In what time will a sum of money double itself @ 20% per annum (p.a) simple interest ?

Options

A. 10 years
B. 5 years
C. 2 years
D. 4 years

Answer

To solve the problem of how long it will take for a sum of money to double itself at a rate of 20% per annum using simple interest, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**: We need to find the time (T) it takes for a principal amount (P) to double itself at a simple interest rate of 20% per annum.

2. **Define the Variables**:
- Let the principal amount (P) be \( x \).
- When the amount doubles, it becomes \( 2x \).

3. **Calculate Simple Interest (SI)**:
- The formula for Simple Interest is:
\[ SI = A - P \]
- Here, \( A \) is the total amount after time \( T \), which is \( 2x \).
- Therefore, the Simple Interest can be calculated as:
\[ SI = 2x - x = x \]

4. **Use the Simple Interest Formula**:
- The formula for Simple Interest is also given by:
\[ SI = \frac{P \times R \times T}{100} \]
- Where:
- \( P \) is the principal amount,
- \( R \) is the rate of interest (20% in this case),
- \( T \) is the time in years.
- Substituting the known values:
\[ x = \frac{x \times 20 \times T}{100} \]

5. **Simplify the Equation**:
- Cancel \( x \) from both sides (assuming \( x \neq 0 \)):
\[ 1 = \frac{20 \times T}{100} \]
- This simplifies to:
\[ 1 = \frac{T}{5} \]

6. **Solve for Time (T)**:
- Multiply both sides by 5:
\[ T = 5 \text{ years} \]

### Final Answer:
The time it will take for the sum of money to double itself at a rate of 20% per annum simple interest is **5 years**.

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