Calculating Simple Interest on ₹4,000 at 6.75%

This question requires calculating the simple interest earned on a principal amount deposited for a specific duration. We need to find the exact number of days the money was deposited and then use the simple interest formula.

Understanding Simple Interest

Simple Interest (SI) is a method used in finance to calculate the interest earned on a sum of money (principal) at a specific rate over a period. The formula for Simple Interest is:

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

Where:

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

Determining the Time Period

The deposit was made on 22 February 2024 and withdrawn on 23 April 2024. We need to calculate the total number of days in this period.

• Days remaining in February: The year 2024 is a leap year, so February has 29 days. Days = 29 - 22 = 7 days.
• Days in March: March has 31 days.
• Days in April: The withdrawal date is 23 April, so we count 23 days.
• Total Days: 7 (Feb) + 31 (Mar) + 23 (Apr) = 61 days.

Now, we need to convert these days into years. Since 2024 is a leap year, a full year has 366 days.

Time (T) = $ \frac{61}{366} $ years.

Calculating the Simple Interest

Given:

• Principal (P) = ₹4,000
• Rate (R) = 6.75% per annum
• Time (T) = $ \frac{61}{366} $ years

Using the Simple Interest formula:

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

Substitute the values:

$ SI = \frac{4000 \times 6.75 \times \frac{61}{366}}{100} $

Simplify the calculation:

$ SI = \frac{4000 \times 6.75 \times 61}{100 \times 366} $

$ SI = \frac{40 \times 6.75 \times 61}{366} $

First, calculate $ 40 \times 6.75 = 270 $.

$ SI = \frac{270 \times 61}{366} $

$ SI = \frac{16470}{366} $

$ SI = 45 $

Final Result

The simple interest calculated for the period is ₹45.