Calculate the difference between the simple interest and the compound interest on रु 4,000 in 2 years at 8% per annum compounded yearly

Explanation

To calculate the difference between the simple interest and the compound interest on रु 4,000 in 2 years at 8% per annum compounded yearly, we will follow these steps:

### Step 1: Calculate Simple Interest (SI)
The formula for Simple Interest is:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \( P = 4000 \) (Principal)
- \( R = 8 \) (Rate of interest)
- \( T = 2 \) (Time in years)

Substituting the values:
\[ SI = \frac{4000 \times 8 \times 2}{100} = \frac{64000}{100} = 640 \text{ rupees} \]

### Step 2: Calculate Compound Interest (CI)
To find the Compound Interest, we will calculate the amount at the end of each year.

#### Year 1:
The amount after the first year is calculated as:
\[ A_1 = P + CI_1 \]
Where:
\[ CI_1 = \frac{P \times R \times 1}{100} = \frac{4000 \times 8 \times 1}{100} = \frac{32000}{100} = 320 \text{ rupees} \]
Thus,
\[ A_1 = 4000 + 320 = 4320 \text{ rupees} \]

#### Year 2:
Now, we calculate the Compound Interest for the second year using the new principal (amount after the first year):
\[ CI_2 = \frac{A_1 \times R \times 1}{100} = \frac{4320 \times 8 \times 1}{100} = \frac{34560}{100} = 345.6 \text{ rupees} \]

Now, the total Compound Interest for 2 years is:
\[ CI = CI_1 + CI_2 = 320 + 345.6 = 665.6 \text{ rupees} \]

### Step 3: Calculate the Difference
Now, we find the difference between Compound Interest and Simple Interest:
\[ \text{Difference} = CI - SI = 665.6 - 640 = 25.6 \text{ rupees} \]

### Final Answer
The difference between the compound interest and simple interest on रु 4,000 in 2 years at 8% per annum is **25.6 rupees**.

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