Whatwill be the difference between the compoundinterest (interest is compounded annually) and simple interest on a sum of ₹ 6400 at the rate of 10% per annum for 2 years?

Options

A. a) ₹ 90
B. b) ₹ 72
C. c) ₹ 128
D. d) ₹ 64

Answer

To find the difference between the compound interest (CI) and simple interest (SI) on a sum of ₹6400 at the rate of 10% per annum for 2 years, we can follow these steps:

### Step 1: Calculate Simple Interest (SI)
The formula for Simple Interest is:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \(P\) = Principal amount (₹6400)
- \(R\) = Rate of interest (10%)
- \(T\) = Time (2 years)

Substituting the values:
\[ SI = \frac{6400 \times 10 \times 2}{100} \]
\[ SI = \frac{64000}{100} = 640 \]

### Step 2: Calculate Compound Interest (CI)
The formula for Compound Interest is:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]
Where \(A\) is the total amount after time \(T\).

Substituting the values:
\[ A = 6400 \left(1 + \frac{10}{100}\right)^2 \]
\[ A = 6400 \left(1 + 0.1\right)^2 \]
\[ A = 6400 \left(1.1\right)^2 \]
\[ A = 6400 \times 1.21 = 7744 \]

Now, to find the Compound Interest (CI):
\[ CI = A - P = 7744 - 6400 = 1344 \]

### Step 3: Find the Difference between CI and SI
Now, we can find the difference between Compound Interest and Simple Interest:
\[ Difference = CI - SI = 1344 - 640 = 704 \]

### Final Answer
The difference between the compound interest and simple interest is ₹704.