Math 312 Mathematical Theory of Interest

Welcome!

Welcome to Math 312 - Mathematical Theory of Interest at Albion College. This site has all the class information that you need to be successful. Here you will find the class schedule, its policies, homework and exams details, as well as various opportunities for help & support. In addition, student accomodation information can be found here.

Who, What, When, Where?

Instructor Information	Professor Darren E. Mason, Ph.D; Palenske Hall 224; dmason@albion.edu.
Course Description	Foundations of interest & discount rates; present/future value of cash flow including annuities, loans, bonds, and other investments; returns on investment; measures of duration & convexity; concepts of portfolio immunization. Applications to a wide variety of practical problems including student loans, car loans, home mortgages, and investment bonds.
Prerequisites	Math 141 - Calculus I
Class Time & Location	MWF: 0915 - 1020 in Palenske 221.
Student Hours	MWF: 1500 - 1600; TR: 1200 - 1300; Or by appointment. Palenske 224. See Student Hours for more information.
Text	Mathematics of Investment & Credit by Samuel A. Broverman, Ph.D., ASA; ACTEX Learning; Mad River Books; 2017.
Asking Questions	If you have question during class or student hours, I will answer them at that time. If you have questions at other times, you can email them to me. I promise to respond within 24 hours, either by email of in person. DO NOT expect a response after 5pm on any given day as I may be busy with my family. However, I will do my best to be as fast as possible.

Course Policies

• Device Etiquette: Using devices during class time for non-class activities (i.e., YouTube, Facebook, Tik-Tok, gaming, etc.) is prohibited. Professional and courteous behavior is demonstrated by turning off distractions and focusing on class. We owe this to each other.


• Email/Writing Expectations: All correspondences to me should be courteous and professional, following standard rules of grammar. One way to guarantee that you don't get a response from me is to send an email that opens with "Hey how do i do problem X". You will get a helpful response if you write "Hi Professor Mason, I am working on problem X and I am stuck. I don't understand how to organize my decision variables. Thank you, Student Name". Regardless of your career path, professional correspondence is a necessity. If not already present, it is a good habit to aquire at this stage of your life.


• Intellectual Property: As members of a learning community, students are expected to respect the intellectual property of course instructors.  All course materials presented to students are the copyrighted property of the course instructor and/or the associated text.



• AI Use: This course requires you to complete various assignments that assess your understanding and application of the course content. You are expected to do your own work and cite any sources you use properly. You are not allowed to use any artificial intelligence (AI) tools, such as chatbots, text generators, paraphrasers, summarizers, or solvers, to complete any part of your assignments. Any attempt to use these tools will be considered academic misconduct and will be dealt with according to the college’s academic integrity policy. Students are expected to complete all work independently and without the assistance of AI-generated content. If you have any questions about what constitutes acceptable use of AI tools, please consult with the instructor before submitting your work.



• Social Media Guideline: Unless explicitly given permission by the instructor, students may not record any classroom activities. This includes posting anything from class to Tik-Tok, Snapchat, YouTube, Kik, Facebook, Instagram, etc. Doing so is a violation of the privacy expectation of your fellow students and the instructor. Any student violating this policy may face academic disciplinary sanctions.


• Attendance and Participation:
  • Daily attendance and participation in class is required and is worth 5% of your final grade.  Coming to class for the time we will meet counts as part of your attendance. If you do not come to class you will not receive attendance points for that day. NOTE: If you are late to class (within reason), you will still earn your attendance score. So don't blow off class!
  • Attendance for quizzes and examinations is required. Legitimate reasons to miss an examination include a  family emergencies (i.e., a death, hardship, car accident, etc.), student illness with a written excuse from a medical professional / appropriate college official, or a college sanctioned event (e.g. class field trip or athletic events).    Students who do miss an exam due to an excused absence must make arrangements as soon as possible to make up the missed work.  If you know in advance that you will be gone, you need to make arrangements with Dr. Mason before the date of the examination in question.
  • Participation requires coming to class ready to learn.   This includes reading the material being covered in class before coming to class.
  • The Albion College policy on attendance is at the bottom of page 23 in the student handbook.


