The compound interest on Rs 50,000 at 4% per annum for 2 years compounded annually is

Options

A. Rs 4,000
B. Rs 4,080
C. Rs 4,280
D. Rs 4,050

Answer

To find the compound interest on Rs 50,000 at a rate of 4% per annum for 2 years compounded annually, we can follow these steps:

### Step 1: Identify the formula for compound interest
The formula to calculate the total amount (A) after n years with compound interest is:
\[ A = P \left(1 + \frac{R}{100}\right)^N \]
Where:
- \( A \) = Total amount after n years
- \( P \) = Principal amount (initial investment)
- \( R \) = Rate of interest per annum
- \( N \) = Number of years

### Step 2: Substitute the values into the formula
Given:
- \( P = 50,000 \)
- \( R = 4 \)
- \( N = 2 \)

Substituting the values into the formula:
\[ A = 50,000 \left(1 + \frac{4}{100}\right)^2 \]

### Step 3: Simplify the equation
Calculate \( \frac{4}{100} \):
\[ \frac{4}{100} = 0.04 \]
So, the equation becomes:
\[ A = 50,000 \left(1 + 0.04\right)^2 \]
\[ A = 50,000 \left(1.04\right)^2 \]

### Step 4: Calculate \( (1.04)^2 \)
Now, calculate \( (1.04)^2 \):
\[ (1.04)^2 = 1.0816 \]
Thus, the equation now is:
\[ A = 50,000 \times 1.0816 \]

### Step 5: Calculate the total amount (A)
Now, calculate \( A \):
\[ A = 50,000 \times 1.0816 = 54,080 \]

### Step 6: Calculate the compound interest
To find the compound interest (CI), subtract the principal from the total amount:
\[ CI = A - P \]
\[ CI = 54,080 - 50,000 \]
\[ CI = 4,080 \]

### Final Answer
The compound interest on Rs 50,000 at 4% per annum for 2 years compounded annually is **Rs 4,080**.

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