MATHEMATICS OF FINANCE

To the student of pure mathematics the term mathematics of finance often seems somewhat of a misnomer since, in solving the problems usu ally presented in textbooks under this title, the types of mathematical operations involved are very few and very elementary. Indeed, in a first course in the mathematics of finance the development of the most impor tant formulas usually involves no greater difficulties than those encountered in the study of geometric progressions. Whether it is because of this seeming simplicity or because of a tendency to limit the problems to the very simplest kinds, the usual presentation has shown a decided lack of generality and flexibility in many of the formulas and their applications. Since no new mathematical principles are involved, a student who can develop and understand the simpler appearing formulas should be able to develop easily the more general for mulas, which are much more useful. And no student should use important formulas whose derivation and meaning, and hence possibilities and limi tations, he does not understand. There is a marked preference in many places in mathematics for presenting general definitions and formulas first, with the special cases following naturally from them. Tn trigonometry, for instance, the main importance of the trigonometric functions of an angle is emphasized by presenting first the general definitions of these functions then the defi nitions of the functions of an acute angle in terms of the elements of a right triangle follow naturally as special cases. Up to the present time, textbooks in the mathematics of finance have not followed this plan of presentation. The foregoing considerations, plus years of experience in teaching the subject, sometimes with the more general formulas presented first and sometimes with the limited formulas presented first, have caused the author to feel the need of such a presentation as is attempted here. As everyone in this field of work is aware, the major problem