The difference between the compound interest and simple interest on Rs. 10,000 for 2 years is Rs.25. The rate of interest per annum is

Options

A. 0.05
B. 0.07
C. 0.04
D. 0.12

Answer

To find the rate of interest per annum given that the difference between the compound interest (CI) and simple interest (SI) on Rs. 10,000 for 2 years is Rs. 25, we can follow these steps:

### Step 1: Understand the formulas
The formulas for calculating Simple Interest (SI) and Compound Interest (CI) are:
- Simple Interest (SI) = \( \frac{P \times R \times T}{100} \)
- Compound Interest (CI) = \( P \left(1 + \frac{R}{100}\right)^T - P \)

Where:
- \( P \) = Principal amount (Rs. 10,000)
- \( R \) = Rate of interest per annum
- \( T \) = Time in years (2 years)

### Step 2: Calculate Simple Interest for 2 years
Using the formula for SI:
\[ SI = \frac{10000 \times R \times 2}{100} = 200R \]

### Step 3: Calculate Compound Interest for 2 years
Using the formula for CI:
\[ CI = 10000 \left(1 + \frac{R}{100}\right)^2 - 10000 \]
Expanding the expression:
\[ CI = 10000 \left(1 + \frac{2R}{100} + \frac{R^2}{10000}\right) - 10000 \]
\[ CI = 10000 + 200R + 10000 \frac{R^2}{10000} - 10000 \]
\[ CI = 200R + R^2 \]

### Step 4: Find the difference between CI and SI
According to the problem, the difference between CI and SI is Rs. 25:
\[ CI - SI = 25 \]
Substituting the values we calculated:
\[ (200R + R^2) - 200R = 25 \]
This simplifies to:
\[ R^2 = 25 \]

### Step 5: Solve for R
Taking the square root of both sides:
\[ R = 5 \]
Thus, the rate of interest per annum is 5%.

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

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