The difference of S.I and C.I on an amount of Rs. 30000 for 2 years is Rs. 147. What is the rate of Interest?

Answer

To find the rate of interest given that the difference between Simple Interest (SI) and Compound Interest (CI) on an amount of Rs. 30,000 for 2 years is Rs. 147, we can follow these steps:

### Step 1: Understand the relationship between SI and CI
The difference between Compound Interest and Simple Interest for 2 years can be expressed as:
\[ \text{Difference} = \text{CI} - \text{SI} = \frac{P \cdot R^2}{100^2} \]
where \( P \) is the principal amount, \( R \) is the rate of interest, and the time is 2 years.

### Step 2: Set up the equation
Given:
- Principal \( P = 30,000 \)
- Difference \( = 147 \)

We can substitute these values into the equation:
\[ 147 = \frac{30000 \cdot R^2}{100^2} \]

### Step 3: Simplify the equation
Rearranging the equation gives:
\[ 147 = \frac{30000 \cdot R^2}{10000} \]
\[ 147 = 3 \cdot R^2 \]

### Step 4: Solve for \( R^2 \)
Now, we can solve for \( R^2 \):
\[ R^2 = \frac{147}{3} \]
\[ R^2 = 49 \]

### Step 5: Find \( R \)
Taking the square root of both sides gives:
\[ R = \sqrt{49} \]
\[ R = 7 \]

### Conclusion
The rate of interest \( R \) is 7% per annum.

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