To determine the rate of change of the simple index over one week, we'll follow these steps:
1. Calculate the total value of each stock on Day 1 and Day 8:
- Stock ABC:
- Day 1: [tex]\( 4000 \times 3.15 = 12600 \)[/tex] dollars
- Day 8: [tex]\( 4000 \times 3.50 = 14000 \)[/tex] dollars
- Stock XYZ:
- Day 1: [tex]\( 5000 \times 4.30 = 21500 \)[/tex] dollars
- Day 8: [tex]\( 5000 \times 3.90 = 19500 \)[/tex] dollars
- Stock QRS:
- Day 1: [tex]\( 6000 \times 4.60 = 27600 \)[/tex] dollars
- Day 8: [tex]\( 6000 \times 4.50 = 27000 \)[/tex] dollars
2. Sum up the total values for each day:
- Total value on Day 1:
[tex]\[
12600 + 21500 + 27600 = 61700 \text{ dollars}
\][/tex]
- Total value on Day 8:
[tex]\[
14000 + 19500 + 27000 = 60500 \text{ dollars}
\][/tex]
3. Calculate the rate of change of the index: The rate of change is calculated as follows:
[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]
Substitute the values:
[tex]\[
\text{Rate of change} = \left( \frac{60500 - 61700}{61700} \right) \times 100
\][/tex]
[tex]\[
\text{Rate of change} = \left( \frac{-1200}{61700} \right) \times 100 \approx -1.9\%
\][/tex]
4. Round the rate of change to the nearest tenth:
The rate of change to the nearest tenth is [tex]\(-1.9\%\)[/tex].
Thus, the rate of change of the simple index over one week is [tex]\(\boxed{-1.9\%}\)[/tex]. Therefore, the correct answer is not listed in the options provided. Please confirm the choices or the problem details.
