A sum amounts to ? 1352 in 2 yr at 4% compound interest. The sum is

Options

A. X 1250
B. X 1200
C. X 1300
D. X 1260

Answer

To find the principal amount (P) that amounts to ₹1352 in 2 years at a compound interest rate of 4%, we can follow these steps:

### Step 1: Understand the formula for compound interest
The formula for the amount (A) in compound interest is given by:
\[ A = P \left(1 + \frac{r}{100}\right)^n \]
Where:
- \( A \) = Amount after time \( n \)
- \( P \) = Principal amount (initial sum)
- \( r \) = Rate of interest per annum
- \( n \) = Number of years

### Step 2: Plug in the known values
From the question, we know:
- \( A = 1352 \)
- \( r = 4\% \)
- \( n = 2 \)

So, we can write the equation as:
\[ 1352 = P \left(1 + \frac{4}{100}\right)^2 \]

### Step 3: Simplify the equation
First, calculate \( 1 + \frac{4}{100} \):
\[ 1 + \frac{4}{100} = 1 + 0.04 = 1.04 \]

Now, calculate \( (1.04)^2 \):
\[ (1.04)^2 = 1.0816 \]

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

### Step 4: Solve for P
To find \( P \), we rearrange the equation:
\[ P = \frac{1352}{1.0816} \]

Now, perform the division:
\[ P = 1250 \]

### Conclusion
The principal amount (P) is ₹1250.

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