A certain principal invested in a scheme of compound interest. The amount obtained after 1 year is Rs 3900 and the amount obtained after 2 years is Rs 5070. What is the rate of interest (in percentage)?

Options

A. 25
B. 30
C. 35
D. `37.5`

Answer

To find the rate of interest in percentage based on the given amounts after 1 year and 2 years, we can use the formula for compound interest.

### Step-by-Step Solution:

1. **Identify the amounts after each year:**
- Amount after 1 year (A1) = Rs 3900
- Amount after 2 years (A2) = Rs 5070

2. **Understand the relationship between the amounts:**
- The amount after 2 years can be expressed in terms of the amount after 1 year and the rate of interest (r):
\[ A2 = A1 \times (1 + r) \]

3. **Substitute the known values into the equation:**
- Substitute A1 = 3900 and A2 = 5070 into the equation:
\[ 5070 = 3900 \times (1 + r) \]

4. **Solve for (1 + r):**
- Divide both sides by 3900:
\[ 1 + r = \frac{5070}{3900} \]

5. **Calculate the value of (1 + r):**
- Perform the division:
\[ 1 + r = 1.3 \]

6. **Isolate r:**
- Subtract 1 from both sides:
\[ r = 1.3 - 1 = 0.3 \]

7. **Convert r to a percentage:**
- Multiply by 100 to convert to percentage:
\[ r = 0.3 \times 100 = 30\% \]

### Conclusion:
The rate of interest is **30%**.