• Time Commitment OUTSIDE of class: Anywhere from 0 hours to 4+ hours per day of classroom instruction.  Typical time commitments that correlate with success in this course is 1-3 hours/day, at least five days per week.  Precisely how much time you will need to spend studying outside of class is based on, at least, how well you are prepared mathematically and the grade you want to earn in the class. Preparation for exams will add to the time you need outside of class.   Your mileage may vary.  

• Homework: Homework problems are assigned in the schedule portion of this website. Homework is worth 20% of your grade. See the homework section for more detail.

• Quizzes: There will be five quizzes during the semester and only the top four quiz scores will count. Therefore, each quiz is worth 5% of your final grade for the course so that quizzes account for 20% of your final grade. If you miss a quiz for illness or any other reason, that will be the quiz that doesn't count (so don't waste a quiz by skipping class). All quizzes are closed book and closed notes. An authorized calculator is allowed. See the quiz section of this webpage for additonal information.
  

• Examinations: There will be two exams during the semester on Thursdays. Your lowest scoring exam is worth 10% of your final grade and the highest scoring exam is worth 20%. Therefore, both exams are worth 30% of your final grade for the course. Each examination is closed book and closed notes. However, you can use an authorized calculator. See the exam section of this webpage for additonal information.
  

• Grading: The following table provides the basic partition of points for this class:
  
  

  Evaluation	Attendance	Homework	Quizzes	Exams	Final Exam
  Weight	5%	20%	20%	30%	25%

  
  

  • Using the above table as a guide, here are step-by-step instructions on how to compute a "ball-park" estimate of your grade.  First, let your average percentage score be A for your attendance, H for your homework, S your weighted exam score, and F the score on your final project, with each corresponding to a number between 0 and 1.  Your total raw score R in the class is then determined by the equation R = 0.05A + 0.20H + 0.20Q + 0.30S + 0.25F. The maximum possible value for R is 1.0; the minimum possible value for R is 0.0.  Then, your grade in the class will be calculated according to the following rubric.

    
    

    If R ≥	0.90	0.87	0.83	0.80	0.77	0.73	0.70	0.67	0.63	0.60
    Your grade is ≥	4.0	3.7	3.3	3.0	2.7	2.3	2.0	1.7	1.3	1.0

    
    



• Important Dates:
  
  

  Event	Date
  Last Day to Drop/Add	Wednesday, September 04
  Last Day to Withdraw (W)	Monday, November 04
  Last Day to Register for CR/NC option	Friday, December 06




• Ethics: As an academic community, Albion College is firmly committed to honor and integrity in the pursuit of knowledge. Therefore, as a member of this academic community, each student acknowledges responsibility for his or her actions and commits to the highest standards of integrity. In doing so, each student makes a covenant with the college not to engage in any form of academic dishonesty, fraud, cheating, or theft.
  
  
  • For detailed information on the expectations of academic honesty by Albion College, please look here.
  • Violation of this policy will be prosecuted to the fullest extent allowed by the College.
  • Documented cases in this class will, at a minimum, result in a ZERO on the corresponding assignment as well as a 10% reduction in your final grade. So be sure to NOT violate the copying policy discussed above.

• Reporting Discriminatory Harassment: Albion College seeks to create a welcoming environment in which all students can learn, but we recognize that harassment may still occur. If a student experiences harassment or discriminatory treatment, there are several ways they can report it. For details, please use this reporting form.

• Bias Reporting: In line with our commitment to fostering a culture of belonging on campus, we have created a bias reporting system for use by all members of our community. This tool allows students, faculty, and staff to report individual incidents of bias on or off campus and serves as a mechanism to help us address systemic issues of bias more broadly.

• Title IX Office and Resources for Survivors of Sex-Based-Discrimination and Harassment: Albion College is committed to providing an educational environment where we are all able to learn, teach, and work freely and where the dignity, safety, and self-respect of all members of our community are protected. Sex-based discrimination, Sex-based harassment, Sexual assault, domestic violence, dating violence, and stalking are incompatible with this mission and will not be tolerated at Albion College.
  
  On-campus confidential resources for victims/survivors of sexual assault include Lisa Winchell-Caldwell, Director of the Center for Gender Equity/Victim Advocate (517-629-0613) and Counseling Services (517-629-0236). More information can be found here.
  
