# Category Understanding the Mathematics of Personal Finance

## Investing: Risk versus Reward

If you kept all your savings in cash in a shoe box under your bed, you would be risking loss due to theft, fire, and so on. On the other hand, while your savings would never add up to anything other than exactly what you put into the shoe box, from a financial point of view, your savings would be absolutely safe. No stock market variations, bank failures, or whatever could impact your savings. Inflation, however, would slowly eat into the actual value of these savings, even though the dollar amount didn’t change.

Government-insured savings are, for all intents and purposes, perfectly safe. In addition, when your money is put into an insured saving product, you don’t have to worry about a burglar making off with it in the night...

The spreadsheet Ch3Amortization. xls, Loan tab, produces an amortization table for a loan with regular monthly payments.

Table 3.7 is a snapshot of a part of this spreadsheet. This table distorts the spreadsheet slightly in that because the spreadsheet is too wide to fit on a printed page, I’ve taken the input data—the data to the left of the green line in the spread – sheet—and put it on top in the table.

The input variables for these calculations are

Start Month the month when you take the loan; a number between 1 and 12;

Start Year the year when you take the loan;

Nr Mnthly Pmts if the loan is described in years, this is 12 (number of years);

Principal the amount you’re borrowing;

Rate the annual percentage rate (APR).

The actual date of the loan is not shown...

## UNDERSTANDING PERSONAL FEDERAL INCOME TAX RATES

Every year in the United States, on April 15, our income tax filings are due. The federal government, most states, and some cities collect income taxes. In almost all cases, the federal tax is by far the highest of the personal income taxes that we must pay.

When you fill out your tax return, you list all of your earnings and then you list your deductions. When you subtract the sum of all your deductions from the sum of your earnings, you get your taxable income. The amount of tax you must pay to the Internal Revenue Service (IRS) is based on this taxable income and your filing status. Your filing status can be single, married filing jointly, and so on. Accompanying each filing status is a Tax Rate Schedule.

Understanding the Mathematics of Personal Finance: An Introduction to Financial Li...

Two approaches to providing readers with computer-based calculators are employed in this book. One approach is to provide links to the many online calculators that provide slick interfaces and useful tutorials. A second approach is to create spread­sheets that, while not quite as elegant looking as the online calculators, allow the user to examine the calculations, modify and/or add features if desired, make avail­able some intermediate or extended results, generate reports, and so on. Also, by creating a set of custom spreadsheets tied to this book, I can provide a consistent interface among all of them.

An advantage of the online calculators for me is that I don’t have to create them; I just find them and then provide links at the appropriate place...

## RULE OF 78

This rule is sometimes called the sum-of-digits method. I’ll explain where both of these names came from shortly. As you shall see, any loan bearing this type of prepayment penalty is to be avoided. Various states have a legislation limiting its use. Hopefully, by the time you’re reading this, the practice will have been banned universally.

The rule of 78 payoff calculation used to be very popular with automobile loans. I understand it is uncommon today. As long as it remains legal, however, you’ll see it being used—principally among somewhat unscrupulous dealers who offer “sub­prime” loans to people who don’t have good credit, probably at an exorbitant interest rate.

I’ll use the auto loan of Table 5.1 as my first example. The spreadsheet Ch5PrepaymentPenalties...