Rajeev invested `Rs. 4500` for 2 years at compound interest in a company which pald him interest of `Rs. 1980`. What will be the rate of interest (in per cent) at which Rajeev invested his money?

Options

A. 10
B. 15
C. 20
D. 18

Answer

To find the rate of interest at which Rajeev invested his money, we can use the formula for compound interest. Let's break down the solution step by step.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Principal (P) = Rs. 4500
- Time (t) = 2 years
- Compound Interest (CI) = Rs. 1980

2. **Calculate the Total Amount (A):**
The total amount after 2 years can be calculated using the formula:
\[ A = P + CI \]
Substituting the values:
\[ A = 4500 + 1980 = 6480 \]

3. **Use the Compound Interest Formula:**
The formula for compound interest is:
\[ A = P \left(1 + \frac{R}{100}\right)^t \]
Substituting the known values:
\[ 6480 = 4500 \left(1 + \frac{R}{100}\right)^2 \]

4. **Divide Both Sides by 4500:**
\[ \frac{6480}{4500} = \left(1 + \frac{R}{100}\right)^2 \]
Simplifying the left side:
\[ 1.44 = \left(1 + \frac{R}{100}\right)^2 \]

5. **Take the Square Root of Both Sides:**
\[ \sqrt{1.44} = 1 + \frac{R}{100} \]
Calculating the square root:
\[ 1.2 = 1 + \frac{R}{100} \]

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

7. **Multiply by 100 to Find R:**
\[ R = 0.2 \times 100 = 20 \]

8. **Conclusion:**
The rate of interest at which Rajeev invested his money is **20%**.