Find detailed and accurate answers to your questions on IDNLearn.com. Join our Q&A platform to get accurate and thorough answers to all your pressing questions.
Sagot :
To find the rate of change of a portfolio of three stocks over one week, we need to follow a detailed step-by-step approach:
1. Calculate the total value of the portfolio on Day 1:
- For Stock ABC: [tex]\( \text{No. of shares} \times \text{Price per share} = 8000 \times 4.25 = 34000 \)[/tex]
- For Stock XYZ: [tex]\( \text{No. of shares} \times \text{Price per share} = 5000 \times 2.90 = 14500 \)[/tex]
- For Stock QRS: [tex]\( \text{No. of shares} \times \text{Price per share} = 2000 \times 6.40 = 12800 \)[/tex]
Summing these values gives us the total value for Day 1:
[tex]\[ 34000 + 14500 + 12800 = 61300 \][/tex]
2. Calculate the total value of the portfolio on Day 8:
- For Stock ABC: [tex]\( \text{No. of shares} \times \text{Price per share} = 8000 \times 3.90 = 31200 \)[/tex]
- For Stock XYZ: [tex]\( \text{No. of shares} \times \text{Price per share} = 5000 \times 2.50 = 12500 \)[/tex]
- For Stock QRS: [tex]\( \text{No. of shares} \times \text{Price per share} = 2000 \times 6.10 = 12200 \)[/tex]
Summing these values gives us the total value for Day 8:
[tex]\[ 31200 + 12500 + 12200 = 55900 \][/tex]
3. Calculate the rate of change of the portfolio’s value from Day 1 to Day 8:
- The formula for rate of change is:
[tex]\[ \text{Rate of Change} = \left( \frac{\text{Total Value on Day 8} - \text{Total Value on Day 1}}{\text{Total Value on Day 1}} \right) \times 100 \][/tex]
- Plugging in the values:
[tex]\[ \text{Rate of Change} = \left( \frac{55900 - 61300}{61300} \right) \times 100 = \left( \frac{-5400}{61300} \right) \times 100 \approx -8.809135 \][/tex]
4. Round the rate of change to the nearest tenth:
[tex]\[ -8.809135 \approx -8.8 \][/tex]
Therefore, the rate of change of this simple index over one week, rounded to the nearest tenth, is [tex]\(-8.8\%\)[/tex].
The correct answer is:
A. [tex]\(-8.4\%\)[/tex]
B. [tex]\(-7.7\%\)[/tex]
C. [tex]\(7.7\%\)[/tex]
D. [tex]\(8.4\%\)[/tex]
The correct choice is not available, which may be a mistake. However, based on our careful calculations and rounding to the nearest tenth, the correct rate of change should be [tex]\(-8.8\%\)[/tex].
1. Calculate the total value of the portfolio on Day 1:
- For Stock ABC: [tex]\( \text{No. of shares} \times \text{Price per share} = 8000 \times 4.25 = 34000 \)[/tex]
- For Stock XYZ: [tex]\( \text{No. of shares} \times \text{Price per share} = 5000 \times 2.90 = 14500 \)[/tex]
- For Stock QRS: [tex]\( \text{No. of shares} \times \text{Price per share} = 2000 \times 6.40 = 12800 \)[/tex]
Summing these values gives us the total value for Day 1:
[tex]\[ 34000 + 14500 + 12800 = 61300 \][/tex]
2. Calculate the total value of the portfolio on Day 8:
- For Stock ABC: [tex]\( \text{No. of shares} \times \text{Price per share} = 8000 \times 3.90 = 31200 \)[/tex]
- For Stock XYZ: [tex]\( \text{No. of shares} \times \text{Price per share} = 5000 \times 2.50 = 12500 \)[/tex]
- For Stock QRS: [tex]\( \text{No. of shares} \times \text{Price per share} = 2000 \times 6.10 = 12200 \)[/tex]
Summing these values gives us the total value for Day 8:
[tex]\[ 31200 + 12500 + 12200 = 55900 \][/tex]
3. Calculate the rate of change of the portfolio’s value from Day 1 to Day 8:
- The formula for rate of change is:
[tex]\[ \text{Rate of Change} = \left( \frac{\text{Total Value on Day 8} - \text{Total Value on Day 1}}{\text{Total Value on Day 1}} \right) \times 100 \][/tex]
- Plugging in the values:
[tex]\[ \text{Rate of Change} = \left( \frac{55900 - 61300}{61300} \right) \times 100 = \left( \frac{-5400}{61300} \right) \times 100 \approx -8.809135 \][/tex]
4. Round the rate of change to the nearest tenth:
[tex]\[ -8.809135 \approx -8.8 \][/tex]
Therefore, the rate of change of this simple index over one week, rounded to the nearest tenth, is [tex]\(-8.8\%\)[/tex].
The correct answer is:
A. [tex]\(-8.4\%\)[/tex]
B. [tex]\(-7.7\%\)[/tex]
C. [tex]\(7.7\%\)[/tex]
D. [tex]\(8.4\%\)[/tex]
The correct choice is not available, which may be a mistake. However, based on our careful calculations and rounding to the nearest tenth, the correct rate of change should be [tex]\(-8.8\%\)[/tex].
We appreciate your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. Your search for answers ends at IDNLearn.com. Thank you for visiting, and we hope to assist you again soon.