What is the difference (in Rs.) in Compound Interest earned in 1 year on a sum of `Rs. 25,000` at `20%` per annum compounded semi-annually and annually?

Options

A. `125 `
B. `250 `
C. `500 `
D. `375 `

Answer

To find the difference in Compound Interest (CI) earned in 1 year on a sum of Rs. 25,000 at 20% per annum compounded semi-annually and annually, we will follow these steps:

### Step 1: Calculate the Compound Interest when compounded semi-annually.

1. **Identify the principal (P)**: Rs. 25,000
2. **Identify the annual interest rate (R)**: 20%
3. **Convert the annual rate to semi-annual rate**:
\[ \text{Semi-annual rate} = \frac{20\%}{2} = 10\% \]
4. **Identify the number of compounding periods (n)**:
\[ n = 2 \text{ (since it is compounded semi-annually for 1 year)} \]
5. **Use the compound interest formula**:
\[ A = P \left(1 + \frac{R}{100}\right)^n \]
Substituting the values:
\[ A = 25000 \left(1 + \frac{10}{100}\right)^2 = 25000 \left(1 + 0.10\right)^2 = 25000 \left(1.10\right)^2 \]
\[ A = 25000 \times 1.21 = 30250 \]
6. **Calculate the Compound Interest (CI)**:
\[ CI = A - P = 30250 - 25000 = 5250 \]

### Step 2: Calculate the Compound Interest when compounded annually.

1. **Use the same principal (P)**: Rs. 25,000
2. **Use the annual interest rate (R)**: 20%
3. **Identify the number of compounding periods (n)**:
\[ n = 1 \text{ (since it is compounded annually for 1 year)} \]
4. **Use the compound interest formula**:
\[ A = P \left(1 + \frac{R}{100}\right)^n \]
Substituting the values:
\[ A = 25000 \left(1 + \frac{20}{100}\right)^1 = 25000 \left(1 + 0.20\right)^1 = 25000 \times 1.20 \]
\[ A = 25000 \times 1.20 = 30000 \]
5. **Calculate the Compound Interest (CI)**:
\[ CI = A - P = 30000 - 25000 = 5000 \]

### Step 3: Find the difference in Compound Interest.

1. **Calculate the difference**:
\[ \text{Difference} = CI_{\text{semi-annually}} - CI_{\text{annually}} = 5250 - 5000 = 250 \]

### Final Answer:
The difference in Compound Interest earned in 1 year on a sum of Rs. 25,000 at 20% per annum compounded semi-annually and annually is **Rs. 250**.

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