A sum of Rs 5000 is invested at a scheme of compound interest. The interest rate is 20%. If the interest is compounded half yearly, then what is interest (in Rs) after 1 year?

Options

A. b. 1000
B. b. 2200
C. c. 1500
D. d. 1050

Answer

To find the compound interest earned on an investment of Rs 5000 at an interest rate of 20% compounded half-yearly after 1 year, we can follow these steps:

### Step 1: Identify the given values
- Principal amount (P) = Rs 5000
- Rate of interest (R) = 20%
- Time period (T) = 1 year
- Compounding frequency (N) = 2 (since it is compounded half-yearly)

### Step 2: Use the formula for compound interest
The formula for compound interest is:
\[ A = P \left(1 + \frac{R}{100N}\right)^{NT} \]
Where:
- \( A \) = the amount after time \( T \)
- \( P \) = principal amount
- \( R \) = rate of interest
- \( N \) = number of times interest is compounded per year
- \( T \) = time in years

### Step 3: Substitute the values into the formula
Substituting the known values into the formula:
\[ A = 5000 \left(1 + \frac{20}{100 \times 2}\right)^{2 \times 1} \]

### Step 4: Simplify the expression
First, calculate \( \frac{20}{100 \times 2} \):
\[ \frac{20}{200} = \frac{1}{10} \]
Now, substitute this back into the equation:
\[ A = 5000 \left(1 + \frac{1}{10}\right)^{2} \]
\[ A = 5000 \left(1.1\right)^{2} \]

### Step 5: Calculate \( (1.1)^{2} \)
\[ (1.1)^{2} = 1.21 \]
Now substitute this value back into the equation:
\[ A = 5000 \times 1.21 \]

### Step 6: Calculate the total amount
\[ A = 6050 \]

### Step 7: Calculate the compound interest
To find the compound interest, subtract the principal from the total amount:
\[ \text{Compound Interest} = A - P \]
\[ \text{Compound Interest} = 6050 - 5000 = 1050 \]

### Final Answer
The compound interest earned after 1 year is **Rs 1050**.

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