The Mathematics of Money

38 Chapter 1 Simple Interest

still fall in 2006, since there aren’t that many days left in the year. It’s not surprising, then,

that following our original method of adding the days on doesn’t work: November 1 is day

305, and day 305 
 300  day 605, which makes no sense.

We can adapt the method of Example 1.4.8 to this situation as well though. The note

starts in 2006. We can ask ourselves what portion of the note’s term will fall in 2006, and

then see how much is left over to run into 2007. From day 305 to the end of 2006 would

be 365  305  60 days. So of the total 300 day term, 60 days fall in 2006, which leaves

300  60  240 days to run into 2007. That would take us to day 240 of 2007, which leads

us to the maturity date of 8/28/07.

A time line may once again be helpful to illustrate this. Also, it may be helpful to keep

a running tally along the side to keep track of how many days we have left to account for

as we fill in the time line.

Running tally

We start with 300 days to account for: 300 days

The note lives for 365  305  60 days in 2006:

11/1/06

Day 305

12/31/06

Day 365

60 days

2006

60 days

Which leaves to carry into the next year: 240 days left

Extending 240 days into 2007 takes us to day 240: 240 days

11/1/06

Day 305

12/31/06

Day 365

60 days 240 days

2006 2007

Day 240

0 days left

Looking to the day of the year table, we see that day 240 is 8/28/07.

We can follow a similar approach to back up from a maturity date to the loan date, as

illustrated in the following example.

Example 1.4.9 Find the loan date for a 500-day note that matured on February 26,

2003.

Running tally

500 days

February 26 is day 57, and obviously we can’t go backward 500 days from that date without

crossing into a prior year. But we can account for 57 days of the term in 2003:

57 days

2/26/03

2003

1/1/03

57 days

Of the remaining 443 days, 2002 takes care of 365: 365 days

(^) 57 days
1/1/02 2/26/03
365 days

2002 2003

1/1/03

78 days

We will be able to cover the remaining 78 days in 2001. The year ends on Day 365, so

moving 78 days backward takes us to 365  78  Day 287. Seeking out Day 287 from the

table gives us a date of October 14.