The difference of S.I and C.I on a sum at 5% per annum for 3 years is Rs. 36.60. Find the sum.

Answer

To solve the problem, we need to find the principal amount (sum) based on the difference between Simple Interest (SI) and Compound Interest (CI) over a period of 3 years at a rate of 5% per annum, which is given as Rs. 36.60.

### Step-by-Step Solution:

1. **Understand the Formula for SI and CI**:
- Simple Interest (SI) for 3 years can be calculated using the formula:
\[ SI = \frac{P \times R \times T}{100} \]
where \( P \) is the principal, \( R \) is the rate of interest, and \( T \) is the time in years.
- Compound Interest (CI) can be calculated using the formula:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]
where \( A \) is the amount after time \( T \).

2. **Calculate the SI for 3 Years**:
- Given \( R = 5\% \) and \( T = 3 \):
\[ SI = \frac{P \times 5 \times 3}{100} = \frac{15P}{100} = 0.15P \]

3. **Calculate the CI for 3 Years**:
- Using the formula for CI:
\[ A = P \left(1 + \frac{5}{100}\right)^3 = P \left(1.05\right)^3 \]
- Calculate \( (1.05)^3 \):
\[ (1.05)^3 = 1.157625 \]
- Therefore, the amount \( A \) becomes:
\[ A = P \times 1.157625 \]
- The Compound Interest (CI) is given by:
\[ CI = A - P = P \times 1.157625 - P = P(1.157625 - 1) = P \times 0.157625 \]

4. **Find the Difference Between CI and SI**:
- The difference between CI and SI is given as:
\[ CI - SI = P \times 0.157625 - P \times 0.15 = P(0.157625 - 0.15) = P \times 0.007625 \]
- We know from the problem that this difference equals Rs. 36.60:
\[ P \times 0.007625 = 36.60 \]

5. **Solve for Principal \( P \)**:
- Rearranging the equation to find \( P \):
\[ P = \frac{36.60}{0.007625} \]
- Calculating the value:
\[ P \approx 4800 \]

### Final Answer:
The principal amount (sum) is Rs. 4800.