The difference between the simple and the compound interest (compounded annually) on Rs. 1250 for 2 yr at 8% per annum will be

Options

A. Rs. 18
B. Rs. 2
C. Rs. 8
D. Rs. 4

Answer

To find the difference between the simple interest (SI) and compound interest (CI) on Rs. 1250 for 2 years at an interest rate of 8% per annum, we can follow these steps:

### Step 1: Calculate Simple Interest (SI)
The formula for Simple Interest is:
\[ \text{SI} = \frac{P \times R \times T}{100} \]
Where:
- \( P = 1250 \) (Principal)
- \( R = 8 \) (Rate of interest per annum)
- \( T = 2 \) (Time in years)

Substituting the values:
\[ \text{SI} = \frac{1250 \times 8 \times 2}{100} \]

### Step 2: Simplify the Calculation
Calculating step-by-step:
\[ \text{SI} = \frac{1250 \times 16}{100} \]
\[ \text{SI} = \frac{20000}{100} \]
\[ \text{SI} = 200 \]

### Step 3: Calculate Compound Interest (CI)
To find the Compound Interest, we first need to calculate the total amount (A) using the formula:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]

Substituting the values:
\[ A = 1250 \left(1 + \frac{8}{100}\right)^2 \]
\[ A = 1250 \left(1 + 0.08\right)^2 \]
\[ A = 1250 \left(1.08\right)^2 \]

### Step 4: Calculate \( (1.08)^2 \)
Calculating \( (1.08)^2 \):
\[ (1.08)^2 = 1.1664 \]

### Step 5: Calculate the Amount (A)
Now substituting back into the amount formula:
\[ A = 1250 \times 1.1664 \]
\[ A = 1458 \]

### Step 6: Calculate Compound Interest (CI)
Now, we can find the Compound Interest using:
\[ \text{CI} = A - P \]
Substituting the values:
\[ \text{CI} = 1458 - 1250 \]
\[ \text{CI} = 208 \]

### Step 7: Calculate the Difference between CI and SI
Finally, we find the difference between Compound Interest and Simple Interest:
\[ \text{Difference} = \text{CI} - \text{SI} \]
Substituting the values:
\[ \text{Difference} = 208 - 200 \]
\[ \text{Difference} = 8 \]

### Final Answer
The difference between the simple interest and compound interest is **8**.

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