Asum of Rs 11700 becomes Rs 16848 in 2 years at the rate of compoundinterest. If the interest is compounded annually, then what will be the rate of interest?

Options

A. `20%`
B. `15%`
C. `17.5%`
D. `25%`

Answer

To find the rate of interest when a sum of Rs 11,700 becomes Rs 16,848 in 2 years at the rate of compound interest, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Variables:**
- Principal (P) = Rs 11,700
- Amount (A) = Rs 16,848
- Time (T) = 2 years
- Rate of Interest (R) = ?

2. **Use the Compound Interest Formula:**
The formula for compound interest is:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]
Substituting the known values:
\[ 16,848 = 11,700 \left(1 + \frac{R}{100}\right)^2 \]

3. **Rearranging the Equation:**
Divide both sides by 11,700:
\[ \frac{16,848}{11,700} = \left(1 + \frac{R}{100}\right)^2 \]

4. **Calculate the Left Side:**
\[ \frac{16,848}{11,700} = 1.44 \]
So, we have:
\[ 1.44 = \left(1 + \frac{R}{100}\right)^2 \]

5. **Taking the Square Root:**
Taking the square root of both sides:
\[ \sqrt{1.44} = 1 + \frac{R}{100} \]
\[ 1.2 = 1 + \frac{R}{100} \]

6. **Isolate R:**
Subtract 1 from both sides:
\[ 1.2 - 1 = \frac{R}{100} \]
\[ 0.2 = \frac{R}{100} \]

7. **Calculate R:**
Multiply both sides by 100:
\[ R = 0.2 \times 100 = 20 \]

8. **Conclusion:**
The rate of interest is:
\[ R = 20\% \]

### Final Answer:
The rate of interest is **20%**.