Find the C.I of Rs. 7500 at 4% for 1 year. If the interest compounded half yearly

Answer

To find the compound interest (C.I) on Rs. 7500 at an interest rate of 4% compounded half-yearly for 1 year, we can follow these steps:

### Step 1: Identify the given values
- Principal (P) = Rs. 7500
- Annual Interest Rate (R) = 4%
- Time (T) = 1 year

### Step 2: Convert the annual interest rate to half-yearly
Since the interest is compounded half-yearly, we need to divide the annual interest rate by 2:
- Half-yearly Rate (R') = R / 2 = 4% / 2 = 2%

### Step 3: Determine the number of compounding periods
For 1 year, there are 2 half-year periods:
- Number of compounding periods (n) = 2

### Step 4: Use the compound interest formula
The formula for compound interest is given by:
\[ A = P \left(1 + \frac{R'}{100}\right)^{n} \]
Where:
- A = Amount after time T
- P = Principal
- R' = Half-yearly interest rate
- n = Number of compounding periods

Substituting the known values:
\[ A = 7500 \left(1 + \frac{2}{100}\right)^{2} \]

### Step 5: Calculate the amount
First, calculate \(1 + \frac{2}{100}\):
\[ 1 + \frac{2}{100} = 1 + 0.02 = 1.02 \]

Now substitute this back into the formula:
\[ A = 7500 \times (1.02)^{2} \]

Next, calculate \((1.02)^{2}\):
\[ (1.02)^{2} = 1.0404 \]

Now, calculate the amount:
\[ A = 7500 \times 1.0404 = 7803 \]

### Step 6: Calculate the compound interest
Compound Interest (C.I) is given by:
\[ C.I = A - P \]
Substituting the values:
\[ C.I = 7803 - 7500 = 303 \]

### Final Answer
The compound interest is Rs. 303.

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