THE MATHEMATICS
OF INDIVIDUAL FINANCE

At its heart, financial planning deals with what happens to money over time. Invested funds generally increase over time, compounding with the rate of return, while borrowed funds, unless repaid, magnify the amount of the debt. Dealing with funds over time involves the so-called "time value of money," which is taught in many courses in the business curriculum.

However, one reason why time value of money is taught in so many different courses is that many students have difficulty remembering the mathematics of finance, unless they are compelled to deal with it on a frequent basis. In this course, you have no choice but to deal with the mathematics of individual finance on a daily basis since it constitutes the basic tools of the trade. The amount of annual savings needed to fund retirement or college in the future can only be determined through the use of these tools.

Fortunately, commonly available technology has made many of the necessary calculations trivial. Finance calculators are available for less than $20 and even low-powered computers can perform these calculations on spreadsheet programs.

This chapter on the mathematics of individual finance will be a review for many and an introduction for some. Even those students who are proficient in the mathematics of finance will find the applications to individual financial management to be instructive. Each tool will be explained verbally and arithmetically and illustrated with one or more examples. In addition, the keys of common financial calculators will be illustrated to show how the problems can be solved using these machines. Also illustrated will be the solution to the problems on a LOTUS spreadsheet. LOTUS was chosen since it predominates in the world of business and most other spreadsheet programs will translate LOTUS commands. Finally, solutions will be illustrated using mathematical tables which are included in the appendix to this chapter. The mechanical apparatus used to carry out the mathematics of individual finance is of far less importance than an understanding of the basic logic which is transportable from one contrivance to another.

Therefore, the objectives of reading this chapter include developing familiarity with the following:

The future value of a sum of money today under compound interest.

The present value of a future sum of money.

The present value of an annuity and the importance of annuities in individual financial management.

The future value of an annuity and an annuity due.