A man invest in `(4)1/2%` stock at 96. the interest obtained by him is

Options

A. `4%`
B. `4.5%`
C. `4.69%`
D. `1/2%`

Answer

To solve the problem of calculating the interest obtained from a `(4)1/2%` stock at a price of 96, we can follow these steps:

### Step 1: Convert the percentage to a fraction
The stock is given as `4 1/2%`, which can be converted to an improper fraction:
\[ 4 \frac{1}{2} = \frac{9}{2} \% \]

### Step 2: Calculate the nominal value of the stock
The nominal value of the stock is typically considered to be 100. Therefore, the interest on the nominal value can be calculated as follows:
\[ \text{Interest} = \frac{9}{2} \% \text{ of } 100 = \frac{9}{2} = 4.5 \]

### Step 3: Calculate the investment amount
The man invests in the stock at 96. This means he pays 96 for a nominal value of 100.

### Step 4: Calculate the actual income from the investment
To find the income based on the amount invested (96), we can set up the following proportion:
\[ \text{Income} = \left(\frac{\text{Nominal Interest}}{\text{Nominal Value}}\right) \times \text{Investment} \]
Substituting the values we have:
\[ \text{Income} = \left(\frac{4.5}{100}\right) \times 96 \]

### Step 5: Perform the calculation
Now we can calculate the income:
\[ \text{Income} = \frac{4.5 \times 96}{100} = \frac{432}{100} = 4.32 \]

### Step 6: Conclusion
Thus, the interest obtained by the man from his investment in the stock is `4.32`.

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