A dividend of `9%` was declared on `100rs` share selling at a certain price. If the rate of return is `7.5%` calculate
(i) the market value of the share
(ii) the amount to be invested to obtain an annual dividend of `630rs`

Answer

To solve the problem step by step, we will break it down into two parts: calculating the market value of the share and then determining the amount to be invested to obtain an annual dividend of Rs. 630.

### Part (i): Calculate the Market Value of the Share

1. **Identify the Given Values:**
- Dividend percentage (D%) = 9%
- Face value of the share (FV) = Rs. 100
- Rate of return (R%) = 7.5%

2. **Use the Formula:**
The relationship between dividend, market value, and rate of return can be expressed as:
\[ \text{Dividend} = \text{Market Value} \times \text{Rate of Return} \]
In terms of percentages, we can write:
\[ \frac{D}{100} \times FV = \frac{R}{100} \times \text{Market Value} \]

3. **Substituting the Values:**
\[ \frac{9}{100} \times 100 = \frac{7.5}{100} \times \text{Market Value} \]
Simplifying this gives:
\[ 9 = \frac{7.5}{100} \times \text{Market Value} \]

4. **Rearranging to Find Market Value:**
\[ \text{Market Value} = \frac{9 \times 100}{7.5} \]

5. **Calculating Market Value:**
\[ \text{Market Value} = \frac{900}{7.5} = 120 \]
Thus, the market value of the share is Rs. 120.

### Part (ii): Calculate the Amount to be Invested for an Annual Dividend of Rs. 630

1. **Identify the Given Annual Dividend:**
- Annual Dividend = Rs. 630

2. **Use the Formula for Investment:**
The amount to be invested can be calculated using the formula:
\[ \text{Amount to be Invested} = \frac{\text{Annual Dividend}}{\text{Rate of Return}} \]
Here, the rate of return should be in decimal form, so we convert 7.5% to decimal:
\[ R = \frac{7.5}{100} = 0.075 \]

3. **Substituting the Values:**
\[ \text{Amount to be Invested} = \frac{630}{0.075} \]

4. **Calculating the Amount:**
\[ \text{Amount to be Invested} = 630 \times \frac{100}{7.5} = 630 \times \frac{100}{7.5} = 8400 \]
Thus, the amount to be invested to obtain an annual dividend of Rs. 630 is Rs. 8400.

### Final Answers:
- (i) Market Value of the Share = Rs. 120
- (ii) Amount to be Invested = Rs. 8400