Category Understanding the Mathematics of Personal Finance


Every credit card statement shows a minimum payment or a minimum amount due. This is the least amount of money that you can send in (before the due date) that will not trigger late payment fees or fines. Typically, this amount is sufficient to reduce your balance a bit—if you haven’t recently made more payments or received more cash advances.

The calculation of the minimum payment varies from credit card company to credit card company and can be slightly complicated. Usually there’s a lowest minimum payment (something like $15). If your balance due is less than this amount, then your minimum payment will be your balance due...

Read More


The spreadsheet Ch13Stocks. xls will do correlation calculations and produces some numbers that I haven’t introduced yet. To use this spreadsheet, you must enter some stock prices. You can do this by typing them in (I’ll go through an example below) or if you’re proficient enough with spreadsheet operations, download them from the Web right into the spreadsheet. An important point is that you must enter stock prices that are uniformly distributed in date. The closing price every Friday afternoon for a year, for example, is a good data set. Entering daily information for the month of January and then end-of-month information for the rest of the year won’t yield any meaningful results...

Read More


When adding up the total interest paid or received for a year for income tax purposes, it is important to look at the details very carefully. For example, suppose you are paying a loan back monthly, with payments due on the first day of the month. If you regularly send your payments right on time, your lender will be crediting your payment, approximately, on the eighth day of the month. An end of the year summary statement mailed to you for tax purposes in 2010 will show the 12 payments made in 2009.

Now, suppose that, for whatever reason, you mailed your January 2010 payment on December 20 of 2009. It is possible that it reached your lender and got credited to your account in 2009. This means that your 2009 statement will correctly show 13 credited payments...

Read More


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...

Read More


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...

Read More


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.


Read More