The compound interest on a sum of money for 3 years at 5% is Rs. 1324.05. What is the simple interest?

Answer

To solve the problem step by step, we need to find the principal amount first using the given compound interest, and then we can calculate the simple interest.

### Step 1: Understand the given data
- Compound Interest (CI) for 3 years = Rs. 1324.05
- Rate of interest (R) = 5%
- Time (T) = 3 years

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

We can also express \( A \) in terms of \( P \):
\[ A = P \left(1 + \frac{R}{100}\right)^T \]

Substituting the values we have:
\[ A = P \left(1 + \frac{5}{100}\right)^3 \]
\[ A = P \left(1.05\right)^3 \]

### Step 3: Calculate \( (1.05)^3 \)
Calculating \( (1.05)^3 \):
\[ (1.05)^3 = 1.157625 \]

### Step 4: Substitute back into the equation for CI
Now we can express the compound interest:
\[ CI = A - P \]
\[ 1324.05 = P \cdot 1.157625 - P \]
\[ 1324.05 = P(1.157625 - 1) \]
\[ 1324.05 = P(0.157625) \]

### Step 5: Solve for Principal (P)
Now, we can solve for \( P \):
\[ P = \frac{1324.05}{0.157625} \]
Calculating this gives:
\[ P \approx 8400 \]

### Step 6: Calculate Simple Interest (SI)
Now that we have the principal amount, we can calculate the Simple Interest using the formula:
\[ SI = \frac{P \cdot R \cdot T}{100} \]
Substituting the values:
\[ SI = \frac{8400 \cdot 5 \cdot 3}{100} \]
\[ SI = \frac{126000}{100} \]
\[ SI = 1260 \]

### Final Answer
The Simple Interest is Rs. 1260.

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