Forgetting to account for compounding

Oct 13, 2025 by wbrum.org 127 views

Terrell's Interest Earnings: A Mathematical Calculation

Understanding the Problem

Terrell has a significant amount of money, $6,749, in an account that earns a 4% interest rate compounded annually. The question is, how much interest will he earn in 5 years? To solve this problem, we need to use the formula for compound interest, which is given by:

B = p(1 + r)^t

where:

$B$ is the future value of the investment (the amount of money Terrell will have after 5 years)
$p$ is the principal amount (the initial amount of money Terrell has, which is $6,749)
$r$ is the annual interest rate (4% in this case)
$t$ is the number of years the money is invested (5 years in this case)

Breaking Down the Formula

Let's break down the formula and understand what each component means.

Future Value (B): This is the amount of money Terrell will have after 5 years, including the interest earned.
Principal Amount (p): This is the initial amount of money Terrell has, which is $6,749.
Annual Interest Rate (r): This is the interest rate earned on the principal amount, which is 4% in this case.
Number of Years (t): This is the number of years the money is invested, which is 5 years in this case.

Calculating the Future Value

Now that we understand the formula, let's calculate the future value of Terrell's investment.

B = p(1 + r)^t

B = 6749(1 + 0.04)^5

B = 6749(1.04)^5

B = 6749 \times 1.216647

B = 8161.19

Calculating the Interest Earned

Now that we have the future value, we can calculate the interest earned by subtracting the principal amount from the future value.

Interest = B - p

Interest = 8161.19 - 6749

Interest = 1412.19

Conclusion

To the nearest cent, Terrell will earn $1412.19 in interest in 5 years, assuming a 4% interest rate compounded annually.

Key Takeaways

The formula for compound interest is $B = p(1 + r)^t$ , where $B$ is the future value, $p$ is the principal amount, $r$ is the annual interest rate, and $t$ is the number of years.
The future value of an investment can be calculated using the formula, and the interest earned can be calculated by subtracting the principal amount from the future value.
In this case, Terrell will earn $1412.19 in interest in 5 years, assuming a 4% interest rate compounded annually.

Real-World Applications

Understanding compound interest is crucial in real-world applications, such as:

Investing: When investing in stocks, bonds, or other financial instruments, it's essential to understand how compound interest works to make informed decisions.
Savings: When saving money, it's essential to understand how compound interest can help your savings grow over time.
Loans: When taking out a loan, it's essential to understand how compound interest can affect the total amount you owe.

Conclusion

In conclusion, Terrell will earn $1412.19 in interest in 5 years, assuming a 4% interest rate compounded annually. Understanding compound interest is crucial in real-world applications, such as investing, savings, and loans. By using the formula for compound interest, we can calculate the future value of an investment and the interest earned.
Terrell's Interest Earnings: A Mathematical Calculation - Q&A

Frequently Asked Questions

In this article, we will answer some frequently asked questions related to Terrell's interest earnings.

Q: What is compound interest?

A: Compound interest is the interest earned on both the principal amount and any accrued interest over time. It's a way to calculate the future value of an investment, taking into account the interest earned on the interest.

Q: How is compound interest calculated?

A: Compound interest is calculated using the formula:

B = p(1 + r)^t

where:

$B$ is the future value of the investment
$p$ is the principal amount
$r$ is the annual interest rate
$t$ is the number of years

Q: What is the principal amount?

A: The principal amount is the initial amount of money invested, which is $6,749 in this case.

Q: What is the annual interest rate?

A: The annual interest rate is the rate at which interest is earned on the principal amount, which is 4% in this case.

Q: What is the number of years?

A: The number of years is the time period over which the interest is earned, which is 5 years in this case.

Q: How is the interest earned calculated?

A: The interest earned is calculated by subtracting the principal amount from the future value.

Q: What is the future value of the investment?

A: The future value of the investment is the amount of money Terrell will have after 5 years, including the interest earned, which is $8161.19.

Q: How much interest will Terrell earn in 5 years?

A: Terrell will earn $1412.19 in interest in 5 years, assuming a 4% interest rate compounded annually.

Q: What are some real-world applications of compound interest?

A: Compound interest has many real-world applications, including:

Investing: When investing in stocks, bonds, or other financial instruments, it's essential to understand how compound interest works to make informed decisions.
Savings: When saving money, it's essential to understand how compound interest can help your savings grow over time.
Loans: When taking out a loan, it's essential to understand how compound interest can affect the total amount you owe.

Q: How can I calculate compound interest?

A: You can calculate compound interest using a calculator or a spreadsheet. You can also use online tools or apps to calculate compound interest.

Q: What are some common mistakes to avoid when calculating compound interest?

A: Some common mistakes to avoid when calculating compound interest include:

Forgetting to account for compounding: Make sure to account for compounding when calculating compound interest.
Using the wrong interest rate: Use the correct interest rate when calculating compound interest.
Using the wrong time period: Use the correct time period when calculating compound interest.

Conclusion

In conclusion, compound interest is a powerful tool for calculating the future value of an investment. By understanding how compound interest works, you can make informed decisions about your finances and achieve your financial goals. Remember to account for compounding, use the correct interest rate, and use the correct time period when calculating compound interest.