Find the compound interest on ₹ 1,60,000 at 10% per annum for 2 years, compounded semi annually.

Options

A. ₹ 34,500
B. ₹ 35,000
C. ₹ 34,481
D. ₹ 30,000

Answer

To find the compound interest on ₹ 1,60,000 at 10% per annum for 2 years, compounded semi-annually, we can follow these steps:

### Step 1: Identify the Variables
- Principal (P) = ₹ 1,60,000
- Rate of interest (r) = 10% per annum = 10/100 = 0.10
- Time (t) = 2 years
- Compounding frequency (n) = 2 (since it is compounded semi-annually)

### Step 2: Calculate the Total Number of Compounding Periods
The total number of compounding periods (N) can be calculated as:
\[ N = n \times t = 2 \times 2 = 4 \]

### Step 3: Calculate the Effective Rate per Compounding Period
The effective rate per compounding period (R) is given by:
\[ R = \frac{r}{n} = \frac{10\%}{2} = 5\% = \frac{5}{100} = 0.05 \]

### Step 4: Use the Compound Interest Formula
The formula for compound interest is:
\[ A = P \left(1 + R\right)^N \]
Where:
- A = Amount after N compounding periods
- P = Principal
- R = Effective rate per compounding period
- N = Total number of compounding periods

Substituting the values:
\[ A = 1,60,000 \left(1 + 0.05\right)^4 \]
\[ A = 1,60,000 \left(1.05\right)^4 \]

### Step 5: Calculate \( (1.05)^4 \)
Now, we calculate \( (1.05)^4 \):
\[ (1.05)^4 = 1.21550625 \]

### Step 6: Calculate the Amount (A)
Now substitute back to find A:
\[ A = 1,60,000 \times 1.21550625 \]
\[ A = 1,94,481 \]

### Step 7: Calculate the Compound Interest (CI)
To find the compound interest, we subtract the principal from the amount:
\[ CI = A - P \]
\[ CI = 1,94,481 - 1,60,000 \]
\[ CI = 34,481 \]

### Final Answer
The compound interest on ₹ 1,60,000 at 10% per annum for 2 years, compounded semi-annually, is ₹ 34,481.

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