The difference between the compound interest and the simple interest of some amount of money for 2 years at `9%` per annum is ₹162. What is the sum of money?

Options

A. ₹20000
B. ₹25000
C. ₹27000
D. ₹30000

Answer

To find the sum of money based on the given information about the difference between compound interest (CI) and simple interest (SI) over 2 years at a rate of 9% per annum, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Difference Between CI and SI**:
The difference between the compound interest and simple interest for 2 years can be expressed as:
\[ \text{Difference} = \text{CI} - \text{SI} = \frac{P \times R^2}{100^2} \]
where \( P \) is the principal amount, and \( R \) is the rate of interest.

2. **Given Values**:
We know that the difference is ₹162 and the rate \( R = 9\% \). Therefore, we can set up the equation:
\[ \frac{P \times 9^2}{100^2} = 162 \]

3. **Calculating the Equation**:
Plugging in the values:
\[ \frac{P \times 81}{10000} = 162 \]

4. **Cross Multiplying to Solve for P**:
To eliminate the fraction, we can cross-multiply:
\[ P \times 81 = 162 \times 10000 \]
\[ P \times 81 = 1620000 \]

5. **Finding the Principal Amount (P)**:
Now, divide both sides by 81 to isolate \( P \):
\[ P = \frac{1620000}{81} \]

6. **Performing the Division**:
Calculating the division:
\[ P = 20000 \]

### Conclusion:
The sum of money (the principal amount) is ₹20,000.