Category Understanding the Mathematics of Personal Finance

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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Compound Interest

The most common, if not universal, way to express the amount of interest to be paid on a loan is the annual percentage rate (APR). The interest is expressed as a per­centage or a fraction of the amount of money loaned if the money were to be loaned, with no intermediate payments or corrections, for a year.

Calculating interest is very simple. An important point to remember is that while interest is usually expressed as a percentage, for example, “6% per year,” calcula­tions must always use the decimal or fractional equivalent of this percentage:

6% = 6 = 0.06.

100

The interest due after a year on a $1,200 loan, for example, is then Interest = ($1,200.00)(0.06) = $72.00.

A type of interest calculation that is rarely used is called simple interest...

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Background Mathematics

1.1 ARITHMETIC, NOTATION, AND FORMULAS

Almost all of the mathematics used in this book involve only the four basic opera­tions of addition, subtraction, multiplication, and division. If you can comfortably read about and then actually perform calculations using these four operations, you have all the math background you need. If you have a pocket calculator or a com­puter with a spreadsheet program, then you have the “machine power” to do what­ever you need to do without resorting to pencil and paper.

Mathematical notation, the way we express what we want to calculate, can sometimes be confusing. Mathematical notation is the vocabulary of the language of mathematical concepts...

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SOME MATHEMATICS

You can skip this section if you aren’t interested in all the details of the calculations. I recommend that you at least glance through this section to try and get an idea of what’s going on in various calculations.

At the outset of the loan, the interest is just the principal times the interest rate per compounding interval, therefore we may write

R

Interest = P—,

n

where P is the principal, R is the interest rate per year, and n is the number of com­pounding intervals per year.

To get the new balance, you add this interest to the principal:

R

Balance = P + P—.

У

You can see that the principal P appears twice in this equation. The rules of algebra let us write this same formula as

Balance = P | 1 + R

К У

Now, suppose you want to get the balance after the second compounding pe...

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MINUS (NEGATIVE) SIGNS

The seemingly benign set of rules for manipulating a minus sign nevertheless manages to cause an endless set of headaches. Let’s see if I can summarize these rules quickly and clearly:

1. (Not so much a rule as a reminder) When a sign is not shown, a positive sign is implied:

34 = +34,

(35) = (+35) =+(35).

2. Subtracting B from A is the same as adding – B to A:

7 – 5 = 7 + (-5) = 2.

3. As implied above, multiplying a positive number by a negative number yields a negative number:

(-3)(6) = -(3)(6) = -18,

(-6 ) = -(6 ) = (-1)(6).

4. Multiplying two negative numbers yields a positive number:

(-5)(-7) = +35.

5.

Подпись: 4 -3 Подпись: -4 = 3 =" -4 -3 Подпись: 4 ^__4 3 J= 3 Подпись: -1.33,

Division rules are the same as multiplication rules...

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