What is the difference (in Rs) between compound interest and simple interest for 3 years on a principal of Rs 1000 at the rate of 20% per annum?

Options

A. 64
B. 120
C. 128
D. 136

Answer

To find the difference between compound interest (CI) and simple interest (SI) for 3 years on a principal of Rs 1000 at the rate of 20% 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 1000
- \( R \) = Rate of interest = 20%
- \( T \) = Time period in years = 3

Substituting the values:
\[ SI = \frac{1000 \times 20 \times 3}{100} = \frac{60000}{100} = 600 \]

### Step 2: Calculate Compound Interest (CI)
The formula for Compound Interest is:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]
Where \( A \) is the amount after time \( T \).

Substituting the values:
\[ A = 1000 \left(1 + \frac{20}{100}\right)^3 = 1000 \left(1 + 0.2\right)^3 = 1000 \left(1.2\right)^3 \]

Calculating \( (1.2)^3 \):
\[ (1.2)^3 = 1.728 \]
Thus,
\[ A = 1000 \times 1.728 = 1728 \]

Now, to find the Compound Interest:
\[ CI = A - P = 1728 - 1000 = 728 \]

### Step 3: Calculate the Difference between CI and SI
Now we can find the difference:
\[ \text{Difference} = CI - SI = 728 - 600 = 128 \]

### Final Answer
The difference between compound interest and simple interest for 3 years on a principal of Rs 1000 at the rate of 20% per annum is Rs 128.