The simple interest accrued on an amount of Rs. 40000 for 2 years is `1/8` of the principal. What is the rate of simple interest per annum?

Options

A. 5
B. 4.5
C. 6.25
D. 7.25

Answer

To solve the problem step by step, we need to find the rate of simple interest per annum given that the simple interest accrued on an amount of Rs. 40,000 for 2 years is \( \frac{1}{8} \) of the principal.

### Step 1: Identify the Principal and Simple Interest
- The principal amount (P) is Rs. 40,000.
- The simple interest (SI) is given as \( \frac{1}{8} \) of the principal.

### Step 2: Calculate the Simple Interest
- Calculate \( \frac{1}{8} \) of the principal:
\[ SI = \frac{1}{8} \times 40,000 = 5,000 \]

### Step 3: Use the Simple Interest Formula
- The formula for simple interest is:
\[ SI = \frac{P \times R \times T}{100} \]
where:
- \( SI \) = Simple Interest
- \( P \) = Principal
- \( R \) = Rate of interest per annum
- \( T \) = Time in years

### Step 4: Substitute Known Values into the Formula
- Substitute the values we have into the formula:
\[ 5,000 = \frac{40,000 \times R \times 2}{100} \]

### Step 5: Simplify the Equation
- Rearranging the equation gives:
\[ 5,000 = \frac{80,000R}{100} \]
- Simplifying further:
\[ 5,000 = 800R \]

### Step 6: Solve for R
- To find \( R \), divide both sides by 800:
\[ R = \frac{5,000}{800} = 6.25 \]

### Step 7: Convert to Percentage
- Since \( R \) is the rate per annum, we express it as:
\[ R = 6.25\% \]

### Final Answer
The rate of simple interest per annum is **6.25%**.

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