Mathematics of Interest Rates, Insurance, Social Security, and Pensions

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9780130094254: Mathematics of Interest Rates, Insurance, Social Security, and Pensions

This text aims to help readers become “literate” in the vocabulary of finance, insurance, and pensions and be able to utilize the appropriate mathematics for professional and personal use. This book covers a wide range of topics not found in other texts, including complex annuities, complex perpetuities, geometrically varying annuities, and bond duration and volatility. This book is a helpful reference to all professionals in the fields of accounting, finance and financial services, management, marketing services, computer information systems, and economics. It is also ideal for anyone who wants a self-study for personal finances.

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This book is intended for individuals whose career paths may include the need for mathematics of finance, insurance, breakeven analyses, and retirement planning via Social Security and private pensions. It is intended to be a helpful adjunct to business concentrations such as:

  • Accounting, since many accounting firms have included retirement planning on a consulting basis.
  • Finance and Financial services, in that the lines of separation between banks, insurance companies, and brokerage houses are no longer firmly delineated.
  • Management, to be able to "converse" in the mathematics of all segments of a business.
  • Marketing services, in order to be "literate" in the vocabulary of finance, insurance, and pensions for professional and personal use.
  • Computer Information Systems, in order to know specific mathematical concepts so as to be able to develop appropriate algorithms for solution.
  • Economics, in order to extend the use of financial mathematics to insurance and pensions.

The book can also be used for those students whose concentrations are in the Liberal Arts. It will help to make them "literate" in the vocabulary of finance, insurance, and pensions and to be able to utilize the appropriate mathematics for professional and personal use.

The prerequisite preparation that is necessary is at least a solid foundation in high school algebra. Knowledge of the contents of this book can be useful for personal financial planning as well as for the business uses cited above.

Chapter 1 discusses concepts that involve Simple Interest and Simple Discount. Chapter 2 introduces Practical Applications of Simple Interest, including the determination of short-term rates of return on investments. Chapter 3 is a presentation of Compound Interest and includes the determination of time-weighted, compounded rates-of-return on long-term investments. Chapter 4 discusses the concepts of Simple Annuities, where the frequency of payments and the frequency of compounding are the same. In Chapter 5, the concepts of annuities are extended to include deferred annuities, complex annuities (where the annual frequency of payments and the annual frequency of compounding are different), annuities in perpetuity, and annuities where the periodic payments vary geometrically. Additional practical applications of annuities are included in Chapter 6 (Bonds). In order to assist in the optimization of investment portfolios, elements of linear programming are introduced in Chapter 7. After a brief introduction to optimization concepts with two variables, the use of the Solver tool in Microsoft Excel is shown for optimization with more than two variables. Advanced topics of Capital Rationing and Working Capital Management are included to show how the Solver can be used in advanced topics of finance. Breakeven Models for cost-revenue, supply-demand, and financial considerations such as the effect of commissions on purchases and early retirement decisions are discussed in Chapter 8. Chapter 9 introduces concepts of life insurance through life annuities, net annual premiums, and terminal reserves. Elements of the mathematics of Social Security are presented in Chapter 10, and Chapter 11 introduces you to the elements of the mathematics associated with private pensions.

This is a better book because of many useful comments and suggestions received from colleagues and correspondents Kevin Charlwood, Washburn University; Jeffrey Forrest, Slippery Rock University; Joseph Greene, Augusta State University; Kerri McMillan, Clemson University; Yujin Shen, The Richard Stockton College of New Jersey; Thomas Springer, Florida Atlantic University, and Jianzhong Su, University of Texas at Arlington.

I wish to give special thanks to Dr. Hsi Li, Professor of Finance, Dr. Alan Olinksy, Professor of Mathematics, and Dr. Phyllis Schumacher, Professor of Mathematics, all of Bryant College, Smithfield, R. L, for their kind suggestions relative to the material. I also wish to give special thanks to Mr. William Pitts, Vice-President, Strategic Planning, Textron Financial Corporation, Providence, R.I., and to Mr. Paul Merlino, Esq. of Lamoriello and Company, Warwick, R.I for comments relative to private pensions. I would especially thank my daughter, Dr. Robin Muksian Schutt, Associate Professor of English, New England Institute of Technology, Warwick R.I., for commenting on the readability of the manuscript.

Robert Muksian
Bryant College, Smithfield, RI

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