The simple interest accrued in 2 years on a principal of 24000 is one-eighth the principal. What is the rate of simple interest per cent per annum ?

Options

A. 5
B. `4.5`
C. `6.25`
D. `7.25`

Answer

To solve the problem, we need to find the rate of simple interest per annum given the principal amount, the time period, and the simple interest accrued.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Principal (P) = 24000
- Time (T) = 2 years
- Simple Interest (SI) = One-eighth of the principal = \( \frac{P}{8} \)

2. **Calculate the Simple Interest:**
- Since \( P = 24000 \), we can calculate SI:
\[ SI = \frac{24000}{8} = 3000 \]

3. **Use the Simple Interest Formula:**
- The formula for Simple Interest is:
\[ SI = \frac{P \times R \times T}{100} \]
- Substituting the known values into the formula:
\[ 3000 = \frac{24000 \times R \times 2}{100} \]

4. **Simplify the Equation:**
- First, multiply both sides by 100 to eliminate the fraction:
\[ 3000 \times 100 = 24000 \times R \times 2 \]
\[ 300000 = 48000R \]

5. **Solve for R:**
- Now, divide both sides by 48000:
\[ R = \frac{300000}{48000} \]
- Simplifying this fraction:
\[ R = \frac{3000}{480} = \frac{25}{4} = 6.25 \]

6. **Conclusion:**
- The rate of simple interest per annum is \( R = 6.25\% \).