Category Understanding the Mathematics of Personal Finance


So far, this chapter presumed that the way to make money is to “buy low, sell high.” This is true, but it isn’t the only way to make money. Buying a stock in the hope that its price will rise is called “going long.” Conversely, if you think a stock’s price will fall, you can “go short” or “sell short.” The way to do this is to arrange to borrow some stock that is selling at, say, $25 a share, and selling it. When the price falls to $20 a share you buy back the stock, return the shares and any costs for the loan, and keep the difference. If the stock price goes up instead of down, you’ll have to pay more than you received when you sold the stock, and you’ll lose money on the transaction.


Corporations may declare dividends...

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I f you decide to make a payment that is larger than your regular payment, your balance will be reduced by an extra amount. Your lender should reduce your balance, and hence the accrued interest until your loan is paid off, accordingly. Similarly, if you make a payment that is smaller than your regular payment, some corrections must be made. In this latter case, penalties might be added to the balance as well as corrections to the calculations.

Different lenders handle these situations differently. This makes it impossible for me to discuss or present a spreadsheet that will handle the general case. Instead, I ’ ll just show a couple of possibilities here. What I ’ m doing is mathematically correct, but remember that it might not apply directly to your loan.

l ’ ll use the same loan as...

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The U. S. government offers several different tax deferral schemes for workers to use to build their “nest egg.” There are 401K plans, individual retirement accounts (IRAs), Roth IRAs, self-employed pension (SEP) IRAs, and so on. Each of these plans serves a different purpose/customer base, and each has its own rules about taxation, contribution, withdrawal, and so on. Many books have been written on this topic, and I couldn’t possibly do it justice in a few pages. What I will do in the fol­lowing pages is to walk through a hypothetical saving for a retirement example and show the potential value of a tax-deferred savings plan. I will be using my online spreadsheet Ch9Taxation. xls.

Г ’ rl begin using the Nest Egg tab on the spreadsheet...

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Each credit card company’s monthly credit card statement has a unique layout, so I can’t specifically explain your statement to you. Statements are similar, however, in having the following sections:

• a tear-off piece showing your name and address, the card company’s name and address, all or part of your account number, your account balance, the payment due date, and possibly the minimum payment due. This piece is returned to the card company with your payment;

• an account summary showing your previous balance, payments and credits during the previous month, finance charges for the previous month, and your new balance;

• a transaction summary detailing your purchases, cash advances, and payments for the month;

• a finance charge summary showing the different rates charged and...

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A single clear, concise, definition of annuity is impossible to create, because there are two principal financial vehicles called annuities and an untold number of varia­tions and combinations within each of these two vehicle categories. A fixed annuity is considered in the United States to be a savings scheme with certain tax advantages and is regulated by the IRS. A variable annuity is considered in the United States to be an investment scheme, again with certain tax advantages, and is regulated by the U. S. Securities and Exchange Commission (SEC).

An annuity is a contract between you and an insurance company by which you give the insurance company money either in a lump sum or over time (the accumula­tion period) and then it starts sending you periodic payments...

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The present value of amounts of money in the future, as the above calculations show, depends on the available interest rate. If interest rates are very low, then the present value looks essentially like the simple sum of all the payments. As interest rates get higher, payments far in the future become pretty worthless.

Table 7.3 shows the total present value of a 24 monthly payment account with $100 being deposited each month for different interest rates. As you can see from the table, the present value falls as the rate of interest increases.

One factor that’s very easy to model on a spreadsheet but very difficult to predict in advance is just what interest rates will be a few years from now...

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