Find the compound interest (in ₹) on ₹25,000 for 2 years at 6% per annum, the interest being compounded half yearly.

Options

A. 3.137.7/-
B. 3.150/-
C. 3.128.85/-
D. 1.298.25/-

Answer

To find the compound interest on ₹25,000 for 2 years at an interest rate of 6% per annum, compounded half-yearly, we can follow these steps:

### Step 1: Identify the given values
- Principal (P) = ₹25,000
- Rate of interest (R) = 6% per annum
- Time (T) = 2 years

### Step 2: Adjust the rate and time for half-yearly compounding
Since the interest is compounded half-yearly, we need to adjust the rate and time:
- Half-yearly rate = R/2 = 6%/2 = 3%
- Number of compounding periods in 2 years = 2 * 2 = 4 (since there are 2 half-years in each year)

### Step 3: Use the compound interest formula
The formula for compound interest is:
\[ A = P \left(1 + \frac{r}{100}\right)^n \]
Where:
- A = the amount after time T
- P = principal amount
- r = rate of interest per compounding period
- n = total number of compounding periods

Substituting the values:
\[ A = 25000 \left(1 + \frac{3}{100}\right)^4 \]

### Step 4: Calculate the amount
First, calculate \(1 + \frac{3}{100}\):
\[ 1 + \frac{3}{100} = 1 + 0.03 = 1.03 \]

Now, raise it to the power of 4:
\[ A = 25000 \times (1.03)^4 \]

Calculating \( (1.03)^4 \):
\[ (1.03)^4 \approx 1.1255 \]

Now, calculate the total amount:
\[ A = 25000 \times 1.1255 \approx 28138.75 \]

### Step 5: Calculate the compound interest
Compound Interest (CI) is given by:
\[ CI = A - P \]
Substituting the values:
\[ CI = 28138.75 - 25000 \]
\[ CI \approx 3138.75 \]

### Final Answer
The compound interest on ₹25,000 for 2 years at 6% per annum, compounded half-yearly, is approximately ₹3,138.75.

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