Compute the total and annual returns on the described investment.
FourFour years after buying 150 shares of XYZ stock for ​$40 per​ share, you sell the stock for $ 8700.
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Part 1
The total return is 45​%. 
​(Do not round until the final answer. Then round to one decimal place as​ needed.)
Part 2
The annual return is

Let's break down the investment calculation to compute both the total and annual returns.

### Part 1: **Total Return**

We are told that:
- Initial investment: You bought 150 shares at $40 per share, so the total purchase price is:
  \[
  150 \times 40 = 6000 \text{ USD}
  \]
- Selling price: You sold the stock for $8,700 after 4 years.

The total return $ R_{\text{total}} $ is the percentage increase in the value of the investment. This can be calculated using the formula:

\[
R_{\text{total}} = \frac{{\text{Selling Price} - \text{Purchase Price}}}{{\text{Purchase Price}}} \times 100
\]

\[
R_{\text{total}} = \frac{8700 - 6000}{6000} \times 100 = \frac{2700}{6000} \times 100 = 45\%
\]

So, the total return is **45%**, as given.

### Part 2: **Annual Return**

The annual return $ R_{\text{annual}} $ can be calculated using the formula for compound annual growth rate (CAGR):

\[
R_{\text{annual}} = \left( \frac{\text{Final Value}}{\text{Initial Value}} \right)^{\frac{1}{t}} - 1
\]

Where:
- Final Value = $8700
- Initial Value = $6000
- $ t = 4 $ years

Now, let’s compute the annual return:

\[
R_{\text{annual}} = \left( \frac{8700}{6000} \right)^{\frac{1}{4}} - 1
\]

Let me calculate that for you.The annual return on the investment is approximately **9.7%**.

Let me know if you'd like further details or have any questions.

Here are five related questions you might find useful:
1. How does the total return change if you sell the stock earlier?
2. What if the stock price had dropped after four years instead of increasing?
3. How would dividends affect the total and annual returns?
4. Can you compare the stock's performance to a market index?
5. How does compounding impact investment returns?

**Tip:** Annual return considers the compounding effect, giving a clearer picture of investment growth over time compared to the total return.

Compute the total and annual returns on the described investment. Four years after buying 150 shares of XYZ stock for $40 per share, you sell the stock for $8700.

Learn how to compute the total return of 45% and the annual return of approximately 9.7% for a stock investment. The example involves purchasing 150 shares at $40 each and selling them for $8700 after four years. This problem covers key concepts like percentage return and compound annual growth rate (CAGR). Suitable for Grades 10-12.

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