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.