You recently purchased a stock that is expected to earn 19 percent in a booming economy, 14 percent in a normal economy, and lose 3 percent in a recessionary economy. There is 21 percent probability of a boom, 70 percent chance of a normal economy, and 9 percent chance of a recession. What is your expected rate of return on this stock?

To calculate the expected rate of return on the stock, you can use the formula for expected value, which is:

\[
\text{Expected Return} = (P_1 \times R_1) + (P_2 \times R_2) + (P_3 \times R_3)
\]

Where:
- \(P_1, P_2, P_3\) are the probabilities of each economic condition.
- \(R_1, R_2, R_3\) are the respective returns for each condition.

In this case:
- \(P_1 = 0.21\) (probability of a boom),
- \(R_1 = 19\%\) (return in a booming economy),
- \(P_2 = 0.70\) (probability of a normal economy),
- \(R_2 = 14\%\) (return in a normal economy),
- \(P_3 = 0.09\) (probability of a recession),
- \(R_3 = -3\%\) (loss in a recessionary economy).

Now, plug in the values:

\[
\text{Expected Return} = (0.21 \times 19\%) + (0.70 \times 14\%) + (0.09 \times -3\%)
\]

First, compute each term:

\[
0.21 \times 19\% = 3.99\%
\]
\[
0.70 \times 14\% = 9.8\%
\]
\[
0.09 \times -3\% = -0.27\%
\]

Now, sum them up:

\[
\text{Expected Return} = 3.99\% + 9.8\% - 0.27\% = 13.52\%
\]

Therefore, the expected rate of return on the stock is **13.52%**.

Would you like further details on this calculation, or do you have any other questions?

### Related Questions:
1. How does the expected return change if the probability of a boom increases?
2. What is the variance and standard deviation of this stock's returns?
3. How does diversification affect expected return in this context?
4. What role does probability play in financial risk assessments?
5. How would changing the recession probability to 15% affect the expected return?

**Tip:** Expected return calculations are useful for assessing potential outcomes, but don't forget to also consider the risk (variance) associated with the investment.

Learn how to calculate the expected rate of return on a stock based on varying economic conditions, including probabilities of a boom, normal economy, and recession. This example covers probability concepts, percentage calculations, and the law of total probability, suitable for students in Grades 10-12.

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