On what sum will the difference between the simple interest and compound interest for 3 years at 5 per cent per annum amount to Rs 12.20?

Answer

To solve the problem of finding the principal sum (P) on which the difference between the simple interest (SI) and compound interest (CI) for 3 years at 5% per annum amounts to Rs 12.20, we can follow these steps:

### Step 1: Understand the Formula for the Difference between CI and SI
The difference between compound interest and simple interest for 3 years can be calculated using the formula:
\[ \text{Difference} = P \times \frac{R}{100} \times \frac{R}{100} \times \left(3 + 1\right) \]
Where:
- \( P \) is the principal amount,
- \( R \) is the rate of interest (5% in this case),
- The factor \( (3 + 1) \) accounts for the 3 years of interest.

### Step 2: Substitute the Given Values into the Formula
We know from the problem that the difference is Rs 12.20, and the rate \( R \) is 5%. Thus, we can rewrite the equation as:
\[ 12.20 = P \times \frac{5}{100} \times \frac{5}{100} \times 4 \]

### Step 3: Simplify the Equation
Calculating the constants:
\[ \frac{5}{100} \times \frac{5}{100} = \frac{25}{10000} \]
So the equation becomes:
\[ 12.20 = P \times \frac{25}{10000} \times 4 \]
This simplifies to:
\[ 12.20 = P \times \frac{100}{10000} \]
\[ 12.20 = P \times \frac{1}{100} \]

### Step 4: Solve for P
To isolate \( P \), multiply both sides by 100:
\[ P = 12.20 \times 100 \]
\[ P = 1220 \]

### Step 5: Conclusion
Thus, the principal sum on which the difference between the simple interest and compound interest for 3 years at 5% per annum amounts to Rs 12.20 is **Rs 1220**.

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