The simple interest on a principal is one-fifth of the given principal at the end of five years. What is the rate of interest per annum?

Options

A. a) `2.5%`
B. b) `5%`
C. c) `4%`
D. d) `2%`

Answer

To solve the problem, we need to find the rate of interest per annum given that the simple interest (SI) on a principal amount (P) is one-fifth of the principal at the end of five years.

### Step-by-step Solution:

1. **Identify the given values:**
- Simple Interest (SI) = \( \frac{1}{5} \times P \)
- Time (T) = 5 years
- Principal (P) = P (unknown value)
- Rate of Interest (R) = ? (what we need to find)

2. **Use the formula for Simple Interest:**
The formula for Simple Interest is:
\[ SI = \frac{P \times R \times T}{100} \]

3. **Substitute the known values into the formula:**
From the problem, we know:
\[ SI = \frac{1}{5} P \]
Therefore, substituting into the SI formula gives:
\[ \frac{1}{5} P = \frac{P \times R \times 5}{100} \]

4. **Simplify the equation:**
To eliminate \( P \) from both sides, we can divide both sides by \( P \) (assuming \( P \neq 0 \)):
\[ \frac{1}{5} = \frac{R \times 5}{100} \]

5. **Cross-multiply to solve for R:**
\[ 1 \times 100 = R \times 5 \times 5 \]
This simplifies to:
\[ 100 = 5R \]

6. **Solve for R:**
Divide both sides by 5:
\[ R = \frac{100}{5} = 20 \]

7. **Calculate the rate per annum:**
Since we used 5 years in our calculation, we need to find the rate per annum:
\[ R = \frac{20}{5} = 4\% \]

### Final Answer:
The rate of interest per annum is **4%**.