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To calculate the price at which you must sell the stock in order to achieve a total return of 11.4%, we can use the following formula for total return:

\[
\text{Total Return} = \frac{(P_{\text{sell}} - P_{\text{buy}} + \text{Dividends})}{P_{\text{buy}}}
\]

Where:
- $ P_{\text{sell}} $ is the price at which you sell the stock (which we need to find),
- $ P_{\text{buy}} = 22 $ is the purchase price of the stock,
- Dividends = 1.05, and
- Total Return = 11.4% = 0.114.

Substituting the known values into the equation:

\[
0.114 = \frac{(P_{\text{sell}} - 22 + 1.05)}{22}
\]

Simplify the equation:

\[
0.114 = \frac{P_{\text{sell}} - 20.95}{22}
\]

Now, multiply both sides by 22 to eliminate the denominator:

\[
0.114 \times 22 = P_{\text{sell}} - 20.95
\]
\[
2.508 = P_{\text{sell}} - 20.95
\]

Add 20.95 to both sides to solve for $ P_{\text{sell}} $:

\[
P_{\text{sell}} = 2.508 + 20.95 = 23.46
\]

Therefore, you must sell the stock at **$23.46** to achieve a total return of 11.4%.

Would you like more explanation on any step, or do you have any other questions?

Here are five related questions:
1. How would the required selling price change if the dividend were higher?
2. What is the formula for total return if there were no dividends?
3. How is total return different from capital gains return?
4. What is the significance of total return when comparing different investments?
5. How do fluctuations in stock prices affect the dividend yield?

**Tip:** Always account for dividends when calculating total return, as they are a crucial part of the stock's profitability.

You purchased a stock one year ago for $22. You just received a dividend of $1.05. In order to realize a total return of 11.4%, at what price must you sell the stock? Round your answer to the nearest penny.

Find out how to calculate the stock selling price needed to achieve a total return of 11.4%. This problem involves percentage calculations, dividend inclusion, and algebraic manipulation. Suitable for high school students in Grades 9-12.

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