What is the Compound Interest on Rs. 20,000 at `12%` interest for 1 year, compounded half - yearly ?

Options

A. Rs. 2,982
B. Rs. 2,742
C. Rs. 2,472
D. Rs. 4,274

Answer

To calculate the Compound Interest (CI) on Rs. 20,000 at a rate of 12% per annum compounded half-yearly for 1 year, we can follow these steps:

### Step 1: Identify the principal amount, rate of interest, and time period.
- Principal (P) = Rs. 20,000
- Annual Rate of Interest (R) = 12%
- Time (T) = 1 year

### Step 2: Adjust the rate and time for half-yearly compounding.
Since the interest is compounded half-yearly:
- The half-yearly rate = 12% / 2 = 6%
- The number of compounding periods in 1 year = 2 (since it's compounded every 6 months)

### Step 3: Use the compound interest formula.
The formula for compound interest is:
\[ A = P \left(1 + \frac{r}{100}\right)^{nt} \]
Where:
- \( A \) = the amount after time \( t \)
- \( P \) = principal amount
- \( r \) = annual interest rate
- \( n \) = number of times interest is compounded per year
- \( t \) = time in years

Substituting the values:
- \( P = 20000 \)
- \( r = 6 \) (half-yearly rate)
- \( n = 2 \) (compounding periods)
- \( t = 1 \)

### Step 4: Calculate the total amount (A).
\[ A = 20000 \left(1 + \frac{6}{100}\right)^{2 \times 1} \]
\[ A = 20000 \left(1 + 0.06\right)^{2} \]
\[ A = 20000 \left(1.06\right)^{2} \]
\[ A = 20000 \times 1.1236 \]
\[ A = 22472 \]

### Step 5: Calculate the Compound Interest (CI).
Compound Interest (CI) is given by:
\[ CI = A - P \]
\[ CI = 22472 - 20000 \]
\[ CI = 2472 \]

### Final Answer:
The Compound Interest on Rs. 20,000 at 12% interest for 1 year, compounded half-yearly, is **Rs. 2472**.

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