The difference between the simple interest and compound interest (compounded annually) on Rs. 40,000 for 3 years at `8 %` per annum is :

Options

A. a) Rs. 684.32
B. b) Rs. 788 .48
C. c) Rs. 784.58
D. d) Rs. 4000

Answer

To find the difference between the simple interest (SI) and compound interest (CI) on Rs. 40,000 for 3 years at an interest rate of 8% 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:
- \(P = 40,000\) (Principal)
- \(R = 8\%\) (Rate of interest)
- \(T = 3\) (Time in years)

Substituting the values:
\[ \text{SI} = \frac{40,000 \times 8 \times 3}{100} \]
\[ \text{SI} = \frac{40,000 \times 24}{100} \]
\[ \text{SI} = \frac{960,000}{100} = 9,600 \]

### 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:
\[ \text{CI} = 40,000 \left(1 + \frac{8}{100}\right)^3 - 40,000 \]
\[ \text{CI} = 40,000 \left(1 + 0.08\right)^3 - 40,000 \]
\[ \text{CI} = 40,000 \left(1.08\right)^3 - 40,000 \]

Calculating \(1.08^3\):
\[ 1.08^3 = 1.259712 \]
Now substituting back:
\[ \text{CI} = 40,000 \times 1.259712 - 40,000 \]
\[ \text{CI} = 50,388.48 - 40,000 \]
\[ \text{CI} = 10,388.48 \]

### Step 3: Calculate the Difference between CI and SI
Now, we find the difference:
\[ \text{Difference} = \text{CI} - \text{SI} \]
\[ \text{Difference} = 10,388.48 - 9,600 \]
\[ \text{Difference} = 788.48 \]

### Final Answer
The difference between the simple interest and compound interest is Rs. 788.48.

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