If Rs. 2500 becomes to Rs. 2970.25 in 2 years at compound interest compounded annually, what is the yearly rate of interest (in %) ?

Options

A. 7
B. 9
C. 11
D. 13

Answer

To find the yearly rate of interest when Rs. 2500 becomes Rs. 2970.25 in 2 years at compound interest compounded annually, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given values:**
- Principal (P) = Rs. 2500
- Amount (A) = Rs. 2970.25
- Time (T) = 2 years
- Rate of interest (R) = ?

2. **Use the formula for compound interest:**
The formula for the amount in compound interest is:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]
Substituting the known values into the formula:
\[ 2970.25 = 2500 \left(1 + \frac{R}{100}\right)^2 \]

3. **Divide both sides by 2500:**
\[ \frac{2970.25}{2500} = \left(1 + \frac{R}{100}\right)^2 \]
Calculating the left side:
\[ 1.1881 = \left(1 + \frac{R}{100}\right)^2 \]

4. **Take the square root of both sides:**
\[ \sqrt{1.1881} = 1 + \frac{R}{100} \]
Calculating the square root:
\[ 1.09 = 1 + \frac{R}{100} \]

5. **Isolate R:**
\[ 1.09 - 1 = \frac{R}{100} \]
\[ 0.09 = \frac{R}{100} \]

6. **Multiply both sides by 100 to find R:**
\[ R = 0.09 \times 100 = 9 \]

7. **Conclusion:**
The yearly rate of interest is **9%**.