# Category Understanding the Mathematics of Personal Finance

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...

## PRORATION—WORKING INSIDE A COMPOUNDING INTERVAL

Suppose I want to pay off a loan 4 months and 20 days after taking the loan.[7] The bank isn’t going to just use the results of the fourth compounding interval calculation and give me the interest they earned in the last 20 days. On the other hand, I don’t think it’ s fair for the bank to use the fifth compounding interval calculation and charge me 10 days’ worth of interest that the bank hasn’t earned.

Let’s say that there are 30 days in the current month. Take the interest rate per

month ^ R j and divide it by 30, giving us an interest rate per day, then we multiply

this by the number of days, giving us an effective interest rate for the 20 days of the month:

The interest is just the above number times the balance after 4 months...

## EXPONENTS

An exponent is another neat notation. Suppose I want to multiply an expression by itself (called “squaring” the expression):

(j + 7)0 + 7) = (j + 7)2.

The little “2” placed high up in the upper right means “square the expression” or more directly, “write the expression down twice, making it clear that you mean multiplication.” This is also sometimes called “raising the expression to the power of 2. ”

Similarly, I can “cube” the expression

(j + 7)0 + 7)0 + 7) = (j + 7)3

and so on.

In general, (anything)" is called raising the expression “anything” to the nth power.

The following discussion of exponents is not needed in order to understand the book; I just thought that some readers might be curious as to why raising an expres­sion to the power of 2 is called “squa...