In how many years will a sum of money becomes double at 5% per annum SI?

Options

A. 18 yr
B. 20 yr
C. 15 yr
D. none of these

Answer

To solve the problem of how many years it will take for a sum of money to double at a simple interest rate of 5% per annum, 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 (let's say P) to double (which means it will become 2P) at a simple interest rate of 5% per annum.

2. **Formula for Simple Interest**: The formula for calculating simple interest (SI) is:
\[ SI = \frac{P \times R \times T}{100} \]
where:
- \( SI \) = Simple Interest
- \( P \) = Principal amount
- \( R \) = Rate of interest per annum
- \( T \) = Time in years

3. **Determine the Simple Interest Needed**: Since we want the amount to double, the simple interest earned must equal the principal amount:
\[ SI = 2P - P = P \]

4. **Substitute the Values into the Formula**:
- We know \( R = 5\% \) and \( SI = P \).
- Substituting these values into the simple interest formula gives:
\[ P = \frac{P \times 5 \times T}{100} \]

5. **Simplify the Equation**: We can cancel \( P \) from both sides (assuming \( P \neq 0 \)):
\[ 1 = \frac{5 \times T}{100} \]

6. **Solve for T**:
- Rearranging the equation gives:
\[ T = \frac{100}{5} = 20 \]

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

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

---