If the interest is compounded half-yearly, then what will be the compound interest (in Rs) on a sum of Rs 10000 for 1 year at the rate of 10% per annum?

Options

A. 1250
B. 525
C. 1000
D. 1025

Answer

To calculate the compound interest when the interest is compounded half-yearly, we can follow these steps:

### Step 1: Identify the given values
- Principal (P) = Rs 10,000
- Rate of interest (R) = 10% per annum
- 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:
- The rate for half a year = R/2 = 10% / 2 = 5%
- The 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 we have:
- P = 10,000
- r = 5%
- n = 2

So, the formula becomes:
\[ A = 10000 \left(1 + \frac{5}{100}\right)^2 \]

### Step 4: Calculate the amount (A)
Calculating inside the parentheses:
\[ A = 10000 \left(1 + 0.05\right)^2 \]
\[ A = 10000 \left(1.05\right)^2 \]
\[ A = 10000 \times 1.1025 \]
\[ A = 11025 \]

### Step 5: Calculate the compound interest (CI)
The compound interest is given by:
\[ CI = A - P \]
Substituting the values:
\[ CI = 11025 - 10000 \]
\[ CI = 1025 \]

### Final Answer
The compound interest on a sum of Rs 10,000 for 1 year at the rate of 10% per annum, compounded half-yearly, is **Rs 1025**.

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