In how many years will a sum of money double itself at 10 % per annum simple interest ?

Options

A. a. 2 Years
B. b. 5 Years
C. c. 7 Years
D. d. 10 Years

Answer

To find out how many years it will take for a sum of money to double itself at a simple interest rate of 10% per annum, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**: We need to determine the time (T) it takes for a principal amount (P) to double at a simple interest rate (R) of 10% per annum.

2. **Define the Variables**:
- Let the principal amount (P) be \( x \).
- The rate of interest (R) is 10% per annum.
- The amount we want to achieve is double the principal, which is \( 2x \).

3. **Use the Simple Interest Formula**:
The formula for simple interest (SI) is given by:
\[ SI = \frac{P \times R \times T}{100} \]
Here, we know that the simple interest earned when the principal doubles is equal to the principal itself:
\[ SI = 2x - x = x \]

4. **Substitute the Values into the Formula**:
Substitute \( P = x \), \( R = 10 \), and \( SI = x \) into the simple interest formula:
\[ x = \frac{x \times 10 \times T}{100} \]

5. **Simplify the Equation**:
Cancel \( x \) from both sides (assuming \( x \neq 0 \)):
\[ 1 = \frac{10T}{100} \]
This simplifies to:
\[ 1 = \frac{T}{10} \]

6. **Solve for T**:
Multiply both sides by 10 to isolate T:
\[ T = 10 \]

### Conclusion:
The time required for the sum of money to double itself at a simple interest rate of 10% per annum is **10 years**.