At what rate of percent a sum of Rs 2000 amounts to Rs. 2662 at CI in 3 years ?

Answer

To find the rate of interest at which a sum of Rs 2000 amounts to Rs 2662 at compound interest in 3 years, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given values**:
- Principal (P) = Rs 2000
- Amount (A) = Rs 2662
- Time (n) = 3 years

2. **Use the formula for compound interest**:
The formula for the amount in compound interest is:
\[ A = P \left(1 + \frac{R}{100}\right)^n \]
Here, we need to find the rate of interest (R).

3. **Substitute the known values into the formula**:
\[ 2662 = 2000 \left(1 + \frac{R}{100}\right)^3 \]

4. **Divide both sides by 2000** to isolate the term with R:
\[ \frac{2662}{2000} = \left(1 + \frac{R}{100}\right)^3 \]

5. **Calculate the left side**:
\[ \frac{2662}{2000} = 1.331 \]
So, we have:
\[ 1.331 = \left(1 + \frac{R}{100}\right)^3 \]

6. **Take the cube root of both sides**:
\[ 1 + \frac{R}{100} = \sqrt[3]{1.331} \]

7. **Calculate the cube root**:
The cube root of 1.331 is approximately:
\[ 1 + \frac{R}{100} = 1.1 \]

8. **Isolate R**:
\[ \frac{R}{100} = 1.1 - 1 = 0.1 \]

9. **Multiply by 100 to find R**:
\[ R = 0.1 \times 100 = 10 \]

10. **Conclusion**:
The rate of interest (R) is **10%**.