Understanding Simple Interest Calculation

The problem asks us to find the difference between the simple interest paid on two loans of equal principal amount but different interest rates over the same period.

Here's a breakdown of the steps involved:

• Identify the Principal (P), Rate (R), and Time (T) for each bank.
• Calculate the Simple Interest (SI) for each loan using the formula.
• Find the positive difference between the two calculated simple interests.

Simple Interest Formula

The formula for Simple Interest (SI) is:

$$ SI = \frac{P \times R \times T}{100} $$

Where:

• P = Principal Amount
• R = Annual Interest Rate (in percent)
• T = Time Period (in years)

Calculating Interest for Bank A

For Bank A:

• Principal Amount (P) = ₹5,00,000
• Annual Interest Rate (R_A) = 3.5%
• Time Period (T) = 4 years

Using the formula:

$$ SI_A = \frac{5,00,000 \times 3.5 \times 4}{100} $$

$$ SI_A = 5000 \times 3.5 \times 4 $$

$$ SI_A = 5000 \times 14 $$

$$ SI_A = \text{₹}70,000 $$

Calculating Interest for Bank B

For Bank B:

• Principal Amount (P) = ₹5,00,000
• Annual Interest Rate (R_B) = 6%
• Time Period (T) = 4 years

Using the formula:

$$ SI_B = \frac{5,00,000 \times 6 \times 4}{100} $$

$$ SI_B = 5000 \times 6 \times 4 $$

$$ SI_B = 5000 \times 24 $$

$$ SI_B = \text{₹}1,20,000 $$

Finding the Difference in Interest

We need to find the positive difference between the simple interest paid to Bank B and Bank A.

Difference = $$ |SI_B - SI_A| $$

Difference = $$ |\text{₹}1,20,000 - \text{₹}70,000| $$

Difference = $$ \text{₹}50,000 $$

Summary of Calculations

The positive difference between the amounts of simple interest paid to the two banks after 4 years is ₹50,000.