# Category Understanding the Mathematics of Personal Finance

## 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.

Division rules are the same as multiplication rules...

If you’d like to try my website spreadsheet calculators, please take a moment and glance through Chapter 15. You’ll find instructions for obtaining a free spreadsheet program if you need one, as well as instructions for downloading and using my spreadsheets.

Tables 2.1 and 2.2 were generated with my spreadsheet Ch2CompoundInterest. xls. After opening the spreadsheet, click on the Basic tab. Table 2.3 shows part of Table 2.2 with the spreadsheet’s row and column designations added.

Table 2.3 Table 2.2 (First Few Entries Only Are Shown) in Spreadsheet Format

 D F G Compounding interval Interest (\$) Balance (\$) 1 0 0.00 10,000.00 2 1 83.33 10,083.33 3 2 84.03 10,167.36 4 3 84.73 10,252.09 5 4 85.43 10,337.52 6 5

## LISTS AND SUBSCRIPTED VARIABLES

Throughout this book, I make frequent use of tables. Tables are lists of numbers that relate variables in different situations. This isn’t as bad as it first sounds. I’m sure you’ve all seen this many times—everything from income tax tables that the Internal Revenue Service provides to automobile value depreciation tables.

Table 1.1 is a hypothetical automobile value depreciation table. Don’t worry about what kind of car it is—I just made up the numbers for the sake of this example.

Looking from left to right, you see two columns: the age of the car and the car’s wholesale price. Looking from top to bottom you see six rows. The top row contains the headings, or descriptions, of what the numbers beneath mean. Then there are

 Table 1...

## ONLINE CALCULATORS

I found so many excellent compound interest calculators that I’ m only listing a representative sample. All of the calculators I found have a good graphical interface. Most of them want the interest rate stated as a percentage, that is, 10%, not 0.1. Some of them let you invert the problem arbitrarily. That is, you can pick any three of the four variables’ future value, principal, years, and rate, and the calculator will solve for the fourth variable. Future value in the examples above is the balance at the end of the loan:

2.1 SCALING

This section is not necessary for understanding and working with the rest of the book...

## CHANGES

When a number that you’re interested in (the cost of a pound of coffee or the cost of a new home) changes, it’s often more relevant to look at the percent change than it is to look at the absolute numbers.

For example, if you ’ ve been paying \$3.00 a pound for coffee and the price changes by \$2.00 up to \$5.00 a pound, this is a relatively big change. On the other hand, if you’ve been considering purchasing a new car for \$25,000 and the price changes by \$2.00 to \$25,002, relatively speaking, this is not a big difference.[2]

The standard way of calculating percent change is by subtracting the new value from the old value, and then by dividing this difference by the old value:

New value – Old value
Old value

The 100 multiplier is just to change the fractional quantity i...