If Ram puts Rs. 2000 in a savings account that earns 20 percent annual interest compounded half yearly, how much money will be in the account after one year?

Options

A. Rs. 3530
B. Rs. 2420
C. Rs. 2630
D. Rs. 3870

Answer

To solve the problem of how much money will be in Ram's account after one year with Rs. 2000 at a 20% annual interest rate compounded half-yearly, we will follow these steps:

### Step 1: Identify the Principal Amount
The principal amount (P) is given as Rs. 2000.

### Step 2: Determine the Annual Interest Rate
The annual interest rate (R) is given as 20%.

### Step 3: Convert the Annual Interest Rate for Half-Yearly Compounding
Since the interest is compounded half-yearly, we need to divide the annual interest rate by 2:
\[ R_{half-yearly} = \frac{20\%}{2} = 10\% \]

### Step 4: Determine the Time Period in Half-Yearly Terms
The time period (T) for one year, when compounded half-yearly, will be:
\[ T_{half-yearly} = 2 \text{ (because there are 2 half-years in 1 year)} \]

### Step 5: Apply the Compound Interest Formula
The formula for compound interest is:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]
Where:
- \(A\) = Amount after time \(T\)
- \(P\) = Principal amount
- \(R\) = Rate of interest per period
- \(T\) = Number of compounding periods

Substituting the values into the formula:
\[ A = 2000 \left(1 + \frac{10}{100}\right)^2 \]

### Step 6: Simplify the Expression
Calculating the expression inside the parentheses:
\[ A = 2000 \left(1 + 0.10\right)^2 = 2000 \left(1.10\right)^2 \]

Calculating \(1.10^2\):
\[ 1.10^2 = 1.21 \]

Now substituting back:
\[ A = 2000 \times 1.21 \]

### Step 7: Calculate the Final Amount
Now, we calculate:
\[ A = 2000 \times 1.21 = 2420 \]

Thus, the amount in the account after one year will be Rs. 2420.

### Final Answer
The total amount in the account after one year is **Rs. 2420**.

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