Compound interest on a certain sum of money at 5% per annum for two years is Rs 246. Calculate simple interest on the same sum for 3 years at 6% per annum.

Answer

To solve the problem step by step, we will first find the principal amount using the compound interest formula, and then calculate the simple interest for the given conditions.

### Step 1: Understand the given information
- Compound Interest (CI) = Rs 246
- Rate of Interest (R) = 5% per annum
- Time (T) = 2 years

### Step 2: Use the formula for Compound Interest
The formula for Compound Interest is:
\[ CI = A - P \]
Where:
- \( A \) = Amount after time \( T \)
- \( P \) = Principal amount

We can also express the amount \( A \) using the formula:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]

### Step 3: Substitute the values into the formula
Substituting the known values into the formula for \( A \):
\[ A = P \left(1 + \frac{5}{100}\right)^2 \]
\[ A = P \left(1 + 0.05\right)^2 \]
\[ A = P \left(1.05\right)^2 \]
\[ A = P \times 1.1025 \]

### Step 4: Relate CI to A and P
From the Compound Interest formula:
\[ 246 = A - P \]
Substituting \( A \):
\[ 246 = P \times 1.1025 - P \]
\[ 246 = P(1.1025 - 1) \]
\[ 246 = P \times 0.1025 \]

### Step 5: Solve for Principal (P)
Now, we can solve for \( P \):
\[ P = \frac{246}{0.1025} \]
Calculating \( P \):
\[ P = 2400 \text{ Rs} \]

### Step 6: Calculate Simple Interest (SI)
Now we need to calculate the Simple Interest for 3 years at 6% per annum. The formula for Simple Interest is:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \( P = 2400 \)
- \( R = 6\% \)
- \( T = 3 \)

### Step 7: Substitute the values into the SI formula
Substituting the values:
\[ SI = \frac{2400 \times 6 \times 3}{100} \]
Calculating:
\[ SI = \frac{43200}{100} \]
\[ SI = 432 \text{ Rs} \]

### Final Answer
The Simple Interest on the same sum for 3 years at 6% per annum is **Rs 432**.

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