AIC121 - Foundations of Real Estate Mathematics

Outline info
Last revision date 2017-09-18 15:32:30.711
Last review date 2017-09-18 15:32:30.713

Subject Title
Foundations of Real Estate Mathematics

Subject Description
This subject introduces the techniques of investment and statistical analysis in a real estate context. Topics include: statistical techniques, cash flow analysis, discounting, compounding, and the mathematics of real estate finance and investment analysis. There is also a brief overview of graphing and surveying. A personal computer with spreadsheet software is required.

Credit Status
This is a credit subject applicable towards the Appraisal Institute of Canada's CRA and AACI designations, as well as UBC's Diploma in Urban Land Economics. Successful completion of the AIC course components of the program also earn students 50-60 degree credits toward the Bachelor of Business in Real Estate Program (BBRE) offered by the University of British Columbia (UBC) and Thompson Rivers University (TRU).

Learning Outcomes
Upon successful completion of this subject the student will be able to:

1. Understand the time value of money and compound interest as the basis of financial analysis.

2. Be able to convert equivalent interest rates based on different compounding periods.

3. Calculate loan information: present and future values, interest rates, annuity payments, outstanding balances, and amortization periods.

4. Understand the impact of bonuses and discounts on the effective interest rate charged on a loan.

5. Calculate the market value of a mortgage under various financing terms.

6. Calculate yields, net present values and profitability indicies in order to be able to compare investments.

7. Manipulate linear equations and draw simple line graphs.

8. Understand measuring and surveying techniques used in Canada.

9. Understand the techniques for arranging and analyzing statistical data.

10. Calculate the various measures of central tendency and dispersion in a statistical sample.

11.Calculate correlation between two variables and perform linear regression analysis.

Cheating and Plagiarism
Each student should be aware of the College's policy regarding Cheating and Plagiarism. Seneca's Academic Policy will be strictly enforced.

To support academic honesty at Seneca College, all work submitted by students may be reviewed for authenticity and originality, utilizing software tools and third party services. Please visit the Academic Honesty site on for further information regarding cheating and plagiarism policies and procedures.

All students and employees have the right to study and work in an environment that is free from discrimination and/or harassment. Language or activities that defeat this objective violate the College Policy on Discrimination/Harassment and shall not be tolerated. Information and assistance are available from the Student Conduct Office at

Accommodation for Students with Disabilities
The College will provide reasonable accommodation to students with disabilities in order to promote academic success. If you require accommodation, contact the Counselling and Disabilities Services Office at ext. 22900 to initiate the process for documenting, assessing and implementing your individual accommodation needs.


Topic Outline
Chapter 1 - The Basis of Financial Analysis

Introduction: Real Estate Analysis
The Basis of Financial Analysis
Simple Interest
Compound Interest: Interest for a Single Rental Period
Nominal Rates
Compound Interest: Multiple Periods
Discounting Single Amounts
Other Compound Interest Calculations: Periodic Rate and Term

Chapter 2 - Interest Rate Conversions
Equivalent Rates
Interest Rate Conversions Using Financial Functions
Equivalent Rates: Calculations Involving Use of Tables
Effective Annual Interest Rates
Interest Only Loans
Interest Adjustment Periods: An Application of Interest Rate Conversion

Chapter 3 - Analysis of Financial Flows and Investments I
Irregular Patterns of Costs and Benefits
Present Values of Cash Flows
Future Values of Irregular Cash Flows
Irregular Cash Flows and Interest Rate Conversion
Regular Payments and Irregular Intervals
Analysing Regular Cash Flows: An Introduction
Present Value of Regular Cash Flows
Present Value of One Dollar Per Period
Calculating Payments
Calculating Interest Rates and Amortization Period

Chapter 4 - Analysis of Financial Flows and Investments II
Constant Payment Mortgage Loan
Present Value Analysis and Ordinary General Annuities
Innovative Option for Constant Payment Mortgages
Present Value Analysis and Ordinary General Annuities
Perpetual Annuities
Reversionary Values and Perpetual Annuities
Deferred Annuities
Analysis of Annuities Due

Chapter 5 - Future Value Analysis
Future Values and Ordinary Simple Annuities
Sinking Funds
Future Value Analysis and Ordinary General Annuities
Equivalent Payments
Future Values and Deferred Annuities

Chapter 6 - Outstanding Balances and Final Payments
Outstanding Balances and Final Payments on Amortized Loans
Calculation of Outstanding Balances
Payments: Principal and Interest Components
Accumulated Interest
Calculation of Final Payments

Chapter 7 - Yields, Bonuses, Discounts, and the Secondary Mortgage Market
Introduction: Primary and Secondary Mortgage Markets
Bonuses and Discounts on Fully Amortized Loans
Bonuses and Discounts on Partially Amortized Loans
The Impact of Partial Amortization on Interest Rates and Yields on Bonused Mortgage Loans

