Tasha Invests $ 5 , 000 \$5,000 $5 , 000 At 6 % 6\% 6% Annual Interest And An Additional $ 5 , 000 \$5,000 $5 , 000 At 8 % 8\% 8% Annual Interest. Thomas Invests $ 10 , 000 \$10,000 $10 , 000 At 7 % 7\% 7% Annual Interest. Which Statement Accurately Compares Tasha's

Introduction

When it comes to investing, understanding the returns on investment (ROI) is crucial in making informed decisions. In this article, we will compare the investment returns of Tasha and Thomas, who have invested different amounts at varying annual interest rates. We will analyze their investment portfolios and determine which statement accurately compares their returns.

Tasha's Investment Portfolio

Tasha has invested a total of $\$10,000$ in two separate accounts. The first account has a principal amount of $\$5,000$ and an annual interest rate of $6\%$. The second account has a principal amount of $\$5,000$ and an annual interest rate of $8\%$.

Calculating Tasha's Returns

To calculate Tasha's returns, we need to calculate the interest earned on each account separately and then add them together.

For the first account with a principal amount of $\$5,000$ and an annual interest rate of $6\%$, the interest earned can be calculated as follows:

$$\text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time}$$

$$\text{Interest} = \$5,000 \times 0.06 \times 1$$

$$\text{Interest} = \$300$$

For the second account with a principal amount of $\$5,000$ and an annual interest rate of $8\%$, the interest earned can be calculated as follows:

$$\text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time}$$

$$\text{Interest} = \$5,000 \times 0.08 \times 1$$

$$\text{Interest} = \$400$$

The total interest earned by Tasha is the sum of the interest earned on both accounts:

$$\text{Total Interest} = \$300 + \$400$$

$$\text{Total Interest} = \$700$$

Thomas's Investment Portfolio

Thomas has invested a principal amount of $\$10,000$ at an annual interest rate of $7\%$.

Calculating Thomas's Returns

To calculate Thomas's returns, we need to calculate the interest earned on his account.

For Thomas's account with a principal amount of $\$10,000$ and an annual interest rate of $7\%$, the interest earned can be calculated as follows:

$$\text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time}$$

$$\text{Interest} = \$10,000 \times 0.07 \times 1$$

$$\text{Interest} = \$700$$

Comparing Tasha's and Thomas's Returns

Now that we have calculated the returns on investment for both Tasha and Thomas, we can compare their returns.

Tasha's total interest earned is $\$700$, while Thomas's interest earned is also $\$700$. Therefore, the statement that accurately compares Tasha's and Thomas's returns is:

• Tasha's and Thomas's returns are equal.

Conclusion

In conclusion, when comparing the investment returns of Tasha and Thomas, we found that their returns are equal. This is because Tasha's total interest earned is $\$700$, which is the same as Thomas's interest earned. Therefore, the statement that accurately compares Tasha's and Thomas's returns is:

• Tasha's and Thomas's returns are equal.

References

• [1] Investopedia. (n.d.). Return on Investment (ROI). Retrieved from https://www.investopedia.com/terms/r/returnoninvestment.asp
• [2] Investopedia. (n.d.). Compound Interest. Retrieved from https://www.investopedia.com/terms/c/compoundinterest.asp

Note

Q: What is the main difference between Tasha's and Thomas's investment portfolios?

A: The main difference between Tasha's and Thomas's investment portfolios is the number of accounts and the interest rates. Tasha has two separate accounts with different interest rates, while Thomas has a single account with a single interest rate.

Q: How do the interest rates affect the returns on investment for Tasha and Thomas?

A: The interest rates have a significant impact on the returns on investment for both Tasha and Thomas. Tasha's higher interest rate on her second account ($8\%$) results in a higher interest earned compared to her first account ($6\%$). Thomas's interest rate of $7\%$ is lower than Tasha's highest interest rate, but higher than her lowest interest rate.

Q: What is the total interest earned by Tasha and Thomas?

A: The total interest earned by Tasha is $\$700$, which is the sum of the interest earned on both her accounts. Thomas's total interest earned is also $\$700$, which is the interest earned on his single account.

Q: Are Tasha's and Thomas's returns on investment equal?

A: Yes, Tasha's and Thomas's returns on investment are equal. Both Tasha and Thomas earned a total interest of $\$700$, making their returns on investment equal.

Q: What factors can affect the returns on investment for Tasha and Thomas?

A: Several factors can affect the returns on investment for Tasha and Thomas, including:

• Interest rates: Changes in interest rates can impact the returns on investment.
• Time period: The length of time the money is invested can affect the returns on investment.
• Principal amount: The amount of money invested can impact the returns on investment.
• Compounding: The frequency of compounding can impact the returns on investment.

Q: How can Tasha and Thomas optimize their investment returns?

A: Tasha and Thomas can optimize their investment returns by:

• Investing in accounts with higher interest rates.
• Increasing the principal amount invested.
• Extending the time period of the investment.
• Considering compounding options.

Q: What are some common mistakes to avoid when comparing investment returns?

A: Some common mistakes to avoid when comparing investment returns include:

• Failing to consider the time period of the investment.
• Ignoring the impact of compounding.
• Not accounting for changes in interest rates.
• Comparing apples to oranges (e.g., comparing a single account to multiple accounts).

Q: What is the best way to compare investment returns?

A: The best way to compare investment returns is to:

• Use a consistent time period for comparison.
• Consider the impact of compounding.
• Account for changes in interest rates.
• Compare like accounts (e.g., comparing multiple accounts with the same interest rate).

Conclusion

In conclusion, comparing investment returns requires careful consideration of several factors, including interest rates, time period, principal amount, and compounding. By understanding these factors and avoiding common mistakes, investors can make informed decisions and optimize their investment returns.