Question

suppose there is a simple index of two stocks, stock A and stock B. stock A opens on monday with 10,000 shares at $5.50 per share. stock B opens on monday with 8000 shares at $6.25 per share. stock A opens on tuesday at $5.80 per share, and stock B opens on tuesday at $6.65 per share. both stocks have the same number of shares that they opened with on monday. what is the rate of change of this simple index over 1 day?

-5.9%
5.9%
5.6%
-5.6%

Answer 1

To calculate the rate of change of the simple index over one day, we first need to determine the value of the index at the opening of trading on Monday and again on Tuesday.

### Step 1: Calculate the Index Value on Monday

**Stock A:**
- Shares: 10,000
- Price per Share: $5.50
- Total Value: \(10,000 \times 5.50 = 55,000\)

**Stock B:**
- Shares: 8,000
- Price per Share: $6.25
- Total Value: \(8,000 \times 6.25 = 50,000\)

**Total Index Value on Monday:**
\[
\text{Total Value} = 55,000 + 50,000 = 105,000
\]

### Step 2: Calculate the Index Value on Tuesday

**Stock A:**
- Shares: 10,000
- Price per Share: $5.80
- Total Value: \(10,000 \times 5.80 = 58,000\)

**Stock B:**
- Shares: 8,000
- Price per Share: $6.65
- Total Value: \(8,000 \times 6.65 = 53,200\)

**Total Index Value on Tuesday:**
\[
\text{Total Value} = 58,000 + 53,200 = 111,200
\]

### Step 3: Calculate the Rate of Change

The rate of change can be calculated using the formula:

\[
\text{Rate of Change} = \frac{\text{New Value} - \text{Old Value}}{\text{Old Value}} \times 100\%
\]

Substituting in our values:

- New Value (Tuesday): 111,200
- Old Value (Monday): 105,000

\[
\text{Rate of Change} = \frac{111,200 - 105,000}{105,000} \times 100\%
\]
\[
= \frac{6,200}{105,000} \times 100\%
\]
\[
= 0.05905 \times 100\%
\]
\[
\approx 5.91\%
\]

When rounded, this is approximately \(5.9\%\).

### Conclusion

The rate of change of the simple index over 1 day is **5.9%**.