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

Answer

To solve the problem of how many years it will take for Rs. 2,000 to amount to Rs. 2,662 at a 10% compound interest rate, 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 the amount in compound interest is:
\[ A = P \left(1 + \frac{R}{100}\right)^t \]
Where:
- \( A \) = Amount
- \( P \) = Principal
- \( R \) = Rate of interest
- \( t \) = Time in years

3. **Substitute the Known Values into the Formula:**
\[ 2662 = 2000 \left(1 + \frac{10}{100}\right)^t \]
Simplifying the term inside the parentheses:
\[ 1 + \frac{10}{100} = 1 + 0.1 = 1.1 \]
So the equation becomes:
\[ 2662 = 2000 \times (1.1)^t \]

4. **Divide Both Sides by 2000:**
\[ \frac{2662}{2000} = (1.1)^t \]
Calculating the left side:
\[ 1.331 = (1.1)^t \]

5. **Take Logarithm on Both Sides:**
To solve for \( t \), we can take the logarithm:
\[ \log(1.331) = t \cdot \log(1.1) \]

6. **Calculate the Logarithms:**
Using a calculator:
\[ \log(1.331) \approx 0.1249 \]
\[ \log(1.1) \approx 0.0414 \]

7. **Solve for \( t \):**
\[ t = \frac{\log(1.331)}{\log(1.1)} \approx \frac{0.1249}{0.0414} \approx 3.02 \]
Since time is typically rounded to the nearest whole number in this context, we can conclude:
\[ t \approx 3 \text{ years} \]

### Final Answer:
It will take approximately **3 years** for Rs. 2,000 to amount to Rs. 2,662 at a 10% compound interest rate.