Understanding Simple Interest Calculation

This question involves calculating the total amount received after a certain period based on a simple interest investment. Simple interest is a basic method of calculating the interest charged on a sum of money borrowed or lent. The interest is calculated on the principal amount only, not on the accumulated interest.

Key Concepts and Formula

To find the total amount received, we first need to calculate the Simple Interest (SI) earned over the given time period. The formula for Simple Interest is:

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

Where:

• P is the Principal amount (the initial investment)
• R is the Rate of interest per annum
• T is the Time period in years

Once the Simple Interest is calculated, the total Amount (A) received is the sum of the Principal and the Simple Interest:

$$ A = P + SI $$

Given Information

Let's identify the values provided in the question:

• Principal Amount (P) = ₹50,500
• Rate of Interest (R) = 6% per annum
• Time Period (T) = 2 years

Step-by-Step Calculation

Follow these steps to find the total amount:

1. Calculate the Simple Interest (SI):

   Using the formula $$ SI = \frac{P \times R \times T}{100} $$, we substitute the given values:

   $$ SI = \frac{50,500 \times 6 \times 2}{100} $$

   First, simplify the calculation:

   $$ SI = 505 \times 6 \times 2 $$

   $$ SI = 505 \times 12 $$

   $$ SI = 6,060 $$

   So, the Simple Interest earned is ₹6,060.

2. Calculate the Total Amount (A):

   Now, add the Simple Interest to the Principal Amount using the formula $$ A = P + SI $$.

   $$ A = 50,500 + 6,060 $$

   $$ A = 56,560 $$

   The total amount the man will receive after 2 years is ₹56,560.

Final Answer Verification

Comparing our calculated amount with the given options:

The calculated amount, ₹56,560, matches Option 3.