The Mathematics of Money

Copyright © 2008, The McGraw-Hill Companies, Inc.

September 23, we would add 243 
 23  266. Note that these dates agree with what we

found from the longer table in Example 1.4.1.

Example 1.4.2 Use the abbreviated day of the year table to fi nd the number of days

between August 19, 2006, and October 1, 2006.

The ordinal date for August 19 is 212 
 19  231. The ordinal date for October 1 is 273 


1  274. Subtracting to fi nd the difference, we fi nd there are 274  231  43 days.

Ordinal dates can also be readily found in other places when a table isn’t handy. Many

planners or daybooks print the day of the year for each date on the bottom of the page.

Often this will give the day of the year followed by the number of days left in the year, as

in the illustration below:

October 13

286/79

The 286/79 indicates that October 13 is the 286th day of the year, and 79 days remain in

the year. For our purposes, we are interested only in the 286.

Many computer spreadsheet programs, such as Microsoft Excel, also provide ordinal dates.

Once we can find the term of a note from its dates, we can go on to calculate other

values that depend on the term.

Example 1.4.3 Find the maturity value for the following promissory note:

Promissory Note

I, Cameron Mills, acknowledge a loan of $2,500 made to me

today, January 19, 2005, by William Burgh, and agree to repay

this loan on June 30, 2005, together with simple interest

calculated at a rate of 10%.

June 30 is day 181, and January 19 is day 19, so the term of this loan is 181  19 

162 days.

Using this to calculate the interest gives us:

I  PRT

I  ($2,500)(0.10)(162/365)

I  $110.96

Adding this onto the principal, we arrive at a maturity value of $2,500 
 $110.96  $2,610.96.

Leap Years

Leap years throw a wrench into the problems we have been considering. In leap years, the

60th day of the year is February 29, not March 1, which throws off all dates thereafter. We

could deal with this by creating separate tables for leap years. However, a simple way of

dealing with the problem is just to add one to the value shown in the table for all dates after

February 28 if the year is a leap year.

Recall that for any year between 1900 and 2100, any year divisible by 4 is a leap year.

When in doubt, you can check this by dividing the year by 4 on your calculator. If the result

is a whole number, then the year is divisible by 4 and is a leap year. If the result is not a

whole number, then it isn’t divisible by 4 and so it isn’t a leap year.

1.4 Promissory Notes 35