The market value of a share is Rs. 90, itsface value is Rs. 80, and the dividend is 8%. The rate of return is ___________.

Options

A. `8 1/3 %`
B. `7 1/9 %`
C. `6 2/3 %`
D. `5 2/3 %`

Explanation

To find the rate of return based on the given values, we can use the relationship between face value, market value, dividend, and rate of return. Here’s a step-by-step solution:

### Step 1: Understand the given values
- Market Value (MV) = Rs. 90
- Face Value (FV) = Rs. 80
- Dividend Rate = 8%

### Step 2: Calculate the Dividend Amount
The dividend amount can be calculated using the formula:
\[ \text{Dividend Amount} = \text{Face Value} \times \left(\frac{\text{Dividend Rate}}{100}\right) \]
Substituting the values:
\[ \text{Dividend Amount} = 80 \times \left(\frac{8}{100}\right) = 80 \times 0.08 = Rs. 6.4 \]

### Step 3: Use the formula for Rate of Return
The formula relating these values is:
\[ \text{Face Value} \times \text{Dividend Rate} = \text{Market Value} \times \text{Rate of Return} \]
Rearranging this gives us:
\[ \text{Rate of Return} = \frac{\text{Face Value} \times \text{Dividend Rate}}{\text{Market Value}} \]

### Step 4: Substitute the values into the formula
Now substituting the known values:
\[ \text{Rate of Return} = \frac{80 \times 8\%}{90} \]
\[ \text{Rate of Return} = \frac{80 \times 0.08}{90} \]
\[ \text{Rate of Return} = \frac{6.4}{90} \]

### Step 5: Simplify the fraction
To simplify \( \frac{6.4}{90} \):
\[ \text{Rate of Return} = \frac{64}{900} \]

### Step 6: Convert to percentage
Now, to convert this into percentage:
\[ \text{Rate of Return} = \frac{64}{900} \times 100\% \]
\[ \text{Rate of Return} = \frac{6400}{900} \]
Calculating this gives:
\[ \text{Rate of Return} = 7.11\% \]

### Final Answer
Thus, the rate of return is approximately **7.11%**.

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