Find the difference between the compound interest and the simple interest on `Rs. 32.000` at `10%` p.a. for 4 years.

Options

A. `Rs. 2051.20`
B. `Rs. 2052.50 `
C. `Rs. 2025.20 `
D. `Rs. 2501.20`

Answer

To find the difference between the compound interest (CI) and the simple interest (SI) on Rs. 32,000 at 10% per annum for 4 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. 32,000
- \(R\) = Rate of interest = 10%
- \(T\) = Time in years = 4 years

Substituting the values:
\[ SI = \frac{32000 \times 10 \times 4}{100} \]
\[ SI = \frac{3200000}{100} = 32000 \]
\[ SI = 12800 \]

### 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. 32,000
- \(R\) = Rate of interest = 10%
- \(T\) = Time in years = 4 years

Substituting the values:
\[ CI = 32000 \left(1 + \frac{10}{100}\right)^4 - 32000 \]
\[ CI = 32000 \left(1 + 0.1\right)^4 - 32000 \]
\[ CI = 32000 \left(1.1\right)^4 - 32000 \]

Now, calculate \( (1.1)^4 \):
\[ (1.1)^4 = 1.4641 \]
So,
\[ CI = 32000 \times 1.4641 - 32000 \]
\[ CI = 46771.2 - 32000 \]
\[ CI = 14771.2 \]

### Step 3: Find the Difference between CI and SI
Now, we find the difference:
\[ \text{Difference} = CI - SI \]
Substituting the values we calculated:
\[ \text{Difference} = 14771.2 - 12800 \]
\[ \text{Difference} = 1971.2 \]

### Final Answer
The difference between the compound interest and the simple interest is **Rs. 1971.2**.

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