Sham invest Rs X for 2 years at 8% per annum compound interest annually, which amounts to Rs 72900 then what is the value of X?

Options

A. Rs 60000
B. Rs 62000
C. Rs 62500
D. Rs 60500

Answer

To find the value of \( X \) that Sham invested, we can use the formula for compound interest:

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

Where:
- \( A \) is the amount after time \( n \),
- \( P \) is the principal amount (the initial investment),
- \( r \) is the rate of interest per annum,
- \( n \) is the number of years the money is invested.

Given:
- \( A = 72900 \)
- \( r = 8\% \)
- \( n = 2 \)

We need to find \( P \) (which is \( X \)).

### Step 1: Substitute the known values into the formula

\[ 72900 = X \left(1 + \frac{8}{100}\right)^2 \]

### Step 2: Simplify the expression inside the parentheses

\[ 1 + \frac{8}{100} = 1 + 0.08 = 1.08 \]

### Step 3: Calculate \( (1.08)^2 \)

\[ (1.08)^2 = 1.1664 \]

### Step 4: Substitute back into the equation

\[ 72900 = X \times 1.1664 \]

### Step 5: Solve for \( X \)

\[ X = \frac{72900}{1.1664} \]

### Step 6: Perform the division

\[ X \approx 62400 \]

Thus, the value of \( X \) is approximately \( 62400 \).