In how much time sum of money becomes five time at 16% simple interest.

Options

A. 20 years
B. 16 years
C. 25 years
D. 40 years

Answer

To solve the problem of how much time it takes for a sum of money to become five times at 16% 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 grow to five times its original amount at a simple interest rate of 16%.

2. **Define Variables**:
- Let the principal amount (P) be \( x \).
- Therefore, the amount (A) after time \( t \) will be \( 5x \).

3. **Calculate Simple Interest (SI)**:
- The formula for Simple Interest is:
\[ SI = P \times \frac{R \times T}{100} \]
- Here, \( R \) is the rate of interest (16%) and \( T \) is the time in years.

4. **Determine the Simple Interest**:
- Since the amount becomes five times the principal, the Simple Interest (SI) can be calculated as:
\[ SI = A - P = 5x - x = 4x \]

5. **Set Up the Equation**:
- Substitute the values into the Simple Interest formula:
\[ 4x = x \times \frac{16 \times t}{100} \]

6. **Simplify the Equation**:
- Divide both sides by \( x \) (assuming \( x \neq 0 \)):
\[ 4 = \frac{16t}{100} \]

7. **Solve for Time (t)**:
- Multiply both sides by 100:
\[ 400 = 16t \]
- Now, divide both sides by 16:
\[ t = \frac{400}{16} = 25 \]

8. **Conclusion**:
- The time required for the sum of money to become five times at 16% simple interest is \( t = 25 \) years.

### Final Answer:
The time required is **25 years**.