A sum of money amounts to Rs. 270.40 in 2 years at 4% per annum, compounded annually. Find the sum.

Answer

To find the principal amount (P) that amounts to Rs. 270.40 in 2 years at an interest rate of 4% per annum, compounded annually, we can use the formula for compound interest:

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

Where:
- \( A \) = Amount after time \( t \)
- \( P \) = Principal amount (the initial sum of money)
- \( r \) = Rate of interest per annum
- \( t \) = Time in years

### Step-by-step Solution:

1. **Identify the given values:**
- Amount (A) = Rs. 270.40
- Rate of interest (r) = 4%
- Time (t) = 2 years

2. **Substitute the values into the formula:**
\[ 270.40 = P \left(1 + \frac{4}{100}\right)^2 \]

3. **Calculate \( 1 + \frac{4}{100} \):**
\[ 1 + \frac{4}{100} = 1 + 0.04 = 1.04 \]

4. **Raise \( 1.04 \) to the power of \( 2 \):**
\[ (1.04)^2 = 1.04 \times 1.04 = 1.0816 \]

5. **Rewrite the equation with the calculated value:**
\[ 270.40 = P \times 1.0816 \]

6. **Solve for \( P \):**
\[ P = \frac{270.40}{1.0816} \]

7. **Calculate \( P \):**
\[ P = 250 \]

### Final Answer:
The principal amount is Rs. 250.

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