Category Understanding the Mathematics of Personal Finance

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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MY WEBSITE SPREADSHEET

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

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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...

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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:

1. www. moneychimp. com/calculator/compound_interest_calculator. htm;

2. www.1728.com/compint. htm;

3. www. webmath. com/compinterest. html .

2.1 SCALING

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

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