I was commissioned by the publisher to write a replacement volume for the long-out-of-print book on actuarial mathematics by the late A. Loewy, which had been published in several editions. In fulfillment of this task, I decided to first publish a "basic" volume, followed by a second "advanced" volume. Considering that this is intended to be a fundamental presentation for students and practitioners, I chose the discontinuous method. In this volume, analysis, and particularly differential and integral calculus, is only utilized in Chapter 8, which contains discussions that are not directly related to the other chapters. Therefore, readers with a mathematical background, such as that of a high school graduate, can read the entire book excluding this chapter.