In how many years will a sum of money double itself at 5 % per annum rate of interest ?

Options

A. 18 years
B. 20 years
C. 22 years
D. 15 years

Answer

To solve the question of how many years it will take for a sum of money to double itself at a 5% per annum rate of interest, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**: We need to find out how many years it will take for a principal amount to double at a simple interest rate of 5% per annum.

2. **Assume a Principal Amount**: For easier calculations, let's assume the principal amount (P) is $100. This makes it easier to visualize the doubling since we will be looking for the amount (A) to be $200.

3. **Calculate the Total Amount**: The total amount after a certain number of years (t) can be calculated using the formula:
\[ A = P + SI \]
where \( SI \) (Simple Interest) is given by:
\[ SI = \frac{P \times r \times t}{100} \]
Here, \( r \) is the rate of interest (5%).

4. **Set Up the Equation**: Since we want the amount to double, we set up the equation:
\[ 200 = 100 + \frac{100 \times 5 \times t}{100} \]

5. **Simplify the Equation**: This simplifies to:
\[ 200 = 100 + 5t \]
Subtract 100 from both sides:
\[ 100 = 5t \]

6. **Solve for t**: Now, divide both sides by 5:
\[ t = \frac{100}{5} = 20 \]

7. **Conclusion**: It will take 20 years for the sum of money to double at a 5% per annum rate of interest.

### Final Answer:
The sum of money will double itself in **20 years**.