Anamica invested an amount of Rs.20,000 in a fixed deposit scheme for 2 years at compound interest rate `4% p.a`. How much amount will she earn on maturity of the fixed deposit?

Options

A. 2342
B. 1632
C. 2324
D. 4120

Answer

To solve the problem of how much amount Anamica will earn on maturity of her fixed deposit, we will use the formula for compound interest. Here are the steps:

### Step 1: Identify the given values
- Principal (P) = Rs. 20,000
- Rate of interest (R) = 4% per annum
- Time (T) = 2 years

### Step 2: Write the formula for compound amount
The formula to calculate the amount (A) at compound interest is:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]

### Step 3: Substitute the values into the formula
Now, we will substitute the values of P, R, and T into the formula:
\[ A = 20000 \left(1 + \frac{4}{100}\right)^2 \]

### Step 4: Simplify the expression inside the parentheses
Calculate \( \frac{4}{100} \):
\[ \frac{4}{100} = 0.04 \]
So, we have:
\[ A = 20000 \left(1 + 0.04\right)^2 \]
\[ A = 20000 \left(1.04\right)^2 \]

### Step 5: Calculate \( (1.04)^2 \)
Now calculate \( (1.04)^2 \):
\[ (1.04)^2 = 1.0816 \]

### Step 6: Calculate the total amount
Now substitute back to find A:
\[ A = 20000 \times 1.0816 \]
\[ A = 21632 \]

### Step 7: Find the interest earned
To find out how much Anamica earned as interest, subtract the principal from the total amount:
Interest Earned = Total Amount - Principal
\[ \text{Interest} = 21632 - 20000 = 1632 \]

### Final Answer
The amount Anamica will earn on maturity of the fixed deposit is Rs. 21,632, and the interest earned is Rs. 1,632.

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