Mathematics of Investment
Prof. Donald H. Pelletier
2000-01 Full year
N506 Ross
AS/MA 2580 BY
416-736-2100 ext.33339

May 23: The final grades are posted at this link: Final Grades   The class average is 4.9 (essentially a C+).

May 6: Our folder on ACADLABS now contains a file called SampleFinal.doc in Microsoft Word format. This file contains an assortment of problems from previous years' exams. Our last class this coming Thursday will be devoted to these; you are advised to work them in advance. It is also a good idea to begin preparing your crib-sheet (one 8 1/2 by 11 page written on both sides) for the final exam (which is NOT open book). Last Thurday, May 3, we covered 9.6 A4, 7.3 A1, A5, B2, B5, B8 (the answer in the text for B8 is wrong), 8.4 A2, A6, and A8.

April 27: Last night, with the computer and overhead projector in class, we demonstrated how to use the spreadsheet Mortality.xlw for solving problems from Chapter 9 using the approach to life annuities and insurance via commutation symbols, as outlined in the file Chap9notes. This material is not in the text but it will be covered on the final exam. We also examined the EXCEL functions NPV and IRR. In the two classes that remain in the term, we will spend a bit more time on insurance-related problems that are not in the text; also, Section 7.3 on Capitalized Costs and Examples 5 and 6 from Section 8.4 will be treated. If time permits, we will speak about Section 7.4 on depreciation but this will not be on the final exam. Recall that the final exam is NOT open book; instead, you are allowed to bring a single 8 1/2 x 11 crib sheet (written on both sides) to the exam.

April 16: The notes for Chapter 9 are now available in our ACADLABS folder. The filename is Chap9notes.doc and it is in Microsoft Word format. This same file in HTML format is at this link:  Chap9notes.html
The related EXCEL spreadsheet is called Mortality.xlw and is also available on ACADLABS.
There is an updated version of the file FinFcns.XLS that contains examples illustrating the use of EXCEL's financial functions IRR and NPV.
The name of the server is ACADLABS.CCS.YORKU.CA and the path to the directory containing these files is  /usr/fac/dhp/ma2581/
We will begin treatment of this material on Thursday.

April 13: In last night's session, April 12, we began by returning class test #2 (the class average and the median are both 26.5 out of 40) and presenting the solutions at the board; we then covered Sections 7.1 and 7.2 and began to cover Section 9.1. Our plan is to complete Chapter 9 and the relevant parts of Chapter 8 before returning to cover Sections 7.3 and 7.4; the point is that because it is essentially trivial, Section 7.4 on depreciation will only be covered if time permits and, even then, will not be included on the final exam. We discussed the worked-out examples 1 and 2 from the body of Section 7.1 and amplified example 2 with a spreadsheet-type calculation that emphasizes the meaning of NPV. The details are in the files 7-1Exs1-4.XLW and 7-2Ex4.XLW in our ACADLABS folder.
From Chapter 8 on probablility, we will only deal with problems that relate to mortality; we will not treat questions involving dice, cards, balls in boxes, and so on, such as those in Section 8.1. Our treatment of Chapter 9 will differ from the one in the text; a set of notes will be available for download from our course website and from ACADLABS.

April 9: In class on April 5, we covered a lot of material: Sections 6.4, 6.5, 6.6 and 6.7. From Section 6.4, we presented and expanded on Examples 1 and 2 from the body of the text. From 6.5, we presented a corrected version of the graph on page 203 and did Exercises 6.5 A1, A6, B1 and  B2. From 6.6, Exercises A3 and A7. From 6.7, Exercise A1. The class tests will be returned next Thursday, April 12. An updated version of the file FinFcns.XLS is now available on ACADLABS.

March 26: Computer Services has informed me that the course files should now be accessible in the normal way on ACADLABS. The temporary fix described in the March 25 note below will also remain operative but just for the rest of the week.

March 25: I have found a temporary fix for the problem.

