Find compound interest on 2000 at 50% per annum. compounded halfyearly, for 2 yr?

Options

A. 444.1
B. 454.1
C. 464.1
D. 504.1

Answer

To find the compound interest on ₹2000 at 50% per annum compounded half-yearly for 2 years, we can follow these steps:

### Step 1: Determine the number of compounding periods
Since the interest is compounded half-yearly, we need to find out how many half-year periods are in 2 years.
- There are 2 half-year periods in 1 year, so in 2 years, there will be:
\[ \text{Number of half-year periods} = 2 \times 2 = 4 \]

**Hint:** Remember that "half-yearly" means the interest is compounded every 6 months.

### Step 2: Adjust the interest rate
The annual interest rate is 50%. Since we are compounding half-yearly, we need to divide the annual interest rate by 2:
\[ \text{Half-yearly interest rate} = \frac{50\%}{2} = 25\% \]

**Hint:** When compounding more frequently than annually, divide the annual rate by the number of compounding periods per year.

### Step 3: Use the compound interest formula
The formula for compound interest is:
\[ A = P \left(1 + \frac{r}{100}\right)^n \]
Where:
- \(A\) = the amount after time \(n\)
- \(P\) = principal amount (initial investment)
- \(r\) = annual interest rate (as a percentage)
- \(n\) = number of compounding periods

Here, \(P = 2000\), \(r = 25\%\), and \(n = 4\):
\[ A = 2000 \left(1 + \frac{25}{100}\right)^4 \]

**Hint:** Make sure to convert the percentage into a decimal when using it in calculations.

### Step 4: Calculate the amount
First, calculate \(1 + \frac{25}{100}\):
\[ 1 + \frac{25}{100} = 1 + 0.25 = 1.25 \]
Now plug this back into the formula:
\[ A = 2000 \times (1.25)^4 \]

**Hint:** Remember to calculate \(1.25\) raised to the power of \(4\) before multiplying by the principal.

### Step 5: Calculate \(1.25^4\)
Calculating \(1.25^4\):
\[ 1.25^4 = 1.25 \times 1.25 \times 1.25 \times 1.25 = 1.953125 \]

**Hint:** You can use a calculator for exponentiation to simplify this step.

### Step 6: Calculate the total amount
Now, substitute back into the equation:
\[ A = 2000 \times 1.953125 = 3906.25 \]

**Hint:** Ensure to perform the multiplication accurately.

### Step 7: Calculate the compound interest
Now, to find the compound interest:
\[ \text{Compound Interest} = A - P = 3906.25 - 2000 = 1906.25 \]

**Hint:** The compound interest is the total amount minus the principal.

### Final Answer
The compound interest on ₹2000 at 50% per annum compounded half-yearly for 2 years is ₹1906.25.