Find the amount and the compound interest on Rs 6000 for 1 year at 10% per annum compounded half- yearly.

Answer

To solve the question of finding the amount and the compound interest on Rs 6000 for 1 year at 10% per annum compounded half-yearly, we can follow these steps:

### Step 1: Understand the Compounding Frequency
Since the interest is compounded half-yearly, we need to adjust the annual interest rate and the time period accordingly.

- **Annual Interest Rate (R)**: 10%
- **Half-Yearly Interest Rate (R/2)**: 10% / 2 = 5%
- **Time Period (T)**: 1 year = 2 half-year periods

### Step 2: Identify the Principal Amount
The principal amount (P) is given as Rs 6000.

### Step 3: Use the Compound Interest Formula
The formula for calculating the amount (A) when interest is compounded is:
\[ A = P \left(1 + \frac{R}{100}\right)^n \]
Where:
- \( P \) = Principal amount
- \( R \) = Rate of interest per period
- \( n \) = Number of compounding periods

### Step 4: Substitute the Values into the Formula
Substituting the values we have:
- \( P = 6000 \)
- \( R = 5 \) (half-yearly rate)
- \( n = 2 \) (two half-year periods)

So, we have:
\[ A = 6000 \left(1 + \frac{5}{100}\right)^2 \]

### Step 5: Simplify the Expression
Calculating inside the parentheses:
\[ 1 + \frac{5}{100} = 1 + 0.05 = 1.05 \]
Now substituting back into the formula:
\[ A = 6000 \times (1.05)^2 \]

### Step 6: Calculate \( (1.05)^2 \)
Calculating \( (1.05)^2 \):
\[ (1.05)^2 = 1.1025 \]
Now substituting this value:
\[ A = 6000 \times 1.1025 \]

### Step 7: Calculate the Amount
Now, multiplying:
\[ A = 6000 \times 1.1025 = 6615 \]

### Step 8: Calculate the Compound Interest
The compound interest (CI) can be found using the formula:
\[ CI = A - P \]
Substituting the values:
\[ CI = 6615 - 6000 = 615 \]

### Final Answers
- **Amount (A)**: Rs 6615
- **Compound Interest (CI)**: Rs 615

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