The simple interset on a sum for 5 years is two -fifth of the sum. The rate of interset per annum is

Options

A. 0.1
B. 0.08
C. 0.06
D. 0.04

Answer

To solve the problem step by step, we need to find the rate of interest per annum given that the simple interest for 5 years is two-fifths of the principal amount.

### Step-by-Step Solution:

1. **Understand the Given Information:**
- Let the principal amount be \( P \).
- The simple interest (SI) for 5 years is given as \( \frac{2}{5} P \).

2. **Use the Formula for Simple Interest:**
The formula for simple interest is:
\[ \text{SI} = \frac{P \times R \times T}{100} \]
where:
- \( P \) = Principal amount
- \( R \) = Rate of interest per annum
- \( T \) = Time in years

3. **Substitute the Known Values:**
We know that:
- \( \text{SI} = \frac{2}{5} P \)
- \( T = 5 \) years

Substituting these values into the formula gives:
\[ \frac{2}{5} P = \frac{P \times R \times 5}{100} \]

4. **Simplify the Equation:**
We can cancel \( P \) from both sides (assuming \( P \neq 0 \)):
\[ \frac{2}{5} = \frac{R \times 5}{100} \]

5. **Cross-Multiply to Solve for R:**
Cross-multiplying gives:
\[ 2 \times 100 = R \times 5 \times 5 \]
Simplifying this, we have:
\[ 200 = 25R \]

6. **Solve for R:**
Dividing both sides by 25:
\[ R = \frac{200}{25} = 8 \]

7. **Conclusion:**
The rate of interest per annum is \( 8\% \).