What is the difference (in Rs.) between compound interest (compounded annually) and simple interest for 3 years on a principal of `Rs. 4000` at the rate of `30% `per annum?

Options

A. 976
B. 1024
C. 1188
D. 1276

Answer

To find the difference between compound interest (CI) and simple interest (SI) for 3 years on a principal of Rs. 4000 at the rate of 30% 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:
- \( P = 4000 \) (Principal)
- \( R = 30 \) (Rate of interest per annum)
- \( T = 3 \) (Time in years)

Substituting the values:
\[ \text{SI} = \frac{4000 \times 30 \times 3}{100} \]
\[ \text{SI} = \frac{4000 \times 90}{100} = \frac{360000}{100} = 3600 \]

### 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:
\[ \text{CI} = 4000 \left(1 + \frac{30}{100}\right)^3 - 4000 \]
\[ \text{CI} = 4000 \left(1 + 0.3\right)^3 - 4000 \]
\[ \text{CI} = 4000 \left(1.3\right)^3 - 4000 \]

Calculating \( (1.3)^3 \):
\[ (1.3)^3 = 1.3 \times 1.3 \times 1.3 = 2.197 \]
Now substituting back:
\[ \text{CI} = 4000 \times 2.197 - 4000 \]
\[ \text{CI} = 8788 - 4000 = 4788 \]

### Step 3: Calculate the Difference
Now we find the difference between CI and SI:
\[ \text{Difference} = \text{CI} - \text{SI} \]
\[ \text{Difference} = 4788 - 3600 = 1188 \]

### Final Answer
The difference between compound interest and simple interest for 3 years on a principal of Rs. 4000 at the rate of 30% per annum is **Rs. 1188**.

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