The difference between compound interest and simple interest on Rs. 10000 for 3 years at 5% per annum is :

Answer

To find the difference between compound interest (CI) and simple interest (SI) on Rs. 10,000 for 3 years at an interest rate of 5% per annum, we can follow these steps:

### Step 1: Calculate Simple Interest (SI)

The formula for Simple Interest is:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \( P \) = Principal amount (Rs. 10,000)
- \( R \) = Rate of interest (5%)
- \( T \) = Time period (3 years)

Substituting the values:
\[ SI = \frac{10000 \times 5 \times 3}{100} = \frac{150000}{100} = 1500 \]

### Step 2: Calculate Compound Interest (CI)

The formula for Compound Interest is:
\[ CI = P \left(1 + \frac{R}{100}\right)^T - P \]
Where:
- \( P \) = Principal amount (Rs. 10,000)
- \( R \) = Rate of interest (5%)
- \( T \) = Time period (3 years)

Substituting the values:
\[ CI = 10000 \left(1 + \frac{5}{100}\right)^3 - 10000 \]
Calculating \( \left(1 + \frac{5}{100}\right)^3 \):
\[ = 10000 \left(1.05\right)^3 - 10000 \]
Calculating \( (1.05)^3 \):
\[ (1.05)^3 = 1.157625 \]
Now substituting back:
\[ CI = 10000 \times 1.157625 - 10000 = 11576.25 - 10000 = 1576.25 \]

### Step 3: Calculate the Difference between CI and SI

Now, we find the difference:
\[ \text{Difference} = CI - SI = 1576.25 - 1500 = 76.25 \]

### Final Answer

The difference between the compound interest and simple interest on Rs. 10,000 for 3 years at 5% per annum is Rs. 76.25.

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