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

Options

A. 18yr
B. 20yr
C. 15yr
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 rate of 5% per annum using simple interest (SI), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**: We need to find out how long it will take for a principal amount (P) to double, which means the total amount (A) will be 2P.

2. **Formula for Simple Interest**: The formula for calculating the amount (A) in simple interest is:
\[ A = P + SI \]
where \( SI = \frac{P \times R \times T}{100} \).

3. **Set Up the Equation**: Since we want the amount to be double the principal, we can write:
\[ 2P = P + \frac{P \times 5 \times T}{100} \]

4. **Simplify the Equation**: We can simplify this equation by subtracting \( P \) from both sides:
\[ 2P - P = \frac{P \times 5 \times T}{100} \]
This simplifies to:
\[ P = \frac{P \times 5 \times T}{100} \]

5. **Cancel Out the Principal (P)**: Since \( P \) is common on both sides, we can divide both sides by \( P \) (assuming \( P \neq 0 \)):
\[ 1 = \frac{5T}{100} \]

6. **Rearrange to Solve for T**: Multiply both sides by 100 to eliminate the fraction:
\[ 100 = 5T \]

7. **Divide by 5**: Now, divide both sides by 5 to isolate \( T \):
\[ T = \frac{100}{5} \]

8. **Calculate T**: Performing the division gives:
\[ T = 20 \]

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

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

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