What sum of money will become Rs. 1,352 in 2 years at 4% per annum compound interest ?

Options

A. Rs. 1,200
B. Rs. 1,225
C. Rs. 1,250
D. Rs. 1,300

Answer

To find the sum of money (the principal) that will become Rs. 1,352 in 2 years at a 4% per annum compound interest, we can use the formula for compound interest:

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

Where:
- \(A\) is the amount after time \(t\),
- \(P\) is the principal amount (the initial sum of money),
- \(R\) is the rate of interest per annum,
- \(t\) is the time in years.

### Step-by-Step Solution:

1. **Identify the given values**:
- Amount \(A = 1352\)
- Rate \(R = 4\%\)
- Time \(t = 2\) years

2. **Substitute the known values into the compound interest formula**:
\[ 1352 = P \left(1 + \frac{4}{100}\right)^2 \]

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

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

5. **Now substitute this back into the equation**:
\[ 1352 = P \times 1.0816 \]

6. **Solve for \(P\)**:
\[ P = \frac{1352}{1.0816} \]

7. **Calculate the value of \(P\)**:
\[ P \approx 1250 \]

Thus, the principal amount is Rs. 1,250.

### Final Answer:
The sum of money that will become Rs. 1,352 in 2 years at 4% per annum compound interest is **Rs. 1,250**.

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