Let's break down the information and compute both the total return and the annualized return on the investment.

Given:

• Initial purchase price per share: $80
• Number of shares purchased: 200
• Total initial investment: $80 \times 200 = 16,000$
• Selling price (total): $22,700
• Investment duration: 4 years

1. Total Return

The total return is the percentage increase in the value of the investment over the 4 years.

$\text{Total Return} = \frac{\text{Selling Price} - \text{Initial Investment}}{\text{Initial Investment}} \times 100$

$\text{Total Return} = \frac{22,700 - 16,000}{16,000} \times 100 = \frac{6,700}{16,000} \times 100 = 41.88\%$

2. Annualized Return (CAGR)

The annualized return (or Compound Annual Growth Rate, CAGR) is the rate at which the investment grows each year over the 4-year period.

$\text{CAGR} = \left( \frac{\text{Selling Price}}{\text{Initial Investment}} \right) ^{\frac{1}{\text{Years}}} - 1$

$\text{CAGR} = \left( \frac{22,700}{16,000} \right) ^{\frac{1}{4}} - 1 = \left( 1.41875 \right)^{\frac{1}{4}} - 1$

Now let's calculate this step.

Results:

1. Total Return: 41.88%
2. Annualized Return (CAGR): 9.14%

This means that the investment grew by a total of 41.88% over the 4 years, with an average annual growth rate of 9.14%.

Would you like further details or clarification?

Here are 5 related questions you might find helpful:

1. How do you interpret the difference between total return and annualized return?
2. What would the return be if you held the investment for a different number of years?
3. How do taxes affect the real return on investment?
4. What happens if the stock pays dividends? How would that affect total and annual returns?
5. What are alternative ways to calculate returns on irregular investment intervals?

Tip: Always check the compound annual growth rate (CAGR) to get a better sense of long-term investment performance compared to just looking at the total return.