Arvind and Govind each invested ₹ 15000 for 3 years at the same rate of interest but Arvind investment is compounded annually while Govind investment is charged on simple interest. What amount did .Arvind receive more than Govind?

Options

A. ₹ 680
B. ₹ 3450
C. data insufficient
D. none of these

Answer

To solve the problem, we need to calculate the final amounts received by both Arvind and Govind after 3 years, and then find the difference between the two amounts.

### Step 1: Calculate the amount received by Govind using Simple Interest (SI)
The formula for Simple Interest is:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \( P \) = Principal amount (initial investment)
- \( R \) = Rate of interest (per annum)
- \( T \) = Time (in years)

Given:
- \( P = 15000 \)
- \( T = 3 \)

The total amount received by Govind after 3 years is:
\[ A_{Govind} = P + SI = P + \frac{P \times R \times T}{100} \]
\[ A_{Govind} = 15000 + \frac{15000 \times R \times 3}{100} \]

### Step 2: Calculate the amount received by Arvind using Compound Interest (CI)
The formula for Compound Interest is:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]
Where:
- \( A \) = Total amount after interest
- \( P \) = Principal amount
- \( R \) = Rate of interest (per annum)
- \( T \) = Time (in years)

Given:
- \( P = 15000 \)
- \( T = 3 \)

The total amount received by Arvind after 3 years is:
\[ A_{Arvind} = 15000 \left(1 + \frac{R}{100}\right)^3 \]

### Step 3: Find the difference between the amounts received by Arvind and Govind
The difference in amounts is:
\[ Difference = A_{Arvind} - A_{Govind} \]
Substituting the expressions we derived:
\[ Difference = 15000 \left(1 + \frac{R}{100}\right)^3 - \left(15000 + \frac{15000 \times R \times 3}{100}\right) \]

### Step 4: Simplify the expression
This expression cannot be simplified further without knowing the value of \( R \). However, we can conclude that Arvind will always receive more than Govind due to the nature of compound interest compared to simple interest.

### Conclusion
Since we do not have the value of \( R \), we cannot calculate the exact difference in amounts. However, we can state that Arvind receives more than Govind due to the compounding effect.