If a sum becomes Rs. 1352 in 2 years at 4% per annum compound interest then the sum is ?

Answer

To find the principal sum (P) when the amount becomes Rs. 1352 in 2 years at a 4% per annum compound interest, we can use the formula for compound interest:

**Step 1: Write down the compound interest formula.**
The formula for the amount (A) in compound interest is:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]
where:
- \( A \) is the amount after time \( T \),
- \( P \) is the principal amount (the sum we want to find),
- \( R \) is the rate of interest,
- \( T \) is the time in years.

**Step 2: Substitute the known values into the formula.**
Here, we know:
- \( A = 1352 \)
- \( R = 4\% \)
- \( T = 2 \)

Substituting these values into the formula gives:
\[ 1352 = P \left(1 + \frac{4}{100}\right)^2 \]

**Step 3: Simplify the expression inside the parentheses.**
Calculate \( 1 + \frac{4}{100} \):
\[ 1 + \frac{4}{100} = 1 + 0.04 = 1.04 \]

Now substitute this back into the equation:
\[ 1352 = P \left(1.04\right)^2 \]

**Step 4: Calculate \( (1.04)^2 \).**
Now calculate \( (1.04)^2 \):
\[ (1.04)^2 = 1.0816 \]

So the equation now becomes:
\[ 1352 = P \times 1.0816 \]

**Step 5: Solve for \( P \).**
To find \( P \), divide both sides by \( 1.0816 \):
\[ P = \frac{1352}{1.0816} \]

Calculating this gives:
\[ P \approx 1250 \]

Thus, the principal sum is approximately Rs. 1250.