  Beyond campus, Sexual Assault Services of Calhoun County, Bronson Health (888-383-2192) provides 24/7 resources for survivors. For additional information about resources on and off campus, visit here.
  
  If you have been the victim of sex-based discrimination, sex-based harassment, domestic violence, dating violence, stalking, or sexual assault, please contact the College’s Title IX Coordinator, Kelly Finn (titleix@albion.edu).

• Cutler Center Information: The Cutler Center for Student Success is located in the Stockwell Library. The Cutler Center provides a number of services to support student success and serves as a one-stop hub connecting students to resources across campus. Through the Cutler Center, students access peer tutoring and writing consulting, accessibility services and accommodations, the TRIO SSS program and other services. To connect with the Cutler Center, please email us at cutler@albion.edu or stop by to be connected to the resources you need to be successful this term.

• Accessibility Services: It is the policy of Albion College to accommodate students with disabilities and qualifying diagnosed conditions in accordance with federal and state laws. Any student who feels that they may need an accommodation based on the impact of a learning, psychiatric, physical, or chronic health diagnosis, should contact Accessibility Services Director, Elizabeth Rudolph (erudolph@albion.edu), to meet and develop a plan for reasonable accommodation(s) based on supporting documentation.
  
  If you have completed this process and requested accommodations for this semester, plan to meet with Elizabeth as early as possible to discuss a plan for implementing these modifications in this class. It is best to schedule these meetings at least one week prior to their implementation.
  
  Accessibility Services is housed in the Cutler Center on the first floor of the Stockwell Library and is open Monday-Friday, 8:00am-5:00pm. Elizabeth Rudolph, the Director for Accessibility Services can be reached at 517-629-0628 or email erudolph@albion.edu for more information.

Class Schedule

This is a tentative schedule of what we will be covering in Math 312 this semester. In the case of unforeseen delays or modifications to our daily life, its subject to change.

Week	Material Covered	Homework	Date Due
08/26 - 08/30	Introduction; Course Overview; Interst accumulation and effective rates of interest; Present value; Equation of value; Nominal rates of interest	1.1.1, 1.1.2 (a & b), 1.1.3, 1.1.6; 1.2.1, 1.2.2, 1.2.3, 1.2.7, 1.2.10, 1.4.1, 1.4.3, 1.4.7	09/06
09/02	Labor Day - No Classes	NA	NA
09/03 - 09/06	Effective and nominal rates of discount; Force of interest; Inflation and the "Real" rate of interest	1.5.1, 1.5.4, 1.5.5, 1.5.7, 1.5.11, 1.6.1, 1.6.2, 1.6.7, 1.6.8, 1.6.9	09/13
09/09 - 09/13	Level payment annuities including some generalizations; Quiz #1	2.1.1, 2.1.2, 2.1.3, 2.1.4, 2.1.8, 2.1.10, 2.1.11, 2.1.12, 2.1.13, 2.1.17, 2.1.19, 2.1.26; 2.2.1, 2.2.3, 2.2.4, 2.2.5, 2.2.8, 2.2.11, 2.2.17, 2.2.24	09/20
09/16 - 09/20	Annuities with non-constant payments; Applications	2.3.1, 2.3.2, 2.3.4, 2.3.7, 2.3.11, 2.3.12, 2.3.13, 2.3.15, 2.3.40	09/27
09/23 - 09/27	Amortization of loan repayment; Amortization of level repayment loans; Quiz #2	3.1.1, 3.1.2, 3.1.4, 3.1.5, 3.1.9, 3.1.10; 3.2.3, 3.2.4, 3.2.5, 3.2.7, 3.2.8, 3.2.11, 3.2.14, 3.2.17, 3.2.29	10/04
09/30 - 10/04	Sinking fund method of loan repayment; Applications including Makeham's Formula	3.3.1, 3.3.3, 3.3.6, 3.4.2	10/11
10/04	Exam #1	NA	NA
10/07 - 10/11	Bond prices; Amortization of a bond	4.1.1, 4.1.2, 4.1.3, 4.1.5, 4.1.6, 4.1.10, 4.1.13	11/01
10/14 - 10/15	Fall Break	NA	NA
10/16 - 10/18	Bond prices; Amortization of a bond - continued	4.1.15, 4.1.19, 4.1.21, 4.1.24, 4.2.4, 4.2.5, 4.2.7	11/01
10/21 - 10/25	Callable bonds & applications; Internal Rates of Return (IRR); Quiz #3	4.3.3, 5.1.1, 5.1.4	11/08
10/28 - 11/01	Net Present Value (NPV); Dollar-weighted and Time-weighted rates of return	5.1.5, 5.1.7, 5.2.1, 5.2.2, 5.2.3, 5.2.4, 5.2.5	11/15
11/04 - 11/08	Applications and other measures of rates of return; Spot rates of interest; Quiz #4	5.3.1, 5.3.3	11/22
11/11 - 11/15	Relationship of spot rates to interest rates and yield to maturity (YTM) of coupon bonds; Forward rates of interest	6.3.2, 6.3.5, 6.3.6	11/29
11/18 - 11/22	Term structure of interest applications; Duration of cashflows; Exam #2	6.4.1, 6.4.3, 6.4.4, 6.4.6, 7.1.1, 7.1.2, 7.1.6	12/06
11/25 - 11/26	Asset-Liability matching an immunization, including Redington Immunization and convexity concepts; Applications	7.2.1ab, 7.2.5, 7.2.7a, 7.2.12a	NA
11/27 - 11/29	Thanksgiving Break	NA	NA
12/02 - 12/06	Quiz #5 + Asset-Liability matching an immunization, including Redington Immunization and convexity concepts; Applications (concluded); Review/td>	NA	NA
12/11	Final Examination; Wednesday; 8:00AM - 10:00AM	NA	NA

