The simple interset on a sum after 4 years is `(1)/(5)` of the sum The rate of interset per annum is

Options

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

Answer

To solve the problem step by step, we will use the information given in the question regarding simple interest.

### Step 1: Understand the relationship between Simple Interest (SI), Principal (P), Rate (R), and Time (T)
The formula for Simple Interest is given by:
\[ SI = \frac{P \times R \times T}{100} \]

### Step 2: Identify the given values
From the question, we know:
- The time (T) is 4 years.
- The Simple Interest (SI) after 4 years is \(\frac{1}{5}\) of the Principal (P). Therefore, we can express this as:
\[ SI = \frac{P}{5} \]

### Step 3: Substitute the known values into the SI formula
We can substitute SI and T into the formula:
\[ \frac{P}{5} = \frac{P \times R \times 4}{100} \]

### Step 4: Simplify the equation
To simplify, we can multiply both sides by 100 to eliminate the fraction:
\[ 100 \times \frac{P}{5} = P \times R \times 4 \]
This simplifies to:
\[ 20P = 4PR \]

### Step 5: Divide both sides by P (assuming P is not zero)
\[ 20 = 4R \]

### Step 6: Solve for R
Now, divide both sides by 4:
\[ R = \frac{20}{4} = 5 \]

### Conclusion
The rate of interest per annum is:
\[ \boxed{5\%} \]