What will be the difference between simple and compound interest on a sum of Rs. 4500 put for 2 years at 5% per annum?

Answer

To find the difference between simple interest (SI) and compound interest (CI) on a sum of Rs. 4500 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:
\[ \text{SI} = \frac{\text{Principal} \times \text{Rate} \times \text{Time}}{100} \]
Substituting the values:
- Principal = Rs. 4500
- Rate = 5%
- Time = 2 years

\[ \text{SI} = \frac{4500 \times 5 \times 2}{100} = \frac{45000}{100} = 450 \text{ Rs.} \]

### Step 2: Calculate Compound Interest (CI)
The formula for Compound Interest is:
\[ \text{CI} = \text{Principal} \times \left(1 + \frac{\text{Rate}}{100}\right)^{\text{Time}} - \text{Principal} \]
Substituting the values:
- Principal = Rs. 4500
- Rate = 5%
- Time = 2 years

Calculating the amount first:
\[ \text{Amount} = 4500 \times \left(1 + \frac{5}{100}\right)^{2} \]
\[ = 4500 \times \left(1 + 0.05\right)^{2} = 4500 \times (1.05)^{2} \]
Calculating \( (1.05)^{2} \):
\[ (1.05)^{2} = 1.1025 \]
Now substituting back:
\[ \text{Amount} = 4500 \times 1.1025 = 4961.25 \text{ Rs.} \]
Now, calculate CI:
\[ \text{CI} = 4961.25 - 4500 = 461.25 \text{ Rs.} \]

### Step 3: Calculate the Difference between CI and SI
Now, we find the difference:
\[ \text{Difference} = \text{CI} - \text{SI} = 461.25 - 450 = 11.25 \text{ Rs.} \]

### Final Answer:
The difference between the compound interest and simple interest on a sum of Rs. 4500 for 2 years at 5% per annum is **Rs. 11.25**.

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