The S.I is the `40% of principal in 8 years. At certain rate of interest. Find the rate %.

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Understand the Problem
We are given that the Simple Interest (SI) is 40% of the principal (P) in 8 years. We need to find the rate of interest (r).

### Step 2: Write the Formula for Simple Interest
The formula for Simple Interest is:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \( SI \) = Simple Interest
- \( P \) = Principal
- \( R \) = Rate of interest (in percentage)
- \( T \) = Time (in years)

### Step 3: Set Up the Equation
From the problem, we know that:
\[ SI = 40\% \text{ of } P = \frac{40}{100} \times P = 0.4P \]
We also know that the time \( T = 8 \) years.

Substituting the values into the SI formula, we get:
\[ 0.4P = \frac{P \times R \times 8}{100} \]

### Step 4: Simplify the Equation
We can cancel \( P \) from both sides (assuming \( P \neq 0 \)):
\[ 0.4 = \frac{R \times 8}{100} \]

### Step 5: Solve for R
To isolate \( R \), we can multiply both sides by 100:
\[ 40 = R \times 8 \]
Now, divide both sides by 8:
\[ R = \frac{40}{8} = 5 \]

### Step 6: Conclusion
The rate of interest \( R \) is 5%.

### Final Answer
The rate of interest is **5%**.

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