Gerver R.K., Sgroi R.J. Financial Algebra
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194 Chapter 4 Consumer Credit
A charge card is a special type of credit card. It allows the card-
holder to make purchases in places that accept the card. The monthly
bill for all purchases must be paid in full. There is no interest charged.
Popular charge cards used today include Diner’s Club and certain types of
American Express cards. Most people informally use the words charge card
and credit card interchangeably.
Using credit cards is both a convenience and a responsibility.
There is a temptation to overspend, and the card also can be lost. The
Truth-in-Lending Act protects you if your card is lost or stolen. If this
happens, notify the creditor who issued the card immediately. You may
be partially responsible for charges made by unauthorized users of cards
you lose. The maximum liability is $50. You are not responsible for any
charges that occur after you notify the creditor.
If the card number, and not the actual card, is stolen, you are not
responsible for any purchases. It is the responsibility of the person selling
the merchandise to make sure the purchaser is actually the card owner.
Cardholders receive a monthly statement of their purchases, and any
payments they made to the creditor. The
Fair Credit Billing Act pro-
tects you if there are any errors in your monthly statement.
It is your responsibility to notify the creditor about the error. You do
not have to pay the amount that is disputed or any fi nance charge based
on that amount, until the problem is cleared up.
If you fi nd yourself unable to meet payments required by a creditor,
notify that creditor immediately. The
Fair Debt Collection Practices
Act
prohibits the creditor from harassing you or using unfair means
to collect the amount owed. As you can see, you need
to be knowledgeable to responsibly use credit and
charge cards.
Another type of plastic card is known as a debit card.
A
debit card is not a credit or charge card, because
there is no creditor extending credit. If you open a debit
account, you deposit money into your account, and the
debit card acts like an electronic check. You are deduct-
ing money directly from your account each time you
make a purchase using the debit card.
You cannot make purchases that exceed the bal-
ance in your debit card account. Keeping a record of
your debit card activity is exactly like keeping the
check register you learned about in Lesson 3-1. The
Electronic Funds Transfer Act protects debit card
users against unauthorized use of their cards. They
are not responsible for purchases made with a lost or
stolen card after the card is reported missing.
Most debit cards carry the Visa or MasterCard
logo and the holder can choose, at the time of a pur-
chase, if the purchase acts as a debit card purchase or
a credit card purchase. At some retailers, when you
use a debit card you are charged a fee, similar to the
fees charged at an ATM.
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4-4 Credit Cards 195
Skills and Strategies
Revolving credit cards can have high interest rates, so it is important to
verify that the fi nance charge on your monthly statement is correct.
EXAMPLE 1
Frank lost his credit card in a local mall. He notifi ed his creditor before
the card was used. However, later in the day, someone found the card
and charged $700 worth of hockey equipment on it. How much is
Frank responsible for paying?
SOLUTION By the Truth in Lending Act, Frank is responsible for zero
dollars, because he reported it lost before it was used.
CHECK
■
YOUR UNDERSTANDING
Carrie’s credit card was stolen. She didn’t realize it for days, at which
point she notifi ed her creditor. During that time, someone charged
$2,000. How much is Carrie responsible for paying?
EXAMPLE 2
Credit card companies issue a monthly statement, therefore APR
(annual percentage rate) must be converted to a monthly percentage
rate. If the APR is 21.6%, what is the monthly interest rate?
SOLUTION To change to a monthly interest rate, divide the APR by 12.
21.6 ÷ 12 = 1.8
The monthly APR is 1.8%. This is the percent that will be used to com-
pute the monthly fi nance charge.
CHECK
■
YOUR UNDERSTANDING
If a monthly statement shows a monthly interest rate of x percent,
express the APR algebraically.
The average daily balance is the average of the amounts you owed
each day of the billing period. It changes due to purchases made and
payments made.
EXAMPLE 3
Rebecca did not pay last month’s credit card bill in full. Below a list of
Rebecca’s daily balances for her last billing cycle.
For seven days she owed $456.11.
For three days she owed $1,177.60.
For six days she owed $990.08.
For nine days she owed $2,115.15.
For fi ve days show owed $2,309.13.
Find Rebecca’s average daily balance.
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196 Chapter 4 Consumer Credit
SOLUTION The average daily balance is an arithmetic average. The
arithmetic average is also called the
mean. To fi nd this average, you
add the balances for the entire billing period, and divide by the num-
ber of days.
Add the number of days in the list to fi nd the number of days in
the cycle.
7 + 3 + 6 + 9 + 5 = 30
There were 30 days in Rebecca’s billing cycle.
To fi nd the sum of the daily balances, multiply the number of days by
the amount owed. Then add these products.
7(456.11) = 3,192.77
3(1,177.60) = 3,532.80
6(990.08) = 5,940.48
9(2,115.15) = 19,036.35
5(2,309.13) = 11,545.65
Total 43,248.05
Divide the total by 30, and round to the nearest cent.
43,248.05 ÷ 30 ≈ 1,441.60
The average daily balance is $1,441.60.
CHECK
■
YOUR UNDERSTANDING
Last month, Paul had a daily balance of x dollars for 6 days, y dollars
for 12 days, w dollars for q days, and d dollars for 2 days. Express the
average daily balance algebraically.
Finance charges are not charged if, in the previous month, the revolv-
ing credit card bill was paid in full. If you pay your card in full every
month, you will never pay a fi nance charge.
EXAMPLE 4
Rebecca (from Example 3) pays a fi nance charge on her average daily
balance of $1,441.60. Her APR is 18%. What is her fi nance charge for
this billing cycle?
