Category Understanding the Mathematics of Personal Finance

GRAPHS AND CHARTS

When looking at relationships between variables, the formula tells it all. Very often, however, a picture is indeed worth a thousand words in “giving us a feeling” for what the formula is telling us.

We will often be presented with a graph that we’ll study to gain some insight into the information the graph is presenting. Conversely, we will often need to be able to create a graph to show a formula that we are interested in. I’ll take this latter approach first.

Let’s start with a simple formula:

у = 27,000 – 2,000x.

This formula gives us a value for the variable у when we give it a value for the variable x. These variables might stand for the depreciation of a car’s value, the interest on a loan, the number of years that you will hold a loan, and so on.

Before I draw a graph...

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APPROXIMATIONS

We frequently don ’ t need to know an answer to many decimal places. When we give someone directions to drive to our house, we usually say something like, “Get off the highway at exit 14, go right and follow the road for about 12mi until you see an old church on the right.”

We could have said “Follow the road for 11.87 mi” but “about 12” gives enough information to tell someone when to start looking for the church. I don’t need to delve into the theory of approximations. Instead, I’ll use some commonsense rules, such as “about 14 mi” means that the number is closer to 14 than it is to 13 or 15.

The mathematical expression
means that “x is approximately equal to 14.” Other ways of writing this are x ~ 14 and x = 14.

The number 2,123,774 has seven significant figures...

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RATES—AVERAGE AND INSTANTANEOUS

This section is useful for understanding the mathematics of the average and incre­mental IRS income tax rates discussed in Chapter 9 ’ It is not necessary for under­standing Chapter 9 or anything else in this book.

Suppose I were to take a walk for 25 minutes. I’m walking along a marked track, so I know exactly how far I’ve walked at all times. Every few seconds, I write down how long I’ve been walking and how far I’ve walked. After I’ve finished my walk, I produce the graph shown in Figure 1.7 ’ interpolating my data as described above.

At the end of 25 minutes, I’ve walked about 2,200 feet. As the graph shows, I started off walking at a good pace and then I slowed down. From about 8 minutes to about 13 minutes, I hardly moved at all...

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Understanding the Mathematics of Personal Finance

^Vhat is personal finance? An informal definition is “how you interact with money.” Among the subcategories of personal finance are topics such as budgeting, saving, borrowing, investing, gambling, and buying and selling real estate. Many books, courses, professional advisors, and software programs are available to help you optimize your path through your financial life.

This book is about various forms of borrowing and saving money, and includes some discussion of investing money. Borrowing money takes many forms, including home mortgage loans, auto loans, and credit card debt. Saving money includes putting money under your mattress, depositing it into a savings bank, and buying certificates of deposit (CDs)...

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INEQUALITIES AND RANGES OF NUMBERS

The symbol < means “is less than,” as in 3 < 4. If x represents the numbers of the months of the year, for example, x <4 means x could be1,2,or3. The symbol < means “is less than or equal to,” so that x < 4 in the above example means x could be 1, 2, 3, or 4.

Similarly, the symbols > and > mean “is greater than” and “ts greater than or equal to,” respectively. For some reason, these latter symbols are rarely used. Instead, the more common approach is to say that x < 3 means that x is less than 3, and 3 < x means that 3 is less than x, or equivalently, that x is equal to or greater than 3.

These symbols let us describe a range of numbers conveniently. For example,

3 < x < 7

means that x is somewhere between 3 and 7, but is not equal to either 3 or 7, while

3 < x < 7

means th...

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Acknowledgments

A tolerant group of relatives and friends helped me to interpret various published documents about different financial instrument rules’ calculations and then read my drafts and commented on whether or not I was explaining things more clearly. This group includes my wife Suzanna, my daughter and son-in-law Gillian and Aaron Madsen, and my friends Mel Slater and Chip Shanley.

Susanne Steitz-Filler at John Wiley and Sons has been patient and helpful as the structure of this book evolved from my original ideas.

I thank you all.

List of Abbreviations

ADB

APR

ARM

ATM

CD

Cmpds

CORR

COL

DB

EAPR

HECM

HUD

IAWPC

INC

Int or INT

IOU

IRA

Mnth

NAPR

Nr

NrPmts

PMT

PV

SEC

SEP

Tot or TOT Vol

Average Daily Balance Annual Percentage Rate Adjustable Rate Mortgage Automatic Teller Machine Certificate of...

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