The rate of simple interest for which a sum of money becomes 5 times of itself in 8 years is :

Options

A. 0.3
B. 0.4
C. 0.5
D. 0.55

Answer

To find the rate of simple interest for which a sum of money becomes 5 times itself in 8 years, we can follow these steps:

### Step 1: Understand the relationship between principal, amount, and interest
Let the principal amount be \( P \). According to the problem, the amount becomes 5 times the principal in 8 years. Therefore, the amount \( A \) can be expressed as:
\[ A = 5P \]

### Step 2: Calculate the simple interest
The simple interest \( SI \) can be calculated using the formula:
\[ SI = A - P \]
Substituting the values we have:
\[ SI = 5P - P = 4P \]

### Step 3: Use the simple interest formula
The formula for simple interest is given by:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \( SI \) is the simple interest,
- \( P \) is the principal,
- \( R \) is the rate of interest,
- \( T \) is the time in years.

### Step 4: Substitute known values into the formula
From the previous steps, we know:
- \( SI = 4P \)
- \( T = 8 \) years

Substituting these into the simple interest formula gives:
\[ 4P = \frac{P \times R \times 8}{100} \]

### Step 5: Simplify the equation
We can cancel \( P \) from both sides (assuming \( P \neq 0 \)):
\[ 4 = \frac{R \times 8}{100} \]

### Step 6: Solve for \( R \)
To isolate \( R \), we can multiply both sides by 100:
\[ 400 = R \times 8 \]
Now, divide both sides by 8:
\[ R = \frac{400}{8} = 50 \]

### Step 7: Convert to decimal form
Since the question asks for the rate in decimal form, we convert 50% to decimal:
\[ R = \frac{50}{100} = 0.50 \]

### Final Answer
The rate of simple interest for which a sum of money becomes 5 times itself in 8 years is:
\[ \text{Rate} = 0.50 \]

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