Find the difference between the simple interest and the compound interest on Rs 5000 for 2 years at 9% per annum.

Answer

To find the difference between the simple interest (SI) and compound interest (CI) on Rs 5000 for 2 years at an interest rate of 9% per annum, 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 5000)
- \( R \) = Rate of interest (9%)
- \( T \) = Time (2 years)

Substituting the values:
\[ SI = \frac{5000 \times 9 \times 2}{100} \]
\[ SI = \frac{90000}{100} \]
\[ SI = 900 \]

### 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:
\[ CI = 5000 \left(1 + \frac{9}{100}\right)^2 - 5000 \]
\[ CI = 5000 \left(1 + 0.09\right)^2 - 5000 \]
\[ CI = 5000 \left(1.09\right)^2 - 5000 \]
Calculating \( (1.09)^2 \):
\[ (1.09)^2 = 1.1881 \]
Now substituting back:
\[ CI = 5000 \times 1.1881 - 5000 \]
\[ CI = 5940.5 - 5000 \]
\[ CI = 940.5 \]

### Step 3: Find the Difference
Now, we find the difference between Compound Interest and Simple Interest:
\[ \text{Difference} = CI - SI \]
Substituting the values:
\[ \text{Difference} = 940.5 - 900 \]
\[ \text{Difference} = 40.5 \]

### Final Answer
The difference between the simple interest and the compound interest on Rs 5000 for 2 years at 9% per annum is Rs 40.5.

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