If a sum of money compounded annually becomes 1.44 times of itself in 2 years, then the rate of interest per annum is

Answer

To find the rate of interest per annum given that a sum of money compounded annually becomes 1.44 times itself in 2 years, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**: We know that the amount (A) after 2 years is 1.44 times the principal (P). Therefore, we can express this as:
\[ A = 1.44P \]

2. **Use the Compound Interest Formula**: The formula for compound interest is given by:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]
where \( R \) is the rate of interest per annum and \( T \) is the time in years.

3. **Substitute Known Values**: In our case, \( T = 2 \) years. So we can write:
\[ 1.44P = P \left(1 + \frac{R}{100}\right)^2 \]

4. **Cancel the Principal**: Since \( P \) is common on both sides, we can cancel it out (assuming \( P \neq 0 \)):
\[ 1.44 = \left(1 + \frac{R}{100}\right)^2 \]

5. **Take the Square Root**: To solve for \( R \), we take the square root of both sides:
\[ \sqrt{1.44} = 1 + \frac{R}{100} \]

6. **Calculate the Square Root**: The square root of 1.44 is 1.2:
\[ 1.2 = 1 + \frac{R}{100} \]

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

8. **Multiply by 100**: To find \( R \), multiply both sides by 100:
\[ R = 0.2 \times 100 = 20 \]

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