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

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 formula for compound interest:

**Formula:**
\[ A = P \left(1 + \frac{R}{100}\right)^t \]

Where:
- \( A \) = Amount after time \( t \)
- \( P \) = Principal amount (the initial sum of money)
- \( R \) = Rate of interest per annum
- \( t \) = Time in years

### Step-by-Step Solution:

1. **Identify the known values:**
- Amount \( A = 3630 \) Rs
- Rate \( R = 10\% \)
- Time \( t = 2 \) years

2. **Set up the equation using the compound interest formula:**
\[ 3630 = P \left(1 + \frac{10}{100}\right)^2 \]

3. **Simplify the equation:**
\[ 3630 = P \left(1 + 0.1\right)^2 \]
\[ 3630 = P \left(1.1\right)^2 \]
\[ 3630 = P \times 1.21 \]

4. **Rearrange to find \( P \):**
\[ P = \frac{3630}{1.21} \]

5. **Calculate \( P \):**
\[ P = \frac{3630}{1.21} \approx 3000 \]

### Final Answer:
The principal amount \( P \) is Rs 3000.

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