I have uploaded the four most relevant files to York's anonymous FTP server so that you can download them to your local machine.
If you do not already have an FTP client on your local machine, it's a good thing to have and you can obtain one at no cost by downloading it from
For a PC, you should use WS-FTP
For a Mac, you should use FETCH

Here are the instructions for using WS-FTP or FETCH.  Enter the following at the obvious locations in your FTP client window:

User ID: anonymous
Directory: incoming

You will now see a window displaying the contents of the 'incoming' directory; it will appear to be empty.  This is because York has set up anonymous ftp so that the user must know the exact names of the files they wish to retrieve. You should now ask your FTP client to 'GET' the files you would like (one at a time).  Just type the appropriate filename into the 'GET' window.

The EXCEL file names are

The filenames are case sensitive and must be input exactly as shown above.

There is also a MSWord file which you only need if you did not receive the handout that I distributed in class.

March 23: There appears to be some problem in accessing the ACADLAB files. I have discussed this on the phone with CNS Client Services and we will try to iron things out tomorrow, Saturday.The ACADLABS setup seems to have changed since I last used it three years ago; I should not have taken this for granted.

March 22: Coverage for next week's class test: Section 4.4 (geometric progression case), Chapter 5 (omitting Section 5.4) and Chapter 6 Sections 1, 2, and 3.
In addition, there is an EXCEL related question whose format will be as explained in the file ZB-problems.xls accessible from ACADLABS.

March 15: Tonight we covered Sections 6.1, 6.2 and 6.3. Here again is a partial list of problems done in class:
6.2 A3, A8 and A10;
6.3 A4, A5, B2 and B5.
Next week, I have arranged for a computer to be brought to class and we will discuss and demonstrate aspects of the spreadsheet program EXCEL, with particular attention to financial functions.
Class test #2 is scheduled for the following week, March 29. It will emphasize material covered since the last class test; in particular, there will be no problems on simple interest.
Although it is "possible" to learn enough EXCEL to succeed in the course without any hands-on experience, it is advisable to get some. If you do not already have a personal copy of EXCEL, you should get a personal account on ACADLABS so that you can access EXCEL from the university's computer labs in Steacie. To do this, go to and follow the instructions. The web is crawling with EXCEL tutorials; I have not yet found a source that I consider ideal but here are some suggestions: (I welcome your feedback in this area; if you find something you really like, please let me know about it.) [this needs to be downloaded and used on your local machine]

March 10: During the classes held on March 1 and March 8, we finished Chapter 5 (omitting Section 5.4), we returned to Section 4.4 to cover the case where the payments form a geometric progression (we will omit the case where they form an arithmetic progression) and we began Chapter 6. Here is a partial list of problems done in class:
4.4 A2, A9 and B2;
in section 5.3, Examples 1 and 3 from the body of the text;
5.3 A10 and B4;
5.6 A4;
5.7 A1 and A4.

January 18: In tonight's class I returned to cover Section 3.6 and Sections 4.1 and 4.2. The following exercises were done at the blackboard: Section 3.7 # 18, 19, Section 4.5 # 14, 18, 28. By popular request, our first class test is now postponed another week. It is rescheduled for Thursday February 1.

January 10, 2001 update: "York University Senate Announces Date for Resumption of Term

The York University Senate Executive Committee has announced that the additional instruction period for students will begin Friday, Jan.12 and continue to Monday, Feb.12, provided that the tentative offer between the university and CUPE 3903 teaching and graduate assistants is ratified.

The second Fall examination period will be held Feb.13 to Feb.23.

Winter Term will begin and Fall/Winter Term (full-year) classes resume Feb. 26 and end May 11."

Our classes in MA2580 will therefore resume on Thursday Jan 18. Our first class test was originally scheduled for Nov. 9, shortly after the strike began. I am hereby rescheduling it for Jan. 25. It will last two hours and will cover the same material that was initially programmed: through and including Section 4.3 of the textbook. The first class period on Jan 18 will be devoted to reviewing material for the test.

On Feb 1, we will briefly review the beginning of Chapter 5 that I covered during the early days of the strike and continue with new material, hoping to complete Chapter 5 on Feb 8.

