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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].
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