On a certain sum of money the compound interest for 2 years is `Rs. 282.15` and the simple interest for the same period of time is `Rs. 270`. The rate of Interest per annum is

Options

A. `6.07%`
B. `10% `
C. `9%`
D. `12.15%`

Answer

To find the rate of interest per annum based on the given compound interest (CI) and simple interest (SI) for 2 years, we can follow these steps:

### Step 1: Identify the given values
- Compound Interest (CI) for 2 years = Rs. 282.15
- Simple Interest (SI) for 2 years = Rs. 270

### Step 2: Calculate the difference between CI and SI
We need to find the difference between the compound interest and simple interest:
\[ \text{Difference} = \text{CI} - \text{SI} = 282.15 - 270 = 12.15 \]

### Step 3: Use the formula to find the rate of interest
The formula to find the rate of interest (R) when we have the difference between CI and SI for 2 years is:
\[ R = \frac{2 \times \text{Difference}}{\text{SI}} \times 100 \]
Substituting the values we found:
\[ R = \frac{2 \times 12.15}{270} \times 100 \]

### Step 4: Calculate the rate of interest
Calculating the above expression:
\[ R = \frac{24.30}{270} \times 100 \]

Now, simplifying:
\[ R = 0.09 \times 100 = 9\% \]

### Final Answer
The rate of interest per annum is **9%**.

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