A certain principal is invested in a scheme of compound interest. The amount obtained after 1 year is Rs 2400 and the amount obtained after 2 years is Rs 2880. What is the rate of interest (in percentage)?

Options

A. 20
B. 15
C. 25
D. 10

Answer

To find the rate of interest in percentage, we will use the information provided about the amounts after 1 year and 2 years.

### Step-by-Step Solution:

1. **Identify the amounts after each year:**
- Amount after 1 year (A1) = Rs 2400
- Amount after 2 years (A2) = Rs 2880

2. **Use the formula for compound interest:**
The formula for the amount after t years in compound interest is:
\[ A = P \left(1 + \frac{r}{100}\right)^t \]
where:
- \(A\) = Amount after t years
- \(P\) = Principal amount
- \(r\) = Rate of interest
- \(t\) = Time in years

3. **Set up the equations:**
From the information given:
- For 1 year:
\[ A_1 = P \left(1 + \frac{r}{100}\right)^1 = 2400 \]
- For 2 years:
\[ A_2 = P \left(1 + \frac{r}{100}\right)^2 = 2880 \]

4. **Divide the second equation by the first:**
\[ \frac{A_2}{A_1} = \frac{P \left(1 + \frac{r}{100}\right)^2}{P \left(1 + \frac{r}{100}\right)^1} \]
This simplifies to:
\[ \frac{2880}{2400} = 1 + \frac{r}{100} \]

5. **Calculate the left side:**
\[ \frac{2880}{2400} = 1.2 \]
So we have:
\[ 1.2 = 1 + \frac{r}{100} \]

6. **Solve for r:**
Subtract 1 from both sides:
\[ 1.2 - 1 = \frac{r}{100} \]
\[ 0.2 = \frac{r}{100} \]
Multiply both sides by 100:
\[ r = 20 \]

7. **Conclusion:**
The rate of interest is \(20\%\).