This undergraduate textbook explores fundamental aspects of personal savings and investing, offering a well-balanced blend of mathematical rigor and economic intuition. Rather than assuming elementary real analysis, the book employs routine financial calculations as both motivation and the foundation for elementary real analysis tools. It covers proofs utilizing induction, recurrence relations, and proofs by contradiction. Various inequalities such as the Arithmetic-Geometric Mean Inequality and the Cauchy-Schwarz Inequality are applied. The text also delves into basic topics in probability and statistics. Students are introduced to practical elements of saving and investing with lifelong relevance, encompassing savings and checking accounts, certificates of deposit, student loans, credit cards, mortgages, as well as buying and selling bonds and stocks.
With a self-contained and accessible approach, the authors adhere to a systematic pattern for each chapter, offering a range of examples and exercises to ensure students engage with real-world scenarios rather than theoretical idealizations. This textbook is suitable for courses in mathematics, investing, banking, financial engineering, and related subjects.
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