Category Understanding the Mathematics of Personal Finance


While determining what interest is taxable and what interest isn’t taxable can be a fairly sophisticated task, figuring out the tax on taxable interest is very straightfor­ward. Let’s say that your taxable income is $50,000 not counting interest. Your tax is approximately $6,700, which is an average tax rate of 13% and an incremental tax rate of 15%. If you have $10,000 of savings earning 4% interest, you earned $400 in interest last year. This interest is taxed at the 15% rate, so the tax on your interest is 0.15(400) = $60.

If your interest was $400 but you had to send $60 back to the government, then you only got to keep $400 – $60 = $340. Your effective interest rate was therefore

$340 $10,000 = 3.4%.

If your taxable income, not counting interest, had been $360,000, your tax would...

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When you enter a number of payments in one of these spreadsheets, the sheet shows entries from Pmt Nr 0 or 1, as appropriate for the topic at hand, up to the number of payments entered. The actual spreadsheet, however, has been programmed down to row 1,000. If you click on a blank cell in the Payment column of the spreadsheets I used above, you’ll see the same formula as in the cells with visible data. If you need to recover the formula in the payment column (or any other column), you can easily do it by copying one of these “blank” cells up into the required cells above it.

The sheets’ ability to stop showing anything after the specified number of pay­ments has been reached is handled by the “If’ statements that are cluttering up all the cell formulas...

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The list of how many different forms of prepayment penalties can be contrived is endless. Here are a few examples I have encountered:

1. Six months’ interest on 80% of the balance. Looking at the rule of 78 example shown in Figure 5.2, after 5 years, the remaining balance is approxi­mately $236,000. Eighty percent of this is approximately $189,000, and 6 months’ interest on this is about $7,560. This is considerably better than the rule of 78 prepayment penalty but still a lot of money.


0 20 40 60 80 100 120 140 160

Payment number

Figure 5.3 Comparison of different penalties for various prepayment penalty formulas (large loan example).

2. A flat 2% of the outstanding balance. In the above example, this would be about $3,600. This is still a lot, but we’re getting better.


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A popular policy with a fixed monthly payment is the so-called whole life policy. There are so many variations on how this can be structured that I can’t possibly cover them all. I’ll look at a 20-year-old typically healthy man and present one pos­sible scenario. You should get the idea of what’s going on pretty easily and be able to understand different variations when they’re put before you.

As was shown above, for a 20-year-old man, a year’s $100,000 1-year term insurance should only cost $127. Suppose, however, that this man pays $900 a year instead. I’ll treat things annually even though payments are usually made monthly, just to keep the table showing these calculations from becoming uncomfortably long.

At the inception of the policy (our young man’s twentieth birthday),...

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The ADB method of calculating finance charges that I presented above is not the only way that finance charges are calculated. Other approaches include the adjusted balance, the two-cycle ADB, the previous balance, and the ending balance. As best as I could ascertain, the ADB method is used by major credit card companies in the United States.

If you wish to learn more about the other approaches, try these websites:

1. www. finweb. com/banking-credit/how-credit-card-finance-charges-are- calculated. html;

2. http://money. howstuffworks. com/personal-finance/debt-management/credit- card8.htm;

3. http://www. bankrate. com/brm/green/cc/basics3-2a. asp.


A debit card looks almost exactly like a credit card...

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Figure 13.8 shows the daily price of three obviously fictitious stocks for about a year’s trading. The stock labeled “going nowhere” starts at 100, then periodically cycles between 75 and 125, ending up at 100. The stocks labeled “climbing” and “falling” also start at 100 and cycle up and down, but end up at 120 and 80, respectively.

Table 13.2 shows the average price for these three fictional stocks and the average purchase cost per share if you bought the same dollar amount (this is not the same number of shares) every day for the year. On days when the stock price is higher than average, a dollar spent buys you comparatively less. On days when the


Day number

Figure 13.8 Dollar cost averaging example.

Table 13.2 Dollar Cost Averaging Examples


Average pr...

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