Chapter 8 - Real Estate Applications of Bonuses and Discounts and the Impact of Financing on Property Prices
Purpose of Disclosure Requirements
Disclosure Requirements - Fully Amortized Loans
Disclosure Requirements - Partially Amortized Loans
Calculation of the Bonus Required to Achieve a Desired Rate of Interest: Buying Down a Rate
Bonused Mortgages: Other Applications
Prepayment of Bonused Mortgages
Vendor Financing Applications
Financing Applications in the Context of New Developments
Assumable Financing
Analysis of Bonused Prices

Chapter 9 - Real Estate Investment and Discounting
Introduction to Equity Analysis
Present Values of Cash Flows
Net Present Values and Present Value Ratios
Profitabilty Indices
Internal Rates of Return: Yield Analysis
Discounted Cash Flow Measures and the Reinvestment Assumptions
Reinvestment Assumption and Ordinary Simple Annuities
Reinvestment Assumptions and Comparison of Investment Alternatives
Time Horizons and Comparisons of Investment Alternatives

Chapter 10 - Mathematics of Graphing and Surveying
Graphing and Surveying
Why study Graphs
Graphs and Formulae
Surveyor’s Mathematics
Basic Measurement Concepts
Basic Survey Concepts

Chapter 11 - Introduction to Statistics and Simple Data Description
What is Statistics?
Definitions and Simple Mathematics
Simple Data Description
Pictoral Data Description

Chapter 12 - Univariate Data Descriptive Measures
Measures of Central Tendency
Measures of Dispersion

Chapter 13 - Introduction to Multivariate Data Analysis
Multivariate Analysis Defined
A Graphical Analysis of the Relationship Between Two Variables
Cross-Tabulation Analysis
Simple Linear Correlation Coefficients
Bivariate Regression Analysis
Multivariate Regression Analysis

Chapter 14 - Analysis of Time Series Data
The Components of Times Series Data
Techniques to Determine the Components of Time Series Data
Moving Averages
Index Numbers and Indices

Chapter 15 - An Introduction to Sampling Theory
Introduction and Terminology
Sampling and Probability
Methods of Sampling
Sample Bias
Statistical Reliability

Chapter 16 - An Introduction to Statistics used in Real Property Assessment
Multiple Regression Analysis
Ratio Studies
Ratio Study Standards

Mode of Instruction
Students learn through classroom lectures and hands-on assignments during classroom hours.  There are homework assignments.  Students must have ready access to a computer with Word for Windows in order to complete homework assignments.  Students have access to computers through the Microcomputer Centre or micro labs where applicable.

Prescribed Texts
Foundations of Real Estate Mathematics. University of British Columbia. Latest edition.

Note: Photocopied texts are not permitted.

You may order textbooks directly from UBC

Reference Material

Required Supplies
HP10B financial calculator and access to MS Excel.

Notebook or three-ring binder, paper, pens, highlighter, above noted text.

All students must have access to a personal computer when taking any Appraisal Institute course. You will find that a computer is a necessary tool in preparing and submitting your assignments, viewing your assignment answer guides, and for creating effective study notes to help you prepare for your examination. Students should also ensure that they have a high-quality printer (e.g., an inkjet or a laser) which will provide clear printouts of information from the Real Estate Division website.

All students must arrange for some form of Internet access. All of the Appraisal Institute’s courses offer numerous online course resources. Students should ensure they have Internet access prior to beginning their course work.

Promotion Policy

Grading Policy
A+ 90%  to  100%
A 80%  to  89%
B+ 75%  to  79%
B 70%  to  74%
C+ 65%  to  69%
C 60%  to  64%
D+ 55%  to  59%
D 50%  to  54%
F 0%    to  49% (Not a Pass)
EXC Excellent
SAT Satisfactory
UNSAT Unsatisfactory

For further information, see a copy of the Academic Policy, available online ( or at Seneca's Registrar's Offices.

Modes of Evaluation
Since this is a professional credit course, marking standards reinforce professional practice by demanding legible, neat documents. Material should be grammatically correct as a result of accurate proof-reading, proper spelling and punctuation. Late assignments are penalized at the discretion of the instructor.

Students should be aware that absenteeism will almost guarantee their inability to achieve satisfactory grades. There is no formal provision for make-up tests to replace tests missed due to absenteeism.

Students must pass the final examination to pass the course.

Note: The required pass mark for all courses in the Appraisal Institute of Canada Program is 60%.  This is also the required pass mark for the University of British Columbia.

Grading is based on the following marking scheme:   

Assignments  10%
Project No. 1 20%
Project No. 2 20%
Final Exam  50%

Please keep this document for future reference.  It will be required if you apply to another educational institution and seek advanced standing.

Academic Program Manager:
Emiliano Introcaso

Approved by: Academic Program Manager Emiliano Introcaso