The Mathematics of Money

(Darren Dugan) #1

Copyright © 2008, The McGraw-Hill Companies, Inc.


10.1 Credit Cards 425

charge on your monthly bill? Assuming that you paid your previous month’s balance in full
(and thus are eligible to take advantage of the grace period), most issuers will send a bill that
shows no interest due. If you fail to pay your balance in full during the grace period, the inter-
est charges for the month will show up on your following month’s statement.

Other Fees and Expenses


Probably the main source of profit for credit card issuers is interest, but interest is not the
issuer’s only way of making money. Two others are annual fees and commissions.
An annual fee is a fee paid by the cardholder simply for having the credit card. Annual
fees can range as high as $100 per year (or even higher), but typically are much more mod-
est. Many credit cards are available that charge no annual fee at all. T&E cards often carry
high annual fees (since the issuer does not make any money from interest charges).
Commissions are not paid by the cardholder, and in fact many credit card users are not
even aware of their existence. When a merchant accepts a payment by a credit card, the
merchant pays a fee to the credit card company. Commissions apply to debit card transac-
tions as well. These commissions may be a percent of the amount charged, a flat amount
per transaction, or a combination of the two.

Example 10.1.5 Tr avis bought a pair of shoes for $107.79 and charged them to
his credit card. The credit card company charges the shoe store 45 cents for each
transaction, plus 1.25% of the amount charged. How much will the credit card
company pay to the shoe store?

The percent portion of the commission would be:

(0.0125)($107.79)  $1.35.

To this, we add the 45 cent charge to arrive at a total commission of $1.35  $0.45 
$1.80. Subtracting this from the amount of the charge, we can determine that the shoe store
will receive $107.79  $1.80  $105.99.

As a consumer, these commissions may not matter much to you, but they can be a signifi-
cant issue for businesses. The shoe store would of course just as soon not have to give up
the $1.80 to the credit card company and instead get the full $107.79 for Travis’s shoes.
However, few merchants can afford to refuse credit card payments. While the shoe store
would just as soon not give up the $1.80, it would probably prefer sacrificing $1.80 on the
sale to losing the business to another store. Plus, with a credit card the store knows that it
will receive the payment quickly, with no risk of a bounced check. And of course, the shoe
store’s owners have to keep in mind that credit cards are a very popular payment method
among consumers, and the store’s competitors probably do accept them. While some busi-
ness owners choose not to accept credit cards, most simply choose to think of the costs
incurred by accepting credit card payments as just another cost of doing business.
Commissions can, however, provide a particular challenge to small businesses. Larger
businesses may be in a position to negotiate lower commission rates, whereas a “mom
and pop” operation doesn’t have much negotiating power. Different commission rates are
often one of the key reasons why some merchants may accept one major credit card but not
another, or why some merchants will accept credit but not debit cards (or vice versa).

Choosing the Best Deal


The credit card industry is highly competitive, with literally hundreds of different card
issuers competing for each potential card holder. Many consumers will simply go with
whatever credit card offer seems most convenient, but cards are offered in a wide range of
interest rates and fees. People who just take whatever offer is first presented to them often
overlook or miss out on opportunities to pay significantly less for their credit card use.
To some extent, the choice of credit card and issuer is not a mathematical matter at
all. If you do all of your banking at Friendly Neighborhood National Bank and decide
that you just want to keep your credit card account at the same place, then there are no
Free download pdf