Insights into Present Value and Duration

The current syllabus of the Casualty Actuarial Society, especially parts four and ten thereof exposes actuaries to mathematical finance, particularly to the valuation and management of cash flows. The Society believes that financial matters will be even more important to actuaries of the twenty-first century. However, the syllabus readings do not take advantage of the mathematical proficiency of actuaries. As a result, their understanding is not as clear as it could be. This paper will apply first-year calculus to the concepts of present value and duration. Also, the calculus will permit the definition of a powerful concept that may yet be unfamiliar to many actuaries, the forward rate. Perhaps actuaries will gain fresh insights into these concepts, be more confident and competent to use them, and be better equipped to study more advanced financial theory.