In how many years will Rs 2,000 amount to Rs. 2,662 at 10 percent p.a C.I ?

Answer

To solve the problem of finding out in how many years Rs. 2,000 will amount to Rs. 2,662 at a compound interest rate of 10% per annum, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Principal (P) = Rs. 2,000
- Amount (A) = Rs. 2,662
- Rate of Interest (R) = 10%

2. **Use the Compound Interest Formula**:
The formula for compound interest is given by:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]
where:
- A = Amount
- P = Principal
- R = Rate of interest
- T = Time (in years)

3. **Substituting the Values into the Formula**:
Substitute the known values into the formula:
\[ 2662 = 2000 \left(1 + \frac{10}{100}\right)^T \]
Simplifying the equation:
\[ 2662 = 2000 \left(1 + 0.1\right)^T \]
\[ 2662 = 2000 \left(1.1\right)^T \]

4. **Divide Both Sides by 2000**:
To isolate the term with \(T\):
\[ \frac{2662}{2000} = (1.1)^T \]
Simplifying the left side:
\[ 1.331 = (1.1)^T \]

5. **Express 1.331 as a Power of 1.1**:
We need to express 1.331 in terms of \(1.1\):
\[ 1.331 = (1.1)^3 \]
This can be verified by calculating \(1.1^3\):
\[ 1.1 \times 1.1 \times 1.1 = 1.331 \]

6. **Equate the Exponents**:
Since the bases are the same, we can equate the exponents:
\[ T = 3 \]

7. **Conclusion**:
Therefore, the time required for Rs. 2,000 to amount to Rs. 2,662 at 10% compound interest is:
\[ \text{Time} = 3 \text{ years} \]

### Final Answer:
**3 years**

---