In what time, does a sum of money become four fold at the simple interest rate of 10% per annum?

Options

A. 40yr
B. 30yr
C. 15yr
D. 25yr

Answer

To solve the problem of determining how long it takes for a sum of money to become fourfold 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 find the time (t) it takes for a principal amount (P) to become four times itself (4P) under simple interest at a rate of 10% per annum.

2. **Identify the Variables**:
- Let the principal amount be \( P \).
- The amount after time \( t \) will be \( A = 4P \).
- The rate of interest \( R = 10\% \) per annum.
- The formula for simple interest is:
\[ A = P + SI \]
- Where \( SI \) (Simple Interest) can be calculated as:
\[ SI = \frac{P \times R \times t}{100} \]

3. **Set Up the Equation**: Since \( A = 4P \), we can substitute into the formula:
\[ 4P = P + \frac{P \times 10 \times t}{100} \]

4. **Simplify the Equation**:
- Subtract \( P \) from both sides:
\[ 4P - P = \frac{P \times 10 \times t}{100} \]
\[ 3P = \frac{P \times 10 \times t}{100} \]

5. **Cancel \( P \)**: Since \( P \) is not zero, we can divide both sides by \( P \):
\[ 3 = \frac{10t}{100} \]

6. **Solve for \( t \)**:
- Multiply both sides by 100:
\[ 300 = 10t \]
- Divide both sides by 10:
\[ t = 30 \]

7. **Conclusion**: The time required for the sum of money to become fourfold at a simple interest rate of 10% per annum is **30 years**.