Find the amount and the compound Interest on Rs 160000 for 2 years at 10% per annum, compounded half- yearly.

Answer

To solve the problem of finding the amount and compound interest on Rs. 160,000 for 2 years at 10% per annum, compounded half-yearly, we will follow these steps:

### Step 1: Identify the given values
- Principal (P) = Rs. 160,000
- Rate of interest (R) = 10% per annum
- Time (T) = 2 years

### Step 2: Adjust the rate and time for half-yearly compounding
Since the interest is compounded half-yearly, we need to adjust the rate and time:
- Half-yearly rate = R/2 = 10% / 2 = 5%
- Total number of compounding periods (n) = 2 years * 2 = 4 periods

### Step 3: Use the formula for compound amount
The formula for the amount (A) when compounded is:
\[ A = P \left(1 + \frac{R}{100}\right)^n \]

Substituting the values we have:
\[ A = 160000 \left(1 + \frac{5}{100}\right)^4 \]

### Step 4: Simplify the expression
First, calculate \(1 + \frac{5}{100}\):
\[ 1 + \frac{5}{100} = 1 + 0.05 = 1.05 \]

Now, substitute this back into the formula:
\[ A = 160000 \times (1.05)^4 \]

### Step 5: Calculate \( (1.05)^4 \)
Calculating \( (1.05)^4 \):
\[ (1.05)^4 = 1.21550625 \] (approximately)

### Step 6: Calculate the amount
Now substitute back to find A:
\[ A = 160000 \times 1.21550625 \]
\[ A \approx 194481 \]

### Step 7: Calculate the compound interest
The formula for compound interest (CI) is:
\[ CI = A - P \]
Substituting the values:
\[ CI = 194481 - 160000 \]
\[ CI = 34481 \]

### Final Results
- Amount (A) = Rs. 194,481
- Compound Interest (CI) = Rs. 34,481

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