ABSTRACT
We begin our study of financial mathematics in this chapter by introducing the key concepts of rate of return and present value . With the stage thus set, we will be prepared to investigate a number of important ideas in the theory of interest: compound interest, annuities, loan repayment, and the valuation of bonds. Prerequisite mathematics for the first few sections of this chapter, in which time moves discretely, is simply standard precalculus material with an emphasis on geometric sequences and series (which will be reviewed). At the end of the chapter we will see how the ideas extend to continuous time models, for which both differential and integral calculus will be necessary. By the end of the chapter students should be prepared to make educated decisions in many financial situations in their personal lives. The groundwork for further study in financial mathematics is laid as well, including study of actuarial mathematics and preparation for the FM exam that is administered by the major actuarial societies. For this purpose, you may find the references Federer Vaaler [5] and Broverman [2] to be very useful. Both Chapters 1 and 2 of this book are heavily influenced by these works. Furthermore, the financial services industry is concerned with how to value firms and tradable assets, and students will acquire the background to continue the pursuit of problems related to this important area.
