A bank offers an interest of 10% per annum which is compounded half yearly. Krishan invests Rs.10000, what is the total amount he will earn after 2 years? (approximately)

Options

A. Rs 14,641
B. Rs 12,155
C. Rs 11,011
D. Rs 13,000

Answer

To find the total amount Krishan will earn after 2 years with an investment of Rs. 10,000 at an interest rate of 10% per annum compounded half yearly, we can follow these steps:

### Step 1: Determine the effective rate and time period
Since the interest is compounded half yearly, we need to adjust the interest rate and the time period:
- The annual interest rate is 10%. Therefore, the half-yearly interest rate is:
\[ R = \frac{10\%}{2} = 5\% \]
- The time period of 2 years will be doubled because it is compounded half yearly:
\[ T = 2 \text{ years} \times 2 = 4 \text{ half-year periods} \]

### Step 2: Use the compound interest formula
The formula for the total amount \( A \) after \( T \) years with principal \( P \), rate \( R \), and time \( T \) is given by:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]
Substituting the values we have:
- \( P = 10,000 \)
- \( R = 5 \)
- \( T = 4 \)

So, we can write:
\[ A = 10,000 \left(1 + \frac{5}{100}\right)^4 \]

### Step 3: Simplify the expression
Calculating \( 1 + \frac{5}{100} \):
\[ 1 + \frac{5}{100} = 1 + 0.05 = 1.05 \]
Now we can substitute this back into the formula:
\[ A = 10,000 \times (1.05)^4 \]

### Step 4: Calculate \( (1.05)^4 \)
Now we need to calculate \( (1.05)^4 \):
\[ (1.05)^4 = 1.21550625 \quad \text{(approximately)} \]

### Step 5: Calculate the total amount
Now substituting back into the equation for \( A \):
\[ A \approx 10,000 \times 1.21550625 \approx 12,155.06 \]

### Step 6: Round off the total amount
Rounding off the total amount, we find:
\[ A \approx 12,155 \]

### Final Answer
Thus, the total amount Krishan will earn after 2 years is approximately Rs. 12,155.

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