A certain sum amounts to Rs.280900 in 2 years at 6% per annum, interest compounded annually. The sum is :

Options

A. Rs. 350000
B. Rs. 250000
C. Rs. 200000
D. Rs. 550000

Answer

To find the principal sum that amounts to Rs. 280,900 in 2 years at an interest rate of 6% per annum, compounded annually, we can use the compound interest formula:

### Step 1: Write down the formula for compound interest
The formula for the amount \( A \) in compound interest is given by:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]
where:
- \( A \) = Amount after time \( T \)
- \( P \) = Principal amount (initial sum)
- \( R \) = Rate of interest per annum
- \( T \) = Time in years

### Step 2: Substitute the known values into the formula
From the problem, we know:
- \( A = 280900 \)
- \( R = 6 \)
- \( T = 2 \)

Substituting these values into the formula gives:
\[ 280900 = P \left(1 + \frac{6}{100}\right)^2 \]

### Step 3: Simplify the expression
First, calculate \( 1 + \frac{6}{100} \):
\[ 1 + \frac{6}{100} = 1 + 0.06 = 1.06 \]
Now substitute this back into the equation:
\[ 280900 = P \cdot (1.06)^2 \]

### Step 4: Calculate \( (1.06)^2 \)
Now calculate \( (1.06)^2 \):
\[ (1.06)^2 = 1.1236 \]
Substituting this value gives:
\[ 280900 = P \cdot 1.1236 \]

### Step 5: Solve for \( P \)
To find \( P \), divide both sides by \( 1.1236 \):
\[ P = \frac{280900}{1.1236} \]
Calculating this gives:
\[ P \approx 250000 \]

### Conclusion
The principal sum is Rs. 250,000.