The compound interest accrued on an amount at the end of two years at the rate of 16 p.c.p.a is ₹ 3041.28. what is the amount ?

Options

A. ₹10500
B. ₹ 9000
C. ₹7250
D. ₹8800

Explanation

To find the principal amount based on the compound interest accrued, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given values**:
- Compound Interest (CI) = ₹ 3041.28
- Rate of interest (R) = 16% per annum
- Time (T) = 2 years

2. **Use the formula for Compound Interest**:
The formula for Compound Interest is:
\[ CI = P \left( \left(1 + \frac{R}{100}\right)^T - 1 \right) \]
where \( P \) is the principal amount.

3. **Substitute the known values into the formula**:
\[ 3041.28 = P \left( \left(1 + \frac{16}{100}\right)^2 - 1 \right) \]

4. **Calculate \( \left(1 + \frac{16}{100}\right)^2 \)**:
- First, calculate \( 1 + \frac{16}{100} = 1 + 0.16 = 1.16 \).
- Now, square it: \( (1.16)^2 = 1.3456 \).

5. **Subtract 1 from the squared result**:
\[ 1.3456 - 1 = 0.3456 \]

6. **Substitute back into the equation**:
\[ 3041.28 = P \times 0.3456 \]

7. **Solve for \( P \)**:
\[ P = \frac{3041.28}{0.3456} \]

8. **Calculate \( P \)**:
\[ P = 8800 \]

### Final Answer:
The principal amount is ₹ 8800.

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