Let's break down the problem into parts to calculate the effective interest rate per year.

Step 1: Calculate the total dividend income

You purchased the stock in two phases:

1. Initial purchase (10 shares at $20 per share):

   • The dividend per share is $0.25 per quarter.
   • You held the first 10 shares for 8 quarters (2 years).

   Total dividend income for the first 10 shares: $10 \, \text{shares} \times 0.25 \, \text{\$/share} \times 8 \, \text{quarters} = 20 \, \text{\$}$

2. Second purchase (10 shares at $16 per share):

   • You bought these 10 shares after 2 years when the price per share was $16.
   • These shares also earned a dividend of $0.25 per share per quarter for 4 more quarters (from year 3 to year 4).

   Total dividend income for the second 10 shares: $10 \, \text{shares} \times 0.25 \, \text{\$/share} \times 4 \, \text{quarters} = 10 \, \text{\$}$

   Total dividend income over 12 quarters: $20 \, \text{\$} + 10 \, \text{\$} = 30 \, \text{\$}$

Step 2: Calculate the total amount you spent to purchase the stock

1. First purchase (10 shares at $20 per share): $10 \, \text{shares} \times 20 \, \text{\$/share} = 200 \, \text{\$}$

2. Second purchase (10 shares at $16 per share): $10 \, \text{shares} \times 16 \, \text{\$/share} = 160 \, \text{\$}$

   Total amount spent to purchase stock: $200 \, \text{\$} + 160 \, \text{\$} = 360 \, \text{\$}$

Step 3: Calculate the total amount when you sell the stock

After 12 quarters, you sold 20 shares at $23 per share: $20 \, \text{shares} \times 23 \, \text{\$/share} = 460 \, \text{\$}$

Step 4: Calculate the total return

Total amount you received (sale + dividends): $460 \, \text{\$} + 30 \, \text{\$} = 490 \, \text{\$}$

Step 5: Calculate the effective interest rate

Now, we use the formula for the compound interest rate over time, where the amount $A$ is equal to the principal $P$ plus the interest earned:

$A = P \times (1 + r)^n$ Where:

• $A = 490$ (final amount)
• $P = 360$ (initial investment)
• $r$ is the quarterly interest rate
• $n = 12$ (quarters)

Solving for $r$:

$490 = 360 \times (1 + r)^{12}$ $\frac{490}{360} = (1 + r)^{12}$ $1.3611 = (1 + r)^{12}$ $(1 + r) = (1.3611)^{1/12}$ $1 + r \approx 1.0274$ $r \approx 0.0274 \, \text{(quarterly rate)}$

Step 6: Calculate the effective annual interest rate

To find the effective annual interest rate, we compound the quarterly rate over 4 quarters:

$\text{Effective annual rate} = (1 + r)^4 - 1$ $\text{Effective annual rate} = (1.0274)^4 - 1$ $\text{Effective annual rate} \approx 0.1134$

So the effective annual interest rate is approximately: $\boxed{11.34\%}$

Additional Details:

If you'd like further breakdowns or clarification on any steps, feel free to ask!

---

Here are some related questions you might find interesting:

1. How would the interest rate change if you held the stock for a different number of quarters?
2. What happens to the effective annual rate if the stock price increases faster or slower?
3. How can you calculate the future value of an investment with monthly compounding instead of quarterly compounding?
4. What would happen to your return if dividends were taxed?
5. How would the calculation change if you sold part of the stock before the full 12 quarters?

Tip: When dealing with stock investments, make sure to also factor in possible capital gains taxes, especially when selling stock for a profit!