What will be the compound interest on a sum of Rs 22,500 at the rate of 16% per annum for 1 year, when interest is compounded half yearly?

Options

A. Rs. 3,744
B. Rs. 3,700
C. Rs. 3,600
D. Rs. 36,244

Answer

To calculate the compound interest on a sum of Rs 22,500 at the rate of 16% per annum for 1 year, when the interest is compounded half-yearly, we can follow these steps:

### Step 1: Identify the principal amount, rate of interest, and time period.
- Principal (P) = Rs 22,500
- Annual Rate of Interest (R) = 16%
- Time (T) = 1 year

### 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 = 16% / 2 = 8%
- Number of compounding periods in 1 year = 2

### 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 period
- n = number of compounding periods

Substituting the values:
- \( A = 22500 \left(1 + \frac{8}{100}\right)^2 \)

### Step 4: Calculate the amount (A).
First, calculate \( 1 + \frac{8}{100} = 1 + 0.08 = 1.08 \).
Now, calculate \( A \):
\[ A = 22500 \times (1.08)^2 \]
\[ A = 22500 \times 1.1664 \]
\[ A = 26244 \]

### Step 5: Calculate the compound interest (CI).
Compound Interest (CI) is given by:
\[ CI = A - P \]
Substituting the values:
\[ CI = 26244 - 22500 \]
\[ CI = 3744 \]

### Final Answer:
The compound interest on Rs 22,500 at the rate of 16% per annum for 1 year, compounded half-yearly, is Rs 3,744.

---