A sum becomes five times of itself in 8 years at simple interest. What is the rate of interest per annum?

Options

A. 37.5%
B. 25%
C. 62.5%
D. 50%

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Understand the Problem
We need to find the rate of interest per annum when a sum of money becomes five times itself in 8 years at simple interest.

### Step 2: Define the Variables
Let the principal amount (initial sum) be \( P \). According to the problem, after 8 years, the amount becomes \( 5P \).

### Step 3: Calculate the Interest Earned
The interest earned over 8 years can be calculated as:
\[ \text{Interest} = \text{Amount} - \text{Principal} = 5P - P = 4P \]

### Step 4: Use the Simple Interest Formula
The formula for simple interest is given by:
\[ \text{Interest} = \frac{P \times R \times T}{100} \]
Where:
- \( P \) is the principal,
- \( R \) is the rate of interest per annum,
- \( T \) is the time in years.

### Step 5: Substitute the Known Values
From Step 3, we know the interest is \( 4P \) and the time \( T \) is 8 years. Substituting these values into the formula gives:
\[ 4P = \frac{P \times R \times 8}{100} \]

### Step 6: Simplify the Equation
We can simplify the equation by dividing both sides by \( P \) (assuming \( P \neq 0 \)):
\[ 4 = \frac{R \times 8}{100} \]

### Step 7: Solve for \( R \)
Now, multiply both sides by 100:
\[ 400 = R \times 8 \]
Next, divide both sides by 8:
\[ R = \frac{400}{8} = 50 \]

### Conclusion
The rate of interest per annum is \( 50\% \).

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