Find the difference between compound interest and simple interest on Rs 8,000 in 2 years and at 5% per annum.

Answer

To find the difference between compound interest (CI) and simple interest (SI) on Rs 8,000 for 2 years at an interest rate of 5% 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 8,000)
- \(R\) = Rate of interest (5%)
- \(T\) = Time period in years (2 years)

Substituting the values:
\[ SI = \frac{8000 \times 5 \times 2}{100} = \frac{80000}{100} = 800 \]

### Step 2: Calculate Compound Interest (CI)
The formula for Compound Interest is:
\[ CI = P \left(1 + \frac{R}{100}\right)^T - P \]
Substituting the values:
\[ CI = 8000 \left(1 + \frac{5}{100}\right)^2 - 8000 \]
Calculating inside the parentheses:
\[ CI = 8000 \left(1 + 0.05\right)^2 - 8000 = 8000 \left(1.05\right)^2 - 8000 \]
Calculating \( (1.05)^2 \):
\[ (1.05)^2 = 1.1025 \]
Now substituting back:
\[ CI = 8000 \times 1.1025 - 8000 = 8820 - 8000 = 820 \]

### Step 3: Find the Difference between CI and SI
Now we can find the difference:
\[ \text{Difference} = CI - SI = 820 - 800 = 20 \]

### Final Answer
The difference between compound interest and simple interest on Rs 8,000 in 2 years at 5% per annum is Rs 20.

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