If the two dates that determine the interest period are known, it is important to calculate the exact number of days between those two dates. To do this, we count the beginning day but not the ending day of the period. We will always use a 365 day year, essentially ignoring leap year.

Be sure to satisfy yourself that this simple subtraction of dates actually includes the first date but not the last.

You should also know that April, June, September and November have 30 days, February has 28 days (29 days during a leap year) and the remaining months have 31 days. Leap years occur every four years and are determined by getting an integer (a whole number) answer when dividing the last two digits of the year by four.

Example 3.2.2

How many days between April 16 and August 12?

Start Date:       April 16 (counted)

End Date:        August 12 (not counted)

Number of days:

Therefore,

[latex]t = \frac{118}{365}\;days[/latex]

Some calculators and computer software will calculate the days for the user.  In this text we present two methods of date counting: using your calculator, and using a table.  We also highly encourage students to take the time to learn how to use the date functionality in Microsoft Excel, as it is well worth the effort.

Using the BA II Plus to Find Exact Dates

We will use Question 16 from the Practice Problems to illustrate the exact date feature of the BA II plus calculator.

• First, find the number of days between the debt and the focal date.

• Next, find the number of days from the $5,000 payment to the focal date.

• Find the number of days from the second payment to the focal date.

We will finish solving this problem later on.

Dates using a Table

If you prefer to use tables, you can use the following:

Table 3-1: Days of the Year

Note carefully: For leap years (those years where the last two digits are divisible by four with an integer result), February 29 must be included and becomes day 60. One day must then be added to all dates following. (Examples of leap years: 2016, 2020, 2024, 2028, 2032 )

There are two occasions when extra care must be taken when using Table 3-1:

Leap Year

In a leap year, if the time period includes the end of February, every date after February 28 increases its count by one.

Be careful when your calculations include a leap year or a period that covers the end of a year.

Write the day count on a diagram.

When the Time Period Includes the End of the Year

Example 3.2.5

How many days between October 15, 2021 and February 13, 2022? The technique is to subtract the first day value from 365 (to get to the end of the year) and then to add the second day value to that difference (which moves you into a second year).

October 15 is the 288th day of the year from Table 3-1. Therefore, the number of days to the end of the year is (365 – 288) or 77.

February 13 is the 44th day of the year from Table 3-1. Therefore, the exact number of days is 77 + 44 = 121. You can draw a time line with the exact dates shown. To assist in calculating the exact time, get into the habit of also writing the day count on the diagram.

This will automatically lead you to an exact count of the number of days between any two dates. To illustrate this, note:

178 – 44 = 134 days between the first two dates,

288 – 178 = 110 days between the second two dates, and

288 – 44 = 244 days between the first and last dates.

Your Own Notes

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