FutureProof FM
The Actuarial Exercise Playbook
Preface
The Society of Actuaries’ Exam FM is the gateway to a career in financial risk and actuarial science. It tests your grasp of core financial mathematics—interest theory, annuities, immunization, and more—and challenges you to apply these concepts under timed, multiple-choice conditions.
In my more than ten years of teaching the FM course and decades of consulting as an actuary, I’ve observed one truth again and again:
Mastery begins with practice
That’s why I’ve designed the exercises in this book to mirror the style, rigor, and pacing of the official Exam FM syllabus published by the Society of Actuaries. Whether you’re encountering a topic for the first time in class or reinforcing it on your own, each problem invites you to:
Engage deeply. Tackle the question from multiple angles—algebraic derivation, numerical example, graphical intuition.
Build intuition. Recognize common traps, shortcuts, and “exam-savvy” strategies that seasoned actuaries use.
Track progress. Watch your speed and accuracy improve as you move through grouped problem sets and timed drills.
Why commit to active practice?
As the legendary mathematician Paul Halmos famously said:
“The only way to learn mathematics is to do mathematics”
In my teaching, I’ve found that students who work systematically through well-crafted exercises not only remember formulas longer—they learn to think like actuaries, spotting patterns and applying theory in novel scenarios.
How to use this book
Chapters 1-3 introduce and reinforce all foundational models: accumulation and discount functions, annuities, loans, and yield rates.
Chapters 4-5 advance to more complex topics: bonds (and other fixed-income securities), spot & forward rates, fund performace measurement, cash flow matching, duration, convexity, and immunization.
Each chapter begins with selected “Supplementary Concepts,” desinged in some cases to elaborate on textbook materials and in other cases, to introduce new approaches to replace traditional rote techniques.
When an exercise relates to a topic not directly tested by the Exam FM, it will be noted.
Make every attempt to solve the exercises and look up the answer only if no solution can be found.
Beyond the book
This book is only one piece of a successful FM preparation plan. For ongoing exam strategies, career guidance, and curated resources—including video tutorials, formula summaries, and community Q&A—visit my blog at arocha-alumni.com .
Whether you’re a first-time candidate or seeking a refresher, I’m confident that FutureProof FM will sharpen your skills and boost your confidence. Commit to the exercises, embrace the challenge, and I look forward to celebrating your exam success!
— Carlos Arocha, FSA
July 2025