Homework

Homework problems from the book are assigned in the schedule portion of this website. Although not collected, you are expected to work out these problems in a dedicated problem book and ask questions as they arise. Numerical answers are in the back of the book. Successful completion of these problems will be of great benefit on required quizzes and examinations.

• Homework is worth 20% of your grade. To receive credit for the recommended homework in a given week, you must upload a single PDF file of your handwritten to the class Moodle site.
• The name of the uploaded PDF file should be "FIRSTNAMELASTNAME_SectionXY-WZ.pdf".
• Your grade will be 0 if you do not show any work, 1 if you do but your work is more incomplete than not (e.g., less than 50% complete), and a 2 if your work is satisfactory (e.g. above 50% complete).
• It is very tempting to use AI and/or a myriad of other online sources to complete your homework. DO NOT NOT DO THIS! There is nothing wrong with using such services to help you understand -- if indeed that is your goal. But if you instead use AI to mainly get answers to turn in by a deadline, then there is great danger that you will convince yourself that you understand the material when, in reality, you likely don't. 75% of your final grade is determined by your performance on quizzes and tests - which are completed under time presssure in a proctored environment where any kind of digital assistance is banned. So it is essential that you are able to efficiently solve a wide variety of problems without AI support.

All homework must satisfy the following requirements:

• Submitted homework must be neat and clearly written. Homework that is unreadable will not be accepted or graded. If you are unsure what is meant by this standard, feel free to drop by and ask!
• Students may work together on homework so long as a) individual assignments that are submitted are NOT identical to another student's homework (i.e., solutions should be clearly written in your own words and style), b) all aspects of the submission is reflective of the student’s efforts, and c) all collaborations are acknowledged.

Advice: Homework assignments in this course vary from being doable in a few minutes to taking considerably longer. Consequently, you should start working on your homework problems as soon as they are assigned. This practice will afford you the time required to understand the material and to ask questions during class/office hours in regards to problems/concepts you may not understand.

Quizzes

There are five quizes during the semester, listed in the below table along with success guides, practice quizzes, and solutions.

Quiz	Date	Topics	Practice Quiz	Solution
1	09/13	Sections 1.1 - 1.6	PQ1 / PQ1S	Q1 Solution
2	09/27	Sections 2.1 - 2.3	PQ2 / PQ2S	Q2 Solution
3	10/25	Chapter 3	PQ3 / PQ3S	Q3 Solution
4	11/08	Chapter 4	PQ4 / PQ4S	Q4 Solution
5	12/02	Chapter 6	PQ5 / PQ5S	Q5 Solution

Grading Note: The semeseter quizzes count for 20% of your final grade, with your lowest score being dropped. Hence, each counted quiz is worth 5% of your final grade.