A divident of `9%` was declear on Rs 100 shares selling at a certain price. If the rate of return is `7.5%,` calclate:
the amount to be invested to obtain an annual dividend of Rs 1,260.

Answer

To solve the problem step by step, we will follow the instructions given in the video transcript and apply the relevant formulas.

### Step 1: Understand the given data
- **Dividend Rate**: 9%
- **Face Value of Shares**: Rs 100
- **Rate of Return**: 7.5%
- **Desired Annual Dividend**: Rs 1,260

### Step 2: Calculate the Market Value of the Shares
We can use the formula that relates face value, dividend, market value, and rate of return:

\[ \text{Face Value} \times \text{Dividend Rate} = \text{Market Value} \times \text{Rate of Return} \]

Substituting the known values:

\[ 100 \times 9\% = \text{Market Value} \times 7.5\% \]

This can be rewritten as:

\[ 100 \times \frac{9}{100} = \text{Market Value} \times \frac{7.5}{100} \]

Simplifying further:

\[ 9 = \text{Market Value} \times 0.075 \]

Now, solving for Market Value:

\[ \text{Market Value} = \frac{9}{0.075} = 120 \text{ Rs} \]

### Step 3: Calculate the Amount to be Invested for the Desired Annual Dividend
We know the formula for calculating the amount to be invested based on the desired annual dividend and the rate of return:

\[ \text{Amount to be Invested} = \frac{\text{Desired Annual Dividend}}{\text{Rate of Return}} \times 100 \]

Substituting the known values:

\[ \text{Amount to be Invested} = \frac{1260}{7.5\%} = \frac{1260}{0.075} \]

Calculating the amount:

\[ \text{Amount to be Invested} = 1260 \times \frac{100}{7.5} = 1260 \times \frac{100}{7.5} = 16800 \text{ Rs} \]

### Final Answer
The amount to be invested to obtain an annual dividend of Rs 1,260 is **Rs 16,800**.

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