Find the amount of Rs 2400 after 3 years at the rate of 8% per annum compounded annually.

Options

A. 3023.30
B. 3033.21
C. 3043.21
D. 3053.21

Answer

To find the amount of Rs 2400 after 3 years at the rate of 8% per annum compounded annually, we can use the formula for compound interest:

\[ A = P \left(1 + \frac{r}{100}\right)^n \]

Where:
- \( A \) = Amount after time \( n \)
- \( P \) = Principal amount (initial investment)
- \( r \) = Rate of interest per annum
- \( n \) = Number of years

### Step 1: Identify the values
- Principal \( P = 2400 \)
- Rate \( r = 8\% \)
- Time \( n = 3 \) years

### Step 2: Substitute the values into the formula
\[ A = 2400 \left(1 + \frac{8}{100}\right)^3 \]

### Step 3: Simplify the expression inside the parentheses
\[ 1 + \frac{8}{100} = 1 + 0.08 = 1.08 \]

### Step 4: Raise the result to the power of 3
\[ A = 2400 \times (1.08)^3 \]

### Step 5: Calculate \( (1.08)^3 \)
\[ (1.08)^3 = 1.08 \times 1.08 \times 1.08 \]
Calculating this step-by-step:
- \( 1.08 \times 1.08 = 1.1664 \)
- \( 1.1664 \times 1.08 \approx 1.259712 \)

### Step 6: Multiply by the principal
\[ A = 2400 \times 1.259712 \approx 3023.4288 \]

### Step 7: Round to two decimal places
\[ A \approx 3023.43 \]

Thus, the amount after 3 years is approximately **Rs 3023.43**.

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