424 Chapter 10 Consumer Mathematics
I PRT
I ($750.13)(0.1599)(31/365)
I $10.19
So her interest for this billing month would be $10.19.Be careful when adding interest onto the balance to determine the total on a monthly statement.
Remember that the ADB is simply a tool used for calculating interest—it is not the amount
that you actually owe. It is a very common mistake in answering these types of questions to
add the interest onto the ADB. We put so much work into finding the ADB, it seems impor-
tant enough that we want to use it wherever possible! But if you stop to think about things, it
makes sense that you would need to repay the total of your charges, not their average. And so,
once the interest is calculated, it should be added to the last balance, not onto the ADB.Example 10.1.3 What will the total balance be on Joanna’s monthly statement?Interest will be added onto her balance at the end of this billing period; the total balance on
her August 17 statement will be $797.48 $10.19 $807.67.Credit Card Interest—The Grace Period
Most credit cards offer a feature known as a grace period, which adds an interesting wrinkle
to the matter of interest. The grace period is a period of time (typically 20 to 25 days),
beginning on the card’s billing date. If you pay the entire balance within this grace period,
and if you paid your previous month’s balance off in full (so that none of your balance is a
carryover from the prior month), you pay no interest at all.^3
For people who use a credit card primarily for convenience’s sake, this can provide
a tremendous savings. Many people have credit cards that they use regularly, yet pay
no interest whatsoever. Such credit card holders are often referred to in the industry as
convenience users.^4 Taking advantage of the grace period is one of the few “free lunches”
in the financial world; charges made to the card become a short-term interest-free loan. A
convenience user benefits from both the convenience of her credit card and from the tem-
porary use of someone else’s money for free. However, grace periods are an all-or-nothing
deal; the grace period will apply only if the balance is paid in full. Paying even one penny
less than the full balance means that interest charges will still apply.Example 10.1.4 The billing date for Nick’s credit card falls on the 18th day of each
month. His card carries an interest rate of 21.99%, and has a 20-day grace period.
On October 18 his balance was $935.14. He made charges of $56.65 on October 20,
$309.25 on October 29, $81.17 on November 9 and $101.42 on November 17. He
paid $935.14 on November 3. If he pays the balance on his November 18 statement in
full before the end of the grace period, how much interest will he owe?Since he paid his October 18 balance in full within the grace period, if he pays the November
balance in full the grace period applies and he will owe no interest. The answer is: $0!In addition to the obvious financial advantage of knowing about this, as a student it is
important to always check for the grace period in questions about credit card interest. Not
only did Nick save himself from paying interest in this example, he also saved us from
having to calculate his ADB!
You don’t have to pay interest if you pay your balance in full within the grace period, but
when the bank prints your statement, it obviously has no way of knowing in advance whether
or not you are going to do this. So how does the bank know whether or not to place an interest(^3) This is the typical deal for the grace period on most cards. However, the exact provisions for any particular card
may vary. For example, some cards have a grace period for purchases made to the card, but no grace period for
cash advances (obtained by using your credit card in an ATM to get cash). For that matter, while an overwhelming
majority of credit cards do offer a grace period, occasionally cards are offered with no grace period at all. You
should make sure to carefully read the terms of any credit card agreement.
(^4) At least that is the polite term.