Mathematical Interest Theory Pdf

0 views

Skip to first unread message

Leda Billock

unread,

Aug 3, 2024, 3:31:51 PM8/3/24

to glasonkofpa

Mathematical Interest Theory provides an introduction to how investments grow over time. This is done in a mathematically precise manner. The emphasis is on practical applications that give the reader a concrete understanding of why the various relationships should be true. Among the modern financial topics introduced are: arbitrage, options, futures, and swaps. Mathematical Interest Theory is written for anyone who has a strong high-school algebra background and is interested in being an informed borrower or investor. The book is suitable for a mid-level or upper-level undergraduate course or a beginning graduate course.

The content of the book, along with an understanding of probability, will provide a solid foundation for readers embarking on actuarial careers. The text has been suggested by the Society of Actuaries for people preparing for the Financial Mathematics exam. To that end, Mathematical Interest Theory includes more than 260 carefully worked examples. There are over 475 problems, and numerical answers are included in an appendix. A companion student solution manual has detailed solutions to the odd-numbered problems. Most of the examples involve computation, and detailed instruction is provided on how to use the Texas Instruments BA II Plus and BA II Plus Professional calculators to efficiently solve the problems. This Third Edition updates the previous edition to cover the material in the SOA study notes FM-24-17, FM-25-17, and FM-26-17.

Mathematical Interest Theory provides an introduction to how investments grow over time. This is done in a mathematically precise manner. The emphasis is on practical applications that give the reader a concrete understanding of why the various relationships should be true. Among the modern financial topics introduced are: arbitrage, options, futures, and swaps. Mathematical Interest Theory is written for anyone who has a strong high-school algebra background and is interested in being an informed borrower or investor. The book is suitable for a mid-level or upper-level undergraduate course or a beginning graduate course.The content of the book, along with an understanding of probability, will provide a solid foundation for readers embarking on actuarial careers. The text has been suggested by the Society of Actuaries for people preparing for the Financial Mathematics exam. To that end, Mathematical Interest Theory includes more than 260 carefully worked examples. There are over 475 problems, and numerical answers are included in an appendix. A companion student solution manual has detailed solutions to the odd-numbered problems. Most of the examples involve computation, and detailed instruction is provided on how to use the Texas Instruments BA II Plus and BA II Plus Professional calculators to efficiently solve the problems. This Third Edition updates the previous edition to cover the material in the SOA study notes FM-24-17, FM-25-17, and FM-26-17.

Shippensburg University mathematics students hone their ability to reason carefully, write precisely, solve problems effectively and use both mathematical theory and technology to deepen their understanding. In addition, students develop mathematical independence and perseverance with the opportunity to experience open-ended research with a professor.

There are no special requirements to enter this program, but students who are at the calculus level or above will find they are making a more informed decision in choosing this program. The core courses are composed of the three-semester calculus sequence, discrete mathematics, statistics, linear algebra, abstract algebra, and analysis. The Applied Mathematics concentration requires additional coursework in traditional applied mathematics topics such as mathematical modeling and differential equations, with electives available in a wide range of areas including data science, mathematical biology, numerical analysis and mathematical interest theory. All mathematics majors complete at least one computer science course to establish a firm basis for coding in upper level coursework.

Many mathematics courses are taught in a computer classroom to provide hands-on experience with software such as Microsoft Excel, MATLAB, Mathematica, and various open source apps. Mathematics students and faculty socialize through activities of the long-standing SU Math Club and provide service to the community through outreach efforts at SU as well as participation in events such as the National Engineering and Science Festival in Washington, D.C. Many mathematics majors are employed by the university to tutor students in lower division mathematics courses. In addition, students in this concentration often complete paid summer internships in their last two years of the program.

TmVal is a Python library for mathematical interest theory, annuity, and bond calculations. This package arose from the need to have more powerful computational finance tools for another project of mine, Miniature Economic Insurance Simulator (MIES). What began as a simple submodule of MIES quickly spun off into its own repository as its complexity grew and as its potential viability in commercial applications became more apparent.

This article begins by highlighting the advantages TmVal has over existing time value of money packages, and then proceeds to demonstrate how TmVal can be used to solve problems found in actuarial science. Feel free to visit the project repository and examine its source code at

TmVal supports growth patterns that are more complex than compound interest. In addition to supporting simple, compound, and nominal interest, TmVal handles growth patterns that may be of theoretical interest to actuaries, such as continuously compounded rates (force of interest), polynomial growth, and arbitrary amount and accumulation functions.

TmVal provides equations of value computations for core financial instruments in actuarial science, such as annuities, loans, bonds, and arbitrary cash flow streams. As development is still in the alpha stage, the types of investments TmVal supports is rapidly expanding. I expect the package to soon offer classes for stocks and options.

TmVal supports the core growth functions of mathematical interest theory, the amount () and accumulation () functions, implemented via the Amount and Accumulation classes. These classes support all sorts of growth patterns, from simple and compound interest to more complex cases such as tiered investment accounts and polynomial growth.

Interest rates are represented by a core data type in TmVal, the Rate class. This custom data type offers a convenient way to perform computations with a variety of interest rate patterns as well as conversions between them. The main patterns supported by the Rate class are:

Unlike other packages, which tend to use functions to represent the different types of annuities, TmVal represents annuities as a class, which gives it access to several methods that can be performed on the annuity, such as equations of value. So rather than simply returning a float value via a function, TmVal expands the manipulations that can be done with an annuity. My aim is to allow the Annuity class to serve as a base class for, or to be embedded into more complex insurance products.

For example, suppose we were to obtain a 2-year loan of 50,000, to be paid back with monthly payments made at the end of each month. If the interest rate were 4% convertible quarterly, what is the amortization schedule?

We can also price bonds that have more complex, nonlevel coupon payments. Suppose instead that the bond in the previous example instead pays 5% annual coupons in the first two years and 6% coupons in the last three years:

Go ahead and give TmVal a try! The next section is the Installation and Quickstart followed by the Usage Tutorial. For technical documentation, consult the API Reference, which links to the source code of the project.

MATH 1000 COLLEGE ALGEBRA (3) LEC. 3. Pr. ALEK score of 1. Fundamental concepts of algebra, equations and inequalities, functions and graphs, polynomial and rational functions. Does not satisfy the core requirement in mathematics. Students who have previous credit in any higher-numbered math course may not also receive credit for this course.

MATH 1100 FINITE MATH AND APPLICATIONS (3) LEC. 3. Pr. ALEK score of 50 or MATH 1000 or MATH 1003. ALEKS Math Placement Assessment score of at least a 50 or MATH 1000. Mathematics Core. Overview of finite mathematics and its applications. Graph theory, matrices, finite and conditional probability; descriptive and inferential statistics, voting methods, game theory.