Find the compound interest on Rs 10000 for 1 year and 6 months at the rate of 20% if interest is compounded semi-annually?

Options

A. ₹ 3310
B. ₹3110
C. ₹ 3300
D. ₹ 3100

Answer

To find the compound interest on Rs. 10,000 for 1 year and 6 months at the rate of 20% compounded semi-annually, we will follow these steps:

### Step 1: Identify the given values
- Principal (P) = Rs. 10,000
- Rate of interest (R) = 20% per annum
- Time (T) = 1 year and 6 months = 1.5 years

### Step 2: Convert the time into semi-annual periods
Since the interest is compounded semi-annually, we need to convert the time into semi-annual periods:
- Semi-annual periods (n) = 1.5 years × 2 = 3 periods

### Step 3: Calculate the effective rate per period
The annual rate is 20%, and since it is compounded semi-annually, we divide the rate by 2:
- Effective rate per period = 20% / 2 = 10%

### Step 4: Convert the rate to a decimal
To use the formula for compound interest, we need to convert the percentage rate into a decimal:
- Effective rate per period (r) = 10% = 0.10

### Step 5: Use the compound interest formula
The formula for compound interest is given by:
\[ A = P \left(1 + r\right)^n \]
Where:
- A = Amount after time T
- P = Principal
- r = Rate per period
- n = Number of periods

Substituting the values:
\[ A = 10,000 \left(1 + 0.10\right)^3 \]

### Step 6: Calculate the amount
Now, calculate the amount:
\[ A = 10,000 \left(1.10\right)^3 \]
\[ A = 10,000 \times 1.331 = 13,310 \]

### Step 7: Calculate the compound interest
Now, we can find the compound interest (CI) by subtracting the principal from the amount:
\[ CI = A - P \]
\[ CI = 13,310 - 10,000 = 3,310 \]

### Final Answer
The compound interest on Rs. 10,000 for 1 year and 6 months at the rate of 20% compounded semi-annually is Rs. 3,310.

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