What rate percent is obtained by investing in `7%` stock at 5 discount?

Options

A. `7.35%`
B. `7.55%`
C. `7.05%`
D. `8%`

Answer

To solve the question of what rate percent is obtained by investing in a 7% stock at a 5% discount, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the nominal value of the stock**:
The nominal value (also called face value) of the stock is typically considered to be 100.

**Hint**: Remember that the nominal value is the standard value used for calculations in stock and shares.

2. **Calculate the market value after the discount**:
Since there is a 5% discount on the nominal value of 100, the market value can be calculated as:
\[ \text{Market Value} = \text{Nominal Value} - \text{Discount} = 100 - 5 = 95 \]

**Hint**: The market value is what you actually pay for the stock after the discount.

3. **Determine the rate percent**:
The rate percent can be calculated using the formula:
\[ \text{Rate Percent} = \left( \frac{\text{Dividend}}{\text{Market Value}} \right) \times 100 \]
Here, the dividend is 7% of the nominal value (which is 100), so:
\[ \text{Dividend} = 7\% \text{ of } 100 = 7 \]
Thus, substituting the values into the formula:
\[ \text{Rate Percent} = \left( \frac{7}{95} \right) \times 100 \]

**Hint**: The dividend is the income you receive from the stock, which is based on its nominal value.

4. **Perform the calculation**:
Now, we need to calculate:
\[ \text{Rate Percent} = \frac{7 \times 100}{95} = \frac{700}{95} \]
To simplify this, we can divide both the numerator and denominator:
\[ \frac{700 \div 5}{95 \div 5} = \frac{140}{19} \]

**Hint**: Simplifying fractions can make calculations easier.

5. **Calculate the final value**:
Now, we can perform the division:
\[ 140 \div 19 \approx 7.3684 \]
Rounding this gives us approximately:
\[ \text{Rate Percent} \approx 7.37\% \]

**Hint**: Rounding can help present the final answer in a more understandable form.

### Final Answer:
The rate percent obtained by investing in 7% stock at a 5% discount is approximately **7.37%**.