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

Answer

To find 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, we will follow these steps:

### Step 1: Calculate Compound Interest for Annual Compounding

1. **Identify the variables:**
- Principal (P) = Rs 25,000
- Rate (R) = 20% per annum
- Time (T) = 1 year

2. **Use the formula for compound interest:**
\[ A = P \left(1 + \frac{R}{100}\right)^T \]
\[ A = 25000 \left(1 + \frac{20}{100}\right)^1 \]
\[ A = 25000 \left(1 + 0.2\right)^1 \]
\[ A = 25000 \times 1.2 = 30000 \]

3. **Calculate the compound interest (CI):**
\[ CI = A - P \]
\[ CI = 30000 - 25000 = 5000 \]

### Step 2: Calculate Compound Interest for Semi-Annual Compounding

1. **Identify the variables:**
- Principal (P) = Rs 25,000
- Rate (R) = 20% per annum (10% per half-year)
- Time (T) = 1 year = 2 half-years

2. **Use the formula for compound interest:**
\[ A = P \left(1 + \frac{R/2}{100}\right)^{2T} \]
\[ A = 25000 \left(1 + \frac{20/2}{100}\right)^{2 \times 1} \]
\[ A = 25000 \left(1 + \frac{10}{100}\right)^2 \]
\[ A = 25000 \left(1 + 0.1\right)^2 \]
\[ A = 25000 \times (1.1)^2 \]
\[ A = 25000 \times 1.21 = 30250 \]

3. **Calculate the compound interest (CI):**
\[ CI = A - P \]
\[ CI = 30250 - 25000 = 5250 \]

### Step 3: Calculate the Difference in Compound Interest

1. **Find the difference between the two compound interests:**
\[ \text{Difference} = CI_{\text{semi-annual}} - CI_{\text{annual}} \]
\[ \text{Difference} = 5250 - 5000 = 250 \]

### 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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