The simple interest on a sum for 5 years is one fourth of the sum. The rate of interest per annum is

Options

A. 0.05
B. 0.06
C. 0.04
D. 0.08

Answer

To solve the problem, we need to find the rate of interest per annum given that the simple interest for 5 years is one fourth of the principal sum. Let's break this down step by step.

### Step 1: Understand the relationship between Simple Interest, Principal, Rate, and Time
The formula for Simple Interest (SI) is given by:
\[ SI = \frac{P \times R \times T}{100} \]
where:
- \( SI \) = Simple Interest
- \( P \) = Principal amount (the initial sum)
- \( R \) = Rate of interest per annum
- \( T \) = Time in years

### Step 2: Set up the equation based on the given information
From the problem, we know that the Simple Interest for 5 years is one fourth of the principal. Therefore, we can express this as:
\[ SI = \frac{P}{4} \]
Given that the time \( T = 5 \) years, we can substitute this into the Simple Interest formula:
\[ \frac{P}{4} = \frac{P \times R \times 5}{100} \]

### Step 3: Simplify the equation
We can simplify the equation by multiplying both sides by 100 to eliminate the fraction:
\[ 100 \times \frac{P}{4} = P \times R \times 5 \]
This simplifies to:
\[ 25P = P \times R \times 5 \]

### Step 4: Cancel \( P \) from both sides
Assuming \( P \neq 0 \), we can divide both sides by \( P \):
\[ 25 = R \times 5 \]

### Step 5: Solve for \( R \)
Now, we can solve for \( R \):
\[ R = \frac{25}{5} = 5 \]

### Conclusion
The rate of interest per annum is:
\[ R = 5\% \]