earned.

Q: How do I calculate the total amount after 3 years?

A: To calculate the total amount after 3 years, you can add the interest earned to the principal amount.

Q: What is the principal amount?

A: The principal amount is $40,000, which is the initial amount invested.

Q: What is the interest rate?

A: The interest rate is 3 \frac{1}{2} %, which is the rate at which the interest is earned.

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

Q: What is the total amount after 3 years?

A: The total amount after 3 years is $44,200, which is the sum of the principal amount ($40,000) and the interest earned ($4,200).

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

Q: What is the annual interest rate in decimal form?

A: The annual interest rate in decimal form is 0.035, which is obtained by dividing the percentage by 100.

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

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

Q: What is the time period in years?

A: The time period in years is 3, which is the number of years over which the interest is earned.

Q: How do I calculate the total amount after 3 years?

A: To calculate the total amount after 3 years, you can add the interest earned to the principal amount.

Q: What is the principal amount?

A: The principal