What is the difference (in Rs) between compound interest (compounded annually) and simple interest for 3 years on a principal of Rs 3000 at the annual rate of 20%?

Options

A. 464
B. 384
C. 356
D. 424

Answer

To find the difference between compound interest (CI) and simple interest (SI) for a principal amount of Rs 3000 at an annual rate of 20% over 3 years, we will 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 3000
- \( R \) = Rate of interest = 20%
- \( T \) = Time in years = 3

Substituting the values:
\[ SI = \frac{3000 \times 20 \times 3}{100} \]

Calculating:
\[ SI = \frac{3000 \times 60}{100} = \frac{180000}{100} = 1800 \]

### 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 3000
- \( R \) = Rate of interest = 20%
- \( T \) = Time in years = 3

Substituting the values:
\[ CI = 3000 \left(1 + \frac{20}{100}\right)^3 - 3000 \]
\[ CI = 3000 \left(1 + 0.2\right)^3 - 3000 \]
\[ CI = 3000 \left(1.2\right)^3 - 3000 \]

Calculating \( (1.2)^3 \):
\[ (1.2)^3 = 1.728 \]
Thus,
\[ CI = 3000 \times 1.728 - 3000 \]
\[ CI = 5184 - 3000 = 2184 \]

### Step 3: Find the Difference between CI and SI
Now, we will find the difference:
\[ \text{Difference} = CI - SI \]
\[ \text{Difference} = 2184 - 1800 = 384 \]

### Final Answer
The difference between compound interest and simple interest for 3 years on a principal of Rs 3000 at an annual rate of 20% is **Rs 384**.

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