What will be the difference between simple interest and compound interest on Rs. 2000 after three years at the rate of 10% per annum?

Answer

To find the difference between simple interest (SI) and compound interest (CI) on Rs. 2000 after three years at a rate of 10% per annum, we can follow these steps:

### Step 1: Calculate Simple Interest (SI)
The formula for Simple Interest is:
\[ \text{SI} = \frac{P \times R \times T}{100} \]
Where:
- \( P \) = Principal amount = Rs. 2000
- \( R \) = Rate of interest = 10%
- \( T \) = Time in years = 3

Substituting the values:
\[ \text{SI} = \frac{2000 \times 10 \times 3}{100} = \frac{60000}{100} = 600 \]

### Step 2: Calculate Compound Interest (CI)
The formula for Compound Interest is:
\[ \text{CI} = P \left(1 + \frac{R}{100}\right)^T - P \]
Substituting the values:
\[ \text{CI} = 2000 \left(1 + \frac{10}{100}\right)^3 - 2000 \]
\[ = 2000 \left(1 + 0.1\right)^3 - 2000 \]
\[ = 2000 \left(1.1\right)^3 - 2000 \]
Calculating \( (1.1)^3 \):
\[ (1.1)^3 = 1.331 \]
Now substituting back:
\[ \text{CI} = 2000 \times 1.331 - 2000 = 2662 - 2000 = 662 \]

### Step 3: Calculate the Difference between CI and SI
Now, we find the difference:
\[ \text{Difference} = \text{CI} - \text{SI} \]
\[ = 662 - 600 = 62 \]

### Final Answer
The difference between the compound interest and simple interest on Rs. 2000 after three years at the rate of 10% per annum is Rs. 62.

---