A certain sum amounts to Rs. 7200 in 2 years at 20 % per annum compound interest, compounded annually. Find the sum.

Options

A. Rs. 4800
B. Rs. 6000
C. Rs. 5400
D. Rs. 5000

Answer

To find the principal sum (P) that amounts to Rs. 7200 in 2 years at a compound interest rate of 20% per annum, 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 sum we need to find)
- \( R \) is the rate of interest per annum
- \( N \) is the number of years

### Step-by-step Solution:

1. **Identify the given values:**
- Amount \( A = 7200 \)
- Rate of interest \( R = 20\% \)
- Time \( N = 2 \) years

2. **Substitute the values into the formula:**
\[ 7200 = P \left(1 + \frac{20}{100}\right)^2 \]

3. **Simplify the expression inside the parentheses:**
\[ 1 + \frac{20}{100} = 1 + 0.2 = 1.2 \]
So, the equation becomes:
\[ 7200 = P (1.2)^2 \]

4. **Calculate \( (1.2)^2 \):**
\[ (1.2)^2 = 1.44 \]
Now the equation is:
\[ 7200 = P \times 1.44 \]

5. **Solve for \( P \):**
\[ P = \frac{7200}{1.44} \]

6. **Perform the division:**
\[ P = 5000 \]

### Conclusion:
The principal sum is Rs. 5000.