To determine the rate of change of the simple index over one week, we'll go through the following steps:
1. Calculate the index value on Day 1:
- For Stock ABC:
[tex]\[
\text{Value of ABC on Day 1} = \text{No. of shares} \times \text{Price per share} = 8000 \times 4.25 = 34000
\][/tex]
- For Stock XYZ:
[tex]\[
\text{Value of XYZ on Day 1} = \text{No. of shares} \times \text{Price per share} = 5000 \times 2.90 = 14500
\][/tex]
- For Stock QRS:
[tex]\[
\text{Value of QRS on Day 1} = \text{No. of shares} \times \text{Price per share} = 2000 \times 6.40 = 12800
\][/tex]
- Sum of these values gives the total index value on Day 1:
[tex]\[
\text{Index on Day 1} = 34000 + 14500 + 12800 = 61300
\][/tex]
2. Calculate the index value on Day 8:
- For Stock ABC:
[tex]\[
\text{Value of ABC on Day 8} = \text{No. of shares} \times \text{Price per share} = 8000 \times 3.90 = 31200
\][/tex]
- For Stock XYZ:
[tex]\[
\text{Value of XYZ on Day 8} = \text{No. of shares} \times \text{Price per share} = 5000 \times 2.50 = 12500
\][/tex]
- For Stock QRS:
[tex]\[
\text{Value of QRS on Day 8} = \text{No. of shares} \times \text{Price per share} = 2000 \times 6.10 = 12200
\][/tex]
- Sum of these values gives the total index value on Day 8:
[tex]\[
\text{Index on Day 8} = 31200 + 12500 + 12200 = 55900
\][/tex]
3. Calculate the rate of change of the index:
- The formula to calculate the rate of change is:
[tex]\[
\text{Rate of change} = \frac{\text{Index on Day 8} - \text{Index on Day 1}}{\text{Index on Day 1}} \times 100
\][/tex]
- Plugging in the values:
[tex]\[
\text{Rate of change} = \frac{55900 - 61300}{61300} \times 100 = \frac{-5400}{61300} \times 100 \approx -8.8 \%
\][/tex]
So the rate of change of the index over one week is approximately -8.8%.
Thus, the correct answer is not represented in the given options A, B, C, or D. There seem to be an error in the provided options. The proper rate of change is -8.8%.
