Which is better investment `4%` stock per with an income tax at the rate of 5 paise per rupee or `(4)1/2%` stock at 110 free from income tax?

Options

A. `4%` at par with income tax
B. `(9)1/2%` at 110
C. `5%`
D. `25%`

Answer

To determine which investment is better, we need to calculate the net income from both options: the 4% stock with income tax and the 4.5% stock that is tax-free.

### Step 1: Calculate the net income from the 4% stock.

1. **Identify the nominal income**:
- The nominal income from the 4% stock is calculated as follows:
\[ \text{Nominal Income} = \text{Face Value} \times \text{Rate of Interest} = 100 \times 0.04 = 4 \text{ Rupees} \]

2. **Calculate the tax**:
- The income tax is 5 paise per rupee, which means for every rupee of income, 0.05 rupees are deducted as tax.
- The tax on the nominal income is:
\[ \text{Tax} = 4 \times 0.05 = 0.20 \text{ Rupees} \]

3. **Calculate the net income**:
- The net income after tax is:
\[ \text{Net Income} = \text{Nominal Income} - \text{Tax} = 4 - 0.20 = 3.80 \text{ Rupees} \]

### Step 2: Calculate the net income from the 4.5% stock.

1. **Identify the nominal income**:
- The nominal income from the 4.5% stock is calculated as follows:
\[ \text{Nominal Income} = \text{Face Value} \times \text{Rate of Interest} = 100 \times 0.045 = 4.5 \text{ Rupees} \]

2. **Since this stock is tax-free**, the net income is equal to the nominal income:
\[ \text{Net Income} = 4.5 \text{ Rupees} \]

### Step 3: Compare the net incomes.

- Net income from the 4% stock (after tax): 3.80 Rupees
- Net income from the 4.5% stock (tax-free): 4.5 Rupees

### Conclusion:
The 4.5% stock at 110 free from income tax is a better investment since it provides a higher net income of 4.5 Rupees compared to 3.80 Rupees from the 4% stock after tax.

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