Simple interest for the sum of X 1500 is X 30 in 4 yr and ? 60 in 8 yr. Find the rate of simple interest.

Options

A. 0.025
B. 0.015
C. 0.005
D. 0.0025

Answer

To solve the problem of finding the rate of simple interest, we will follow these steps:

### Step 1: Understand the given information
We have:
- Principal (P) = 1500
- Simple Interest (SI) for 4 years = 30
- Simple Interest (SI) for 8 years = 60

### Step 2: 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 3: Set up the equation for the first case (4 years)
Using the information for the first case (4 years):
\[ 30 = \frac{1500 \times R \times 4}{100} \]

### Step 4: Simplify the equation
Now, we simplify the equation:
\[ 30 = \frac{6000R}{100} \]
\[ 30 = 60R \]

### Step 5: Solve for R
To find \(R\), we divide both sides by 60:
\[ R = \frac{30}{60} = \frac{1}{2} \]

### Step 6: Convert R to percentage
Since \(R\) is in fraction, we convert it to percentage:
\[ R = \frac{1}{2} \text{ percent} = 0.5 \text{ percent} \]

### Step 7: Conclusion
Thus, the rate of simple interest is \(0.5\%\).

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