The compound interest earned in two years at 15% per annum is Rs 20640 what is the sum invested

Options

A. 64000
B. 60000
C. 56000
D. 52000

Answer

To find the sum invested based on the compound interest earned in two years at a rate of 15% per annum, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given values**:
- Compound Interest (CI) = Rs 20,640
- Rate of Interest (R) = 15% per annum
- Time (T) = 2 years

2. **Use the formula for Compound Interest**:
The formula for Compound Interest is:
\[ CI = A - P \]
where \( A \) is the total amount after time \( T \) and \( P \) is the principal amount (sum invested).

3. **Express the amount \( A \) in terms of \( P \)**:
The amount \( A \) can be calculated using the formula:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]
Substituting the values we have:
\[ A = P \left(1 + \frac{15}{100}\right)^2 = P \left(1.15\right)^2 \]

4. **Calculate \( (1.15)^2 \)**:
\[ (1.15)^2 = 1.3225 \]
Therefore, we can rewrite the amount as:
\[ A = P \times 1.3225 \]

5. **Substitute \( A \) back into the CI formula**:
\[ CI = A - P = P \times 1.3225 - P = P(1.3225 - 1) = P(0.3225) \]

6. **Set up the equation using the given CI**:
We know that the compound interest earned is Rs 20,640, so:
\[ P(0.3225) = 20,640 \]

7. **Solve for \( P \)**:
\[ P = \frac{20,640}{0.3225} \]
Calculating this gives:
\[ P = 64,000 \]

### Final Answer:
The sum invested is Rs 64,000.