A sum fetched a total simple interest of Rs. 4016.25 at the rate of 9 p.c.p.a. in 5 years. What is the sum ?

Options

A. Rs. 4462.50
B. Rs. 8032.50
C. Rs. 8900
D. Rs. 8925

Answer

To find the sum (or principal) that fetched a total simple interest of Rs. 4016.25 at the rate of 9% per annum over 5 years, we can use the formula for calculating simple interest:

### Step-by-Step Solution:

1. **Identify the given values:**
- Total Simple Interest (I) = Rs. 4016.25
- Rate of Interest (R) = 9% per annum
- Time (T) = 5 years

2. **Use the formula for Simple Interest:**
The formula for calculating the principal (P) using simple interest is:
\[ P = \frac{I \times 100}{R \times T} \]

3. **Substitute the known values into the formula:**
\[ P = \frac{4016.25 \times 100}{9 \times 5} \]

4. **Calculate the denominator:**
\[ 9 \times 5 = 45 \]

5. **Now substitute the denominator back into the equation:**
\[ P = \frac{4016.25 \times 100}{45} \]

6. **Calculate \(4016.25 \times 100\):**
\[ 4016.25 \times 100 = 401625 \]

7. **Now divide by 45:**
\[ P = \frac{401625}{45} \]

8. **Perform the division:**
\[ P = 8925 \]

9. **Conclusion:**
The sum (or principal) is Rs. 8925.

### Final Answer:
The sum is Rs. 8925.

---