Steven purchased 1000 shares of a certain stock for $27,600 (including commissions). He sold the shares 3 years later and received $34,900 after deducting commissions. Find the effective annual rate of return on his investment over the 3-year period. (Round your answer to two decimal places.)

To find the effective annual rate of return on Steven's investment, we can use the formula for the annual rate of return, which is based on the compound interest formula:

\[
A = P \left(1 + r\right)^t
\]

Where:
- $ A $ is the amount received after $ t $ years,
- $ P $ is the initial amount invested,
- $ r $ is the effective annual rate of return,
- $ t $ is the time in years.

Given:
- $ P = 27,600 $ dollars,
- $ A = 34,900 $ dollars,
- $ t = 3 $ years.

We need to solve for $ r $. Rearranging the formula to solve for $ r $:

\[
\left(1 + r\right)^t = \frac{A}{P}
\]

\[
1 + r = \left(\frac{A}{P}\right)^{\frac{1}{t}}
\]

\[
r = \left(\frac{A}{P}\right)^{\frac{1}{t}} - 1
\]

Substituting the given values:

\[
r = \left(\frac{34,900}{27,600}\right)^{\frac{1}{3}} - 1
\]

Let's calculate this step by step.

1. Calculate the ratio $ \frac{A}{P} $:

\[
\frac{34,900}{27,600} \approx 1.2645
\]

2. Raise this ratio to the power of $ \frac{1}{3} $:

\[
1.2645^{\frac{1}{3}} \approx 1.0806
\]

3. Subtract 1 to find the effective annual rate of return:

\[
r = 1.0806 - 1 \approx 0.0806
\]

4. Convert to a percentage:

\[
r \approx 8.06\%
\]

Thus, the effective annual rate of return on Steven's investment is **8.06%**.

Would you like more details or have any questions?

Here are 5 related questions:
1. How would the effective annual rate of return change if Steven held the stock for 5 years instead of 3 years?
2. What is the difference between the effective annual rate of return and the nominal rate of return?
3. How can the rate of return be affected by fluctuations in stock prices during the holding period?
4. If Steven reinvested the proceeds after selling the stock, how could compound interest affect his returns?
5. How does the concept of the time value of money relate to the calculation of the rate of return?

**Tip:** When calculating investment returns, always consider the effects of compounding, as it can significantly impact your overall earnings!

Learn how to calculate the effective annual rate of return on Steven's investment of $27,600 in a certain stock, which yielded $34,900 after 3 years. Detailed step-by-step solution using the compound interest formula. Suitable for undergraduate students and investors.

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