Following a two-week break for the Fall Term make-up exam period, we will begin the spreadsheet component of the course. If you do not have personal access to EXCEL (or to some compatible spreadsheet), you will need to rely on campus computer labs and should, very soon if you do not already have one, set up your personal account on ACADLABS using the MAYA account management system. Details for doing this are posted on the walls in various labs. EXCEL runs on both PCs and MACs and the file format is common to both platforms, so you can use whichever you are more comfortable with. If you have no prior experience with computers, you will need to use the break to become familiar on your own with their general use because our focus in class will be on the software.

November 29 update: The Administration has posted guidelines for the eventual balance of the academic sessions at

In view of these guidelines, I have decided that the lectures in MA2580B will resume whenever the 22 'Instructional Days Following the Disruption" occur. Our first class test will take place during the second week of this resumption. Under the 'Changes in Course Requirements" guideline, I have decided that it is no longer possible to have three class tests since a full-year course will now have six fewer lecture hours than normal. So there will be two class tests, worth 30% each, and a final exam worth 40%.

November 16 announcement: Lectures in this course are now suspended until the end of the strike. The University Senate has mandated the scheduling of make-up classes for courses that have continued to meet but with low attendance. Please visit the Administration's main website for detailed information. When classes resume, we will meet once and the postponed first class test will then take place on the following Thursday. It will cover what was originally planned (everything through and including Section 4.3) despite the fact that we have continued to treat new material in classes.

November 16: We derived the general formulas for the entries in the k-th row of an amortization table, as in Exercise 5.1 B1. As an application, we then spent a lot of time on 5.1 B13.

November 9: From section 4.1 we presented exercise B8. From Section 4.2, we did A6, A9 and A11. We did Exercise 5.1 B4 using the data from 4.1 A11. From Section 4.3, we covered Exercises A4 and A5. We will now postpone Section 4.4 until after the strike because this is the most difficult section of the text. We will continue with Chapter 5 next week, treating Sections 5.1 and 5.2 together as a single unit.

I recommend visiting the websites of various banks to become familiar with the vocabulary relating to mortgages.

The following specific pages are useful; to get there in one step, you have to enter the full address, otherwise you have to hunt it down on their website.

Since the website is completely controlled by the administration, I also recommend visiting if you wish to balance your sources of information.

November 2: Tonight in class we covered all of Section 3.6 and began Section 4.1. Specifically, From Section 3.6, we presented exerices A 3, B 1, and, from Appendix 3, example 2 on page 317. From Section 4.1, we analysed exercises A 6, 15, and 24. From Section 4.1, we intend to omit exercises B 2, 3, 6, and 7 which deal with a systematic approach to the equivalent payment method.

October 31: We will meet this week and cover Sections 3.6 and 4.1. It is now definite that the class test scheduled for Nov. 9 is postponed.


Prerequisite: Grade 12 Mathematics. The three appendices in the textbook provide a review of the topics that are most relevant for the course: exponents, logarithms, arithmetic and geometric progressions, and linear interpolation.

Degree-credit exclusions: Math 1581, Math 2581 (Business Mathematics I and II) and Math 2280 (Theory of Interest). For students in the Actuarial Mathematics stream, Math 2280.03 is required in place of Math 2580.

Textbook and supplies: Mathematics of Finance, 4th edition, by P. Zima and R.L. Brown. McGraw-Hill Ryerson, publisher. This is a hardback and is available in the York bookstore. The course will cover all of this text. Caution: McGraw-Hill Ryerson also publishes in its Schaumís Outline series another book by the same authors with the same title; this is NOT our textbook. Another essential item is a basic scientific calculator with the ability to compute logarithms, exponentials, reciprocals, and powers.

Tests and exams: There will be three in-class tests --- each worth 20% of the course grade. The exact dates for these have not yet been decided but you should expect them in mid-November, mid-January and early March. There will be a 3-hour final exam during the April examination period worth 40% and that will be in common with the other section of MA2580. All the class tests will be "open-book" and open notes. Unfortunately, I have absolutely no control over the precise scheduling of the final exam; you must be prepared for it to fall on any date within the official exam period: April 11 to April 30, 2001.

