Understanding the Mathematics of Personal Finance


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 your spe­cific finance charges for the month;

• a list of all transactions with the dates of these transactions and usually a very terse explanation to help identify the transaction;

• an information section (usually on the back of the sheet) explaining how to report a disputed item, how your finance charges are calculated, how the minimum payment is calculated, and so on.

Other information may also be found in any or all of these sections. Also, a several page document comes with the credit card itself—this is your contract with the credit card company. It includes many more details of how your account will be

Подпись: Amazing Card Account balance: $139.36 Minimum payment: $15.00 Cardholder: Harry Consumer Enter amount enclosed: Scottsdale, AZ 85258 $ Acct # 1234 5678 9876 5432 Payment due date: 04/20/09 Closing date: 03/26/09 Credit line: $12,000.00 PO Box 12345 New York, NY 10034-4321 Cash or credit available: $11,840.64 Figure 6.1 Fictional credit card payment sheet.
Подпись: Finance charge schedule
Подпись: Category Daily periodic rate NAPR Balance transfers 0.016164% 5.90% Purchases 0.016164% 5.90% Cash advances 0.032328% 11.80%

Figure 6.2 Fictional credit charge schedule.

handled. This contract is revised occasionally; the revisions come on a separate piece of paper that accompanies your statement (or might possibly come in the mail by itself).

In Figures 6.1-6.3, I’ve created some fictitious generic credit card statement sections. They’re not exactly sections from any statement that I know of, but they should be close enough to your statement sections for you to be able to find and understand the relevant information.

Figure 6.1 shows the tear-off piece of the statement. In this example, the balance isn’t very high—only $139.36. The due date for the payment is April 20, 2009. The minimum payment that must be made by this date is $15.00. If at least $15.00 doesn’t

Transaction summary

Previous balance:


Payments and credits:


Purchases and adjustments:


Finance charge:


New balance:


Figure 6.3 Fictional credit card transaction summary sheet.

reach the Amazing Card bank by April 20, 2009, late charges will be applied in addition to the interest accrued. If $139.36 reaches the bank by April 20, 2009, there might not be any new interest charges—depending on factors that will be discussed below.

What if I pay at least $15.00 but less than $139.36 before the due date? How much interest must I pay on an unpaid balance? How is the unpaid balance calcu­lated? To find the answers to these questions, I must now look to the other sheets (or sections of sheets) on my statement.

Figure 6.2 shows the finance charge schedule for this credit card. I’ll talk about balance transfers in a bit. The interest rate for purchases is 5.90% annual percentage rate (APR). The interest rate for cash advances is higher—13.80% APR. In both cases, the daily periodic rate is just the nominal annual percentage rate (NAPR) divided by 365. The difference between the two rates will be relevant when I discuss how payments are allocated. Remember that these are fictitious numbers. In some cases, the cash advance and purchase rates are the same; in some cases, they ’ re higher or lower than shown here.

Figure 6.3 shows the account (activity) summary for the month.[14] Last month’s balance had been $152.86. A $15.00 payment had been made, leaving a balance of about $137.86. The word “about” is needed here because the actual date of the payment is important, as will be shown soon. If I assume that a full 31-day month has gone by since the last payment and that this is a purchase balance, the interest due should be ($137.86)(0.00016164)(31) = about 70 cents. Why is the listed finance charge $1.50?

The answer to this lies in the details found either on the back of the statement or in the card contract. There is a minimum finance charge of $1.50. In a sense, the credit card company is charging you extra for not owing them as much money as they ’ d like you to owe them. This finance charge is more than 13% APR.

The transaction list should be scrutinized for errors and possible fraudulent entries. Compare listed purchases to your receipts. Do not delay in reporting discrepancies.

The back of the statement presents the details of how your credit card company calculates your balance and finance charge and how it credits your payments. Since money is coming and going (purchase, cash advances, payments) pretty much on a daily basis, it makes sense for the credit card lenders to calculate interest on a daily basis. This means that we need to understand how the daily balance is calculated.

First, however, I’ll discuss balance transfers.

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