Find what sum of money 1 must invest in a 10 percent stock at 102 to obtain an income of RS 400 per year

Options

A. Rs 4800
B. Rs 8040
C. Rs 4080
D. Rs 8400

Answer

To solve the problem of finding the sum of money that must be invested in a 10% stock at 102 to obtain an income of Rs 400 per year, we can follow these steps:

### Step 1: Understand the terms
- **Stock Percentage**: The stock is 10%, which means for every Rs 100 of face value, the stock pays Rs 10 as dividend.
- **Market Price**: The stock is priced at Rs 102 in the market.
- **Desired Income**: The desired income is Rs 400 per year.

### Step 2: Calculate the annual income from the investment
The income from the investment can be calculated using the formula:
\[ \text{Income} = \text{Investment} \times \left(\frac{\text{Dividend Rate}}{100}\right) \]
In this case, the dividend rate is 10%.

### Step 3: Set up the equation
Let \( x \) be the amount of money invested. The income from this investment will be:
\[ \text{Income} = x \times \left(\frac{10}{100}\right) = 0.1x \]
We want this income to equal Rs 400:
\[ 0.1x = 400 \]

### Step 4: Solve for \( x \)
To find \( x \), we can rearrange the equation:
\[ x = \frac{400}{0.1} = 4000 \]

### Step 5: Conclusion
Thus, the sum of money that must be invested in the 10% stock at 102 to obtain an income of Rs 400 per year is **Rs 4000**.

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