The 7 Most Important Equations for Your Retirement: The Fascinating People and Ideas Behind Planning Your Retirement Income

From the introduction: An equation can′t predict your future . . . But it can help you plan for it Most books about retirement planning are written as guides, instruction manuals or "how–to" books. The authors tell you what to do, when to do it, and what to expect. I know this quite well because I have authored many such tomes myself. Rest assured, this is not one of those books. This book tells stories which I hope will lead into conversations. It is a narrative involving seven people, their discoveries and the conceptual innovations that made it possible for you to stop working and enjoy the money you have accumulated, one day. These protagonists—or scientific heroes—didn′t achieve their breakthroughs while hunched over a laboratory workbench, peering through a microscope or trekking through jungles. They made their discoveries sitting in front of a blank sheet of paper, but while thinking very carefully about life and money. And, like the greatest thinker of them all, Albert Einstein, they too expressed their discoveries using a very beautiful language called mathematics. Alas, the seven equations profiled in this book aren′t as famous or as elegant as the simplicity of E = MC 2, but they are far more practical for your retirement. Yes, I know from many years of teaching experience that financial conversations are often dry and humorless. So I promise to do my best to lighten up the topic by keeping the technicalities to a minimum and focusing on the art. "Art," you say? Yes. In my mind, famous equations are like beautiful Picassos. Even if I don′t quite understand the painting or the mathematics I can certainly appreciate the beauty and genius behind it. The seven equations presented in this book typify, at least for me, the conciseness, elegance and beauty that the best of the best equations demonstrate. By the end of this book, if you′re not already inclined to appreciate mathematical equations for what they are, I hope you′ll agree about the beauty.

Introduction: An Equation Can′t Predict Your Future . . .But It Can Help You Plan for It 1 Chapter 1: How Long Will My Number Last? Equation #1: Leonardo Fibonacci (1170–1250) 7 Chapter 2: How Long Will I Spend in Retirement? Equation #2: Benjamin Gompertz (1779–1865) 31 Chapter 3: Is a Pension Annuity Worth It? Equation #3: Edmond Halley (1656–1742) 53 Chapter 4: What Is a Proper Spending Rate? Equation #4: Irving Fisher (1867–1947) 77 Chapter 5: How Much in Risky Stocks versus Safe Cash? Equation #5: Paul Samuelson (1915–2009) 101 Chapter 6: What Is Your Financial Legacy Today? Equation #6: Solomon S. Huebner (1882–1964) 125 Chapter 7: Is My Current Plan Sustainable? Equation #7: Andrei N. Kolmogorov (1903–1987) 151 Conclusion: Controversies, Omissions and Concluding Thoughts 175 Appendix: Crash Course on Natural and Unnatural Logarithms 179 References and Sources 185 Acknowledgments 195 About the Author 197 Short Poem by Maya Milevsky (age 11) 199 Index 201

Moshe A. Milevsky, Ph.D. , is a professor at York University (Toronto). He has graduate degrees in finance and mathematics, and is a fellow of the Fields Institute for Research in Mathematical Sciences, where he is the executive director of the IFID Centre. He has written nine books, published over 60 peer–reviewed research studies and over 200 magazine articles—including a featured story in the Wall Street Journal and a profile in Money Magazine —on the topic of retirement income planning. He has delivered over 1,000 seminars, keynote presentations and training sessions to audiences all over the world. His popular writing earned him two National Magazine Awards (Canada). In 2009 he was given a lifetime achievement award from the U.S.–based Retirement Income Industry Association (RIIA). Moshe grew up in Latin America and the U.S., but currently lives in Toronto with his wife and four daughters.