Calculating Simple Interest from Date to Date

Let's calculate the simple interest based on the given information. We need to find the simple interest (SI) on a principal amount (P), for a specific time period (T), and at a given rate of interest (R).

The details provided are:

• Principal (P) = Rs. 2,400
• Rate of Interest (R) = \(6{1 \over 4}\) % per annum
• Time Period = From March 20, 2019 to May 31, 2019

Step 1: Calculate the Time Period in Days

The time period is given from March 20, 2019, to May 31, 2019. We need to count the exact number of days:

• Number of days in March from March 20 = (31 - 20) + 1 = 12 days
• Number of days in April = 30 days
• Number of days in May = 31 days

Total number of days = 12 + 30 + 31 = 73 days.

Step 2: Convert the Time Period into Years

Simple interest rate is given per annum. We need to convert the total number of days into years. We assume a standard year of 365 days (unless specified otherwise, which is common for simple interest calculations):

Time (T) in years = \(\frac{\text{Total number of days}}{\text{Number of days in a year}}\)

Time (T) = \(\frac{73}{365}\) years

We know that 365 is divisible by 73 (specifically, 365 = 5 \(\times\) 73). So, we can simplify the fraction:

Time (T) = \(\frac{73}{365} = \frac{1}{5}\) years.

Step 3: Convert the Rate of Interest to a Fraction

The rate of interest is given as \(6{1 \over 4}\) % per annum. Let's convert this mixed fraction to an improper fraction:

Rate (R) = \(6{1 \over 4}\)% = \(\left(6 + \frac{1}{4}\right)\)% = \(\left(\frac{6 \times 4 + 1}{4}\right)\)% = \(\frac{25}{4}\) % per annum.

Step 4: Calculate the Simple Interest

The formula for Simple Interest (SI) is:

SI = \(\frac{P \times R \times T}{100}\)

Substitute the values we have:

• P = Rs. 2400
• R = \(\frac{25}{4}\) %
• T = \(\frac{1}{5}\) years

SI = \(\frac{2400 \times \frac{25}{4} \times \frac{1}{5}}{100}\)

Let's simplify the calculation:

SI = \(\frac{2400 \times 25 \times 1}{4 \times 5 \times 100}\)

SI = \(\frac{2400 \times 25}{20 \times 100}\)

SI = \(\frac{2400 \times 25}{2000}\)

We can cancel out common factors. Cancel 100 from numerator (2400) and denominator (2000):

SI = \(\frac{24 \times 25}{20}\)

Now, cancel out common factors between 24 and 20 (both divisible by 4), and between 25 and the remaining denominator:

SI = \(\frac{6 \times 25}{5}\) (Dividing 24 and 20 by 4)

SI = \(6 \times 5\) (Dividing 25 and 5 by 5)

SI = 30

The simple interest is Rs. 30.

Simple Interest Calculation Summary

Therefore, the simple interest on Rs. 2,400 from March 20, 2019, to May 31, 2019, at \(6{1 \over 4}\)% rate is Rs. 30.

Revision Table: Key Simple Interest Concepts

Additional Information: Simple Interest Calculations

Simple interest is a straightforward way to calculate the interest on a loan or investment. It differs from compound interest, where interest is calculated on the principal amount plus any accumulated interest.

• When calculating simple interest for a period given in days, it's crucial to count the exact number of days between the start and end dates.
• The number of days in a year is typically taken as 365 for normal years and 366 for leap years when calculating interest based on days. In this specific problem (2019 is not a leap year), we used 365 days.
• The rate of interest is usually given per annum (per year), so the time period must also be expressed in years for the formula \(\frac{P \times R \times T}{100}\) to work correctly.