Grades: The official grades at York University are LETTER grades. Qualitative descriptions of these grades can be found in the York Calendar. Your test marks will be on a numerical scale because these have to be weighted and averaged in various ways, but THERE IS NO AUTOMATIC PREDETERMINED CORRELATION BETWEEN NUMERICAL GRADES AND LETTER GRADES in this course. In particular, the "numerical" grades you receive are NOT to be interpreted as percentages. The median letter grade will likely fall between C and C+.

Homework: Throughout the year, the everyday homework assignment is to do as many of the problems from the textbook as you find necessary to develop your understanding of the course material. These are not to be submitted nor graded; they should be viewed as practice for the tests that will contain, for the most part but not exclusively, questions very similar to those from the text. I will occasionally make specific suggestions concerning problems to do or to avoid. The back of the textbook contains the answers to all the numerical problems so it is quite practical to work on your own or together in small groups. Also, several copies of a complete solutions manual are available at the reserve desk in Steacie library and these can also be purchased at the York bookstore.

Excel: A component of the course is devoted to an introduction to the use of spreadsheets for financial calculations. We will be using Microsoftís EXCEL which functions on both the PC and Macintosh platforms. Some class sessions will be devoted to demonstrations of this software but students will be expected to work on their own in the microcomputer laboratories that are scattered throughout the Steacie Science building; these are open 24 hours per day, 7 days a week. The software manuals for EXCEL are on 2-hour reserve at the desk in Steacie library; but you should rarely need these because the program itself has substantial on-line help files. To access these programs, you will require a personal "ACADLABS" account because this is the name of the server on which EXCEL resides. To obtain such an account, follow the instructions concerning MAYA available at the Computing Help Services desk in Steacie. Note that this account is different from your e-mail account. There will be one required spreadsheet assignment to be done in the winter term, to be submitted on diskette, and that will be graded on a "pass-fail" basis as follows: the result will either raise your letter grade by one point, leave it unchanged, or lower it by one point (exception: a D will not be lowered to an E).

Policy on missed tests or exams: No make-ups will be given for the class tests. Absence from any ONE of the three class tests, however, will be tolerated with no documentation required; the missed marks will be "forwarded" to the final exam. (This route is dangerous, however, and is not recommended.) Students who are absent from the final exam without a properly documented medical reason receive a grade of F. Note that travel plans should not be made prior to the announcement of the final exam schedule: having a plane ticket for Hawaii on April 25 is NOT a legitimate excuse for absence from a final exam on April 29.

Syllabus: The pair of half-courses 1581-2581 is equivalent to the full course 2580. Both will cover the entire textbook plus the material on spreadsheets. Either MATH 1581 3.0 or MATH 2580 6.0 will serve to satisfy part of the Core requirements of the Business and Society Programme. Roughly speaking, 1581 contains all of the easy material from 2580 while 2581 deals with the 'complications'. Students who intend to take 6 rather than 3 credits in this area will find a more balanced distribution of workload by taking 2580. In particular, the material on spreadsheets is distributed over the full year in MA2580 but is covered only in the second term of the 1581-2581 sequence.

Dates and deadlines: Last day to enrol without approval of the course director --- Sat. Sept. 23; last day to enrol with the written approval of the course director --- Friday Oct. 20; last day to DROP the course without receiving a grade --- Friday February 9.

Office hours: Feel free to drop in at my office any time; I have no objection to unscheduled meetings; but if you wish to be certain to find me, however, it is best to set up an appointment by speaking with me before or after class or by sending me an email message. Written messages can also be left for me in the office of the mathematics department, N520 Ross.

Generalities: Students are responsible for familiarizing themselves with York University Policy and Regulations. These can be found in the Undergraduate Programmes Calendar. Take special notice of the Senate Policy on Academic Honesty; cheating and/or impersonation are subject to serious academic penalties. Photo identification will be required at all tests and examinations. Also, some test papers (randomly selected) will be photocopied before they are returned so that subsequent alterations can be detected.