How long will a sum of money invested at 5% per annum SI take to increase its value by 50%?

Options

A. 10yr
B. 12yr
C. 15yr
D. 25yr

Answer

To solve the problem of how long a sum of money invested at 5% per annum simple interest will take to increase its value by 50%, we can follow these steps:

### Step-by-Step Solution:

1. **Define the Principal Amount**:
Let the principal amount (initial investment) be denoted as \( P \).

2. **Calculate the Increased Amount**:
Since the amount increases by 50%, the new amount \( A \) can be expressed as:
\[ A = P + 0.5P = 1.5P \]

3. **Determine the Simple Interest**:
The simple interest \( SI \) earned can be calculated as:
\[ SI = A - P = 1.5P - P = 0.5P \]

4. **Use the Simple Interest Formula**:
The formula for simple interest is given by:
\[ SI = \frac{P \cdot r \cdot t}{100} \]
where \( P \) is the principal, \( r \) is the rate of interest (5% in this case), and \( t \) is the time in years.

5. **Substitute the Known Values**:
Substitute \( SI = 0.5P \) and \( r = 5 \) into the formula:
\[ 0.5P = \frac{P \cdot 5 \cdot t}{100} \]

6. **Simplify the Equation**:
Cancel \( P \) from both sides (assuming \( P \neq 0 \)):
\[ 0.5 = \frac{5t}{100} \]

7. **Cross-Multiply to Solve for \( t \)**:
Rearranging gives:
\[ 0.5 \cdot 100 = 5t \]
\[ 50 = 5t \]

8. **Isolate \( t \)**:
Divide both sides by 5:
\[ t = \frac{50}{5} = 10 \]

9. **Conclusion**:
The time it takes for the sum of money to increase by 50% at 5% per annum simple interest is:
\[ \boxed{10 \text{ years}} \]