Consider an investment that pays off $700 or $1,600 per $1,000 invested with equal probability. Suppose you have $1,000 but are willing to borrow to increase your expected return. What would happen to the expected value and standard deviation of the investment if you borrowed an additional $1,000 and invested a total of $2,000? What if you borrowed $2,000 to invest a total of $3,000? Instructions: Fill in the table below to answer the questions above. Enter your responses as whole numbers and enter percentage values as percentages not decimals (.e., 20% not 0.20). Enter a negative sign (-) to indicate a negative number if necessary. Invest $1,000 Invest $2,000 Invest $3,000 Expected Value Percent Increase Standard Deviation $ 1150 28 % $ 8 B $ Expected Return N/A Doubled Tripled :

ENGR.ECONOMIC ANALYSIS
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Chapter1: Making Economics Decisions
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**Investment Analysis Exercise**

Consider an investment that pays off $700 or $1,600 per $1,000 invested with equal probability. Suppose you have $1,000 but are willing to borrow to increase your expected return. 

- What would happen to the expected value and standard deviation of the investment if you borrowed an additional $1,000 and invested a total of $2,000?
- What if you borrowed $2,000 to invest a total of $3,000?

**Instructions:** Fill in the table below to answer the questions above. Enter your responses as whole numbers and enter percentage values as percentages, not decimals (i.e., 20% not 0.20). Enter a negative sign (-) to indicate a negative number if necessary.

| Investment Amount | Expected Value | Percent Increase | Standard Deviation | Expected Return |
|-------------------|----------------|------------------|--------------------|-----------------|
| Invest $1,000     |    $1150       |      15%         |      450            |      N/A        |
| Invest $2,000     |                |                  |                    |     Doubled     |
| Invest $3,000     |                |                  |                    |      Tripled    |

- **Expected Value:** The average value of the possible outcomes of the investment.
- **Percent Increase:** The percentage change in the expected value compared to the initial investment.
- **Standard Deviation:** A measure of the amount of variation or dispersion of the possible outcomes.
- **Expected Return:** How the return on investment compares to the initial investment. 

To start, use the following formulas:
- **Expected Value**: \[(\text{Probability of Outcome 1} \times \text{Value of Outcome 1}) + (\text{Probability of Outcome 2} \times \text{Value of Outcome 2})\]
- **Standard Deviation**: Calculate the square root of the variance of the returns.
- **Expected Return**: The ratio between the investment increase and the initial amount invested.

Make sure to follow these steps carefully and input the correct values in the table based on your calculations.
Transcribed Image Text:**Investment Analysis Exercise** Consider an investment that pays off $700 or $1,600 per $1,000 invested with equal probability. Suppose you have $1,000 but are willing to borrow to increase your expected return. - What would happen to the expected value and standard deviation of the investment if you borrowed an additional $1,000 and invested a total of $2,000? - What if you borrowed $2,000 to invest a total of $3,000? **Instructions:** Fill in the table below to answer the questions above. Enter your responses as whole numbers and enter percentage values as percentages, not decimals (i.e., 20% not 0.20). Enter a negative sign (-) to indicate a negative number if necessary. | Investment Amount | Expected Value | Percent Increase | Standard Deviation | Expected Return | |-------------------|----------------|------------------|--------------------|-----------------| | Invest $1,000 | $1150 | 15% | 450 | N/A | | Invest $2,000 | | | | Doubled | | Invest $3,000 | | | | Tripled | - **Expected Value:** The average value of the possible outcomes of the investment. - **Percent Increase:** The percentage change in the expected value compared to the initial investment. - **Standard Deviation:** A measure of the amount of variation or dispersion of the possible outcomes. - **Expected Return:** How the return on investment compares to the initial investment. To start, use the following formulas: - **Expected Value**: \[(\text{Probability of Outcome 1} \times \text{Value of Outcome 1}) + (\text{Probability of Outcome 2} \times \text{Value of Outcome 2})\] - **Standard Deviation**: Calculate the square root of the variance of the returns. - **Expected Return**: The ratio between the investment increase and the initial amount invested. Make sure to follow these steps carefully and input the correct values in the table based on your calculations.
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