In how many years any amount will be doubled at rate of 10% simple interest annually?

Options

A. 2 years
B. 5 years
C. 10 years
D. 15 years

Answer

To solve the problem of how many years it will take for any amount to double at a rate of 10% simple interest annually, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**: We need to determine how many years it takes for a principal amount (P) to double (which becomes 2P) at a simple interest rate of 10% per annum.

2. **Use the Simple Interest Formula**: The formula for calculating simple interest (SI) is:
\[ SI = \frac{P \times R \times T}{100} \]
where:
- \( P \) = principal amount
- \( R \) = rate of interest (10% in this case)
- \( T \) = time in years

3. **Set Up the Equation**: Since we want the final amount (A) to be double the principal amount, we can express it as:
\[ A = P + SI \]
Therefore, if the amount doubles, we have:
\[ 2P = P + SI \]
This simplifies to:
\[ SI = 2P - P = P \]

4. **Substitute SI in the Formula**: Now, we can substitute \( SI \) back into the simple interest formula:
\[ P = \frac{P \times 10 \times T}{100} \]

5. **Cancel Out P**: Since \( P \) is common on both sides, we can cancel it out (assuming \( P \neq 0 \)):
\[ 1 = \frac{10 \times T}{100} \]

6. **Simplify the Equation**: This simplifies to:
\[ 1 = \frac{T}{10} \]

7. **Solve for T**: To find \( T \), multiply both sides by 10:
\[ T = 10 \]

8. **Conclusion**: Therefore, it will take 10 years for any amount to double at a rate of 10% simple interest annually.

### Final Answer:
It will take **10 years** to double the amount at a rate of 10% simple interest annually.