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 :
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 :
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9c9e2dde-1c19-44ed-a9d3-170191d095c3%2F5c1ab593-1e86-47dc-8db5-27e0f0cc173b%2Ffn8ituv_processed.jpeg&w=3840&q=75)
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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