What sum of money will amount to Rs 3,630/- in 2 years at 10% per annum compound interest

Answer

To find the sum of money (Principal, P) that will amount to Rs. 3,630 in 2 years at a compound interest rate of 10% per annum, we can use the compound interest formula:

### Step-by-Step Solution:

1. **Identify the formula for compound interest**:
\[ A = P \left(1 + \frac{R}{100}\right)^n \]
where:
- \( A \) = Amount after time \( n \)
- \( P \) = Principal amount (initial sum of money)
- \( R \) = Rate of interest per annum
- \( n \) = Time in years

2. **Substitute the known values into the formula**:
- Given \( A = 3630 \), \( R = 10\% \), and \( n = 2 \):
\[ 3630 = P \left(1 + \frac{10}{100}\right)^2 \]

3. **Simplify the equation**:
- Calculate \( 1 + \frac{10}{100} \):
\[ 1 + \frac{10}{100} = 1 + 0.1 = 1.1 \]
- Now substitute this back into the equation:
\[ 3630 = P (1.1)^2 \]

4. **Calculate \( (1.1)^2 \)**:
\[ (1.1)^2 = 1.1 \times 1.1 = 1.21 \]
- Now the equation becomes:
\[ 3630 = P \times 1.21 \]

5. **Solve for \( P \)**:
- Rearranging gives:
\[ P = \frac{3630}{1.21} \]
- Now perform the division:
\[ P = \frac{3630 \times 100}{121} = \frac{363000}{121} = 3000 \]

6. **Final answer**:
- Therefore, the sum of money (Principal) is:
\[ P = 3000 \text{ Rupees} \]