The compound intesret earned on a sum in 3 years at 15% per annum compounded annually is ₹6500.52. What is the sum?

Options

A. `₹12,480`
B. ₹10,500
C. ₹14,800
D. ₹13,620

Explanation

To find the principal amount (sum) for the given compound interest, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Given Information**:
- Compound Interest (CI) = ₹6500.52
- Time (n) = 3 years
- Rate of Interest (R) = 15% per annum

2. **Use the Formula for Compound Interest**:
The formula for compound interest is:
\[ CI = P \left( \left(1 + \frac{R}{100}\right)^n - 1 \right) \]
Where:
- \( CI \) = Compound Interest
- \( P \) = Principal amount (sum)
- \( R \) = Rate of interest
- \( n \) = Time in years

3. **Substitute the Known Values**:
Substitute the values into the formula:
\[ 6500.52 = P \left( \left(1 + \frac{15}{100}\right)^3 - 1 \right) \]
Simplifying the expression inside the parentheses:
\[ 1 + \frac{15}{100} = 1.15 \]
Now calculate \( (1.15)^3 \):
\[ (1.15)^3 = 1.15 \times 1.15 \times 1.15 \approx 1.520875 \]
Therefore:
\[ 6500.52 = P \left( 1.520875 - 1 \right) \]
\[ 6500.52 = P \times 0.520875 \]

4. **Solve for Principal (P)**:
Rearranging the equation to solve for \( P \):
\[ P = \frac{6500.52}{0.520875} \]
Now calculate \( P \):
\[ P \approx 12480 \]

5. **Conclusion**:
The principal amount (sum) is approximately ₹12,480.