36 Chapter 1 Simple Interest
Example 1.4.4 Find the number of days (a) between January 6, 2004, and May 1,
2004, and (b) between September 3, 2004, and November 16, 2004.(a) In a non-leap year, January 6 is day 6, and May 1 is day 121. However, 2004 was a leap
year. Since January 6 falls before the leap day, it requires no adjustment. Since May 1 falls
after the leap day, we add one and conclude that May 1 was day 122 of 2004. Once we’ve
adjusted for the leap year, we proceed as before: 122 6 116 days.(b) In a non-leap year, September 3 is day 246, and November 16 is day 320. We must add
one to each of these, though, since both fall after the leap day: 321 247 74 days.If you are getting the day of the year from a day planner or computer program, though,
it will have taken the leap year into account already and so you should not add the day
in those cases. These would have given January 6, 2004, as day 6, but would have given
May 1, 2004, as day 122.Finding Loan Dates and Maturity Dates
So far, we’ve found an efficient way to find the term of a note, given its date and maturity
date. We can also find the maturity date given the loan date and term, or the loan date given
the maturity date and term.
Suppose that you borrow a library book on July 6, and the book will be due in 14 days.
It is not hard to see that the due date for the book will be July 20. When we move forward
in time, we add, and 6 plus 14 makes 20. This applies equally well to longer terms.Example 1.4.5 Find the maturity date of a 135-day note signed on March 7, 2005.March 7 is day 66. If we start at day 66 and go forward 135 days, we arrive at day 201,
because 66 135 201.Now, to convert this back to the usual calendar. Using the full day of year table, we
go looking through the table for day 201 and fi nd that it is July 20, 2005, so that is
the maturity date of the note. Using the abbreviated table, we can see that the last
day of June is day 181 and the last day of July is day 212, so day 201 must fall in July.
Subtract: 201 181 20. So it must be the 20th day of July, so we conclude that the
maturity date is July 20, 2005.Suppose on the other hand that you have a movie rental due on October 17. If the rental
period is 5 days, it’s not hard to see that you must have rented it on October 12. When we
move backward in time we subtract, and 17 take away 5 makes 12.Example 1.4.6 Find the date of a 200-day note that matures on November 27, 2006.November 27 is day 331. If we go backward 200 days, we arrive at day 131, since 331
200 131.If we look through the body of the day of the year table we fi nd that day 131 is May 11. Or,
using the abbreviated table, we see that the last day of April is day 120, and 131 120 11.
Either way, we see the note’s date must be May 11, 2006.Be careful, though, if a leap year is involved.Example 1.4.7 A 100-day note was signed on January 3, 2008. When does the note
mature?January 3 is day 3, and so 100 days after that is day 103. Remember, though, that 2008 is a
leap year. Using the full table, we can see that this must fall after the leap day, so we actually
want to fi nd day 102 in the table. The note’s maturity date is thus April 12, 2008.Using the abbreviated table, we remember that every month from February on should have
one added to its ending date. The table shows March ending on day 90, which we realize
in a leap year should actually be 91. Subtracting, 103 91 12, and so we conclude that
the maturity date is April 12.