Simple interest on a sum for 5 years is equal to 20% of the principal. In how many years interest will be equal to the principal?

Options

A. 20
B. 25
C. 15
D. 16

Answer

To solve the problem step by step, we will follow the logic presented in the video transcript.

### Step-by-Step Solution:

1. **Understand the Problem**: We need to find out in how many years the simple interest (SI) will be equal to the principal (P). We are given that the simple interest for 5 years is equal to 20% of the principal.

2. **Set Up the Equation**:
- Let the principal amount be \( P \).
- The formula for simple interest is given by:
\[ SI = \frac{P \times R \times T}{100} \]
- According to the problem, for 5 years, the simple interest is:
\[ SI = \frac{P \times R \times 5}{100} \]
- We know that this simple interest is equal to 20% of the principal:
\[ \frac{P \times R \times 5}{100} = 0.2P \]

3. **Simplify the Equation**:
- We can cancel \( P \) from both sides (assuming \( P \neq 0 \)):
\[ \frac{R \times 5}{100} = 0.2 \]
- Multiply both sides by 100:
\[ 5R = 20 \]
- Divide both sides by 5:
\[ R = 4\% \]

4. **Find the Time When SI Equals Principal**:
- Now we need to find the time \( T \) when the simple interest equals the principal:
\[ P = \frac{P \times R \times T}{100} \]
- Substituting \( R = 4\% \):
\[ P = \frac{P \times 4 \times T}{100} \]
- Cancel \( P \) from both sides:
\[ 1 = \frac{4T}{100} \]
- Multiply both sides by 100:
\[ 100 = 4T \]
- Divide both sides by 4:
\[ T = 25 \]

5. **Conclusion**: The time in which the interest will be equal to the principal is \( 25 \) years.

### Final Answer:
The interest will be equal to the principal in **25 years**.