I want to purchase a `6%` stock which must yield `5%` on my capital . At what price must I buy the stock?

Options

A. Rs 111
B. Rs 101
C. RS 83.33
D. Rs 120

Answer

To solve the problem of purchasing a 6% stock that must yield 5% on your capital, we can follow these steps:

### Step 1: Understand the Terms
- **6% Stock**: This means that the stock pays 6% of its nominal value (face value) as dividends.
- **Yield**: This is the return on investment expressed as a percentage of the capital invested.

### Step 2: Determine the Dividend Income
To find out how much dividend income you want, we can use the yield percentage. Since the stock is 6%, we can denote the nominal value of the stock as Rs.100 (a common assumption for calculations).

The dividend from the stock would be:
\[ \text{Dividend} = \text{Nominal Value} \times \text{Dividend Rate} = 100 \times \frac{6}{100} = Rs.6 \]

### Step 3: Calculate the Required Investment
You want the stock to yield 5% on your capital. The formula for yield is:
\[ \text{Yield} = \frac{\text{Dividend Income}}{\text{Investment}} \times 100 \]
We need to rearrange this formula to find the investment:
\[ \text{Investment} = \frac{\text{Dividend Income}}{\text{Yield}} \times 100 \]

### Step 4: Substitute the Values
We know the dividend income from the 6% stock is Rs.6 and the desired yield is 5%. Now we can substitute these values into the formula:
\[ \text{Investment} = \frac{6}{5} \times 100 = \frac{600}{5} = Rs.120 \]

### Conclusion
Therefore, to achieve a yield of 5% from a 6% stock, you must buy the stock at Rs.120.

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