Find the difference between compound interest and simple interest on 5000 for 2 years at `8%` p.a. payable annually.

A. 45

B. 32

C. 57

D. 84

Options

A. A
B. C
C. D
D. B

Answer

To solve the problem of finding the difference between compound interest (CI) and simple interest (SI) on a principal amount of ₹5000 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 given by:
\[ \text{SI} = \frac{P \times R \times T}{100} \]
Where:
- \( P \) = Principal amount = ₹5000
- \( R \) = Rate of interest = 8%
- \( T \) = Time in years = 2

Substituting the values:
\[ \text{SI} = \frac{5000 \times 8 \times 2}{100} = \frac{5000 \times 16}{100} = \frac{80000}{100} = ₹800 \]

### Step 2: Calculate Compound Interest (CI)
The formula for Compound Interest is given by:
\[ \text{CI} = P \left(1 + \frac{R}{100}\right)^T - P \]
Substituting the values:
\[ \text{CI} = 5000 \left(1 + \frac{8}{100}\right)^2 - 5000 \]
Calculating \( \left(1 + \frac{8}{100}\right)^2 \):
\[ \left(1 + 0.08\right)^2 = (1.08)^2 = 1.1664 \]
Now substituting back:
\[ \text{CI} = 5000 \times 1.1664 - 5000 = 5832 - 5000 = ₹832 \]

### Step 3: Calculate the Difference between CI and SI
Now, we find the difference:
\[ \text{Difference} = \text{CI} - \text{SI} = 832 - 800 = ₹32 \]

### Final Answer
The difference between compound interest and simple interest on ₹5000 for 2 years at 8% p.a. is **₹32**.