SOLUTION Finance charges are computed monthly, so the 18% APR
must be divided by 12 to get a monthly percentage rate of 1.5%. Take
1.5% of the average daily balance to get the fi nance charge.
Change 1.5% to an equivalent decimal, multiply, and round to the
nearest cent.
0.015(1,441.60) ≈ 21.62
The fi nance charge is $21.62.
CHECK
■
YOUR UNDERSTANDING
Steve owes a fi nance charge this month because he didn’t pay his bill
in full last month. His average daily balance is d dollars and his APR is
p percent. Express his fi nance charge algebraically.
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4-4 Credit Cards 197
1. Interpret the quote in the context of what you learned.
2. Janine’s credit card was stolen, and the thief charged a $44 meal
using it before she reported it stolen. How much of this is Janine
responsible for paying?
3. Dan’s credit card was lost on a vacation. He immediately reported it
missing. The person who found it days later used it, and charged $x
worth of merchandise on the card, where x > $200. How much of
the $x is Dan responsible for paying?
4. Felix and Oscar applied for the same credit card from the same bank.
The bank checked both of their FICO scores. Felix had an excellent
credit rating, and Oscar had a poor credit rating.
a. Felix was given a card with an APR of 12%. What was his
monthly percentage rate?
b. Oscar was given a card with an APR of 15%. What was his
monthly payment?
c. If each of them had an average daily balance of $800 and had to
pay a fi nance charge, how much more would Oscar pay than Felix?
5. Vincent had these daily balances on his credit card for his last bill-
ing period. He did not pay the card in full the previous month, so he
will have to pay a fi nance charge. The APR is 19.2%.
nine days @ $778.12
eight days @ $1,876.00
four days @ $2,112.50
ten days @ $1,544.31
a. What is the average daily balance?
b. What is the fi nance charge?
6. Express the average daily balance algebraically given this set of daily
balances.
x days @ y dollars w days @ d dollars
r days @ q dollars m days @ p dollars
7. Suzanne’s average daily balance for last month was x dollars. The
fi nance charge was y dollars.
a. What was the monthly percentage rate?
b. What was the APR?
8. Jared’s average daily balance for last month was $560. The fi nance
charge was $8.12.
a. What was the monthly percentage rate?
b. What was the APR?
Life was a lot simpler when what we honored was father and
mother rather than all major credit cards.
Robert Orben, American Comedy Writer
Applications
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198 Chapter 4 Consumer Credit
9. Helene’s credit card has an APR of 16.8%. She never pays her balance
in full, so she always pays a fi nance charge. Her next billing cycle
starts today. The billing period is 30 days. Today’s balance is $712.04.
She is only going to use the credit card this month to make a $5,000
down payment on a new car.
a. If she puts the down payment on the credit card today, what will
her daily balance be for each of the 30 days of the cycle?
b. Find her average daily balance for the 30-day period if she puts
the down payment on the credit card today.
c. Find the fi nance charge for this billing period based on the aver-
age daily balance from part a.
d. Find her average daily balance for the 30-day period if she puts the
down payment on the credit card on the last day of the billing
cycle.
e. Find the fi nance charge on the average daily balance from
part d.
f. How much can Helene save in fi nance charges if she makes the
down payment on the last day, as compared to making it on the
fi rst day?
10. Gino has a debit card. The account pays no interest. He keeps track
of his purchases and deposits in this debit card register. Find the
missing entries a–f.
11. Ron did not pay his credit card bill in full last month. He wants to
pay it in full this month. On this month’s bill, there is a mistake in
the average daily balance. The credit card company lists the average
daily balance on his bill as $510.50. Ron computed it himself and
found that it is $410.50.
a. The APR is 18%. What fi nance charge did the credit card com-
pany compute on Ron’s bill?
b. If Ron’s average daily balance is correct, what should the fi nance
charge be?
12. The terms of Medina’s credit card state that the APR is 12.4%, and if
a payment is not received by the due date, the APR will increase by
w%. The credit card company received Medina’s payment three days
after the due date in February. Write the interest rate, in decimal
form that she will be charged in March, assuming she carried a bal-
ance from February.
CODE
NUMBER OR
DATE TRANSACTION DESCRIPTION
AMOUNT
PAYMENT
AMOUNT
DEPOSIT
$
$
BALANCE
8/4
8/5
8/7
8/7
8/7
Baseball Bat
Gas
Deposit
Gas
Dinner at Spooner’s
92 19
51 00
25 00
71 12
FEE
400 00
778.19
92.19
a.
51.00
b.
400.00
c.
25.00
d.
71.12
e.
On the Beach
8/11 Books for Fall Semester 491 51
491.51
f.
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4-4 Credit Cards 199
13. Express the missing entries in the debit card register algebraically.
14. Jill’s credit card was stolen. The thief charged a $900 kayak on the
card before she reported it stolen.
a. How much of the thief’s purchase is Jill responsible for?
b. Jill’s average daily balance would have been $1,240 without the
thief’s purchase. What was the sum of her daily balances for the
30-day billing period? Explain.
c. The thief’s purchase was on her daily balances for 10 out of the
30 days during the billing cycle. What was the sum of Jill’s daily
balances with the thief’s purchase included?
d. What was the average daily balance with the thief’s purchase
included?
15. Kristin’s credit rating was lowered, and the credit card company
raised her APR from 12% to 13.2%. If her average daily balance this
month is x dollars, express algebraically the increase in this month’s
fi nance charge due to the higher APR.
16. It is important to check your credit card bill each month. In the next
lesson, you will carefully examine a credit card statement and learn
how to look for errors. Most people would notice a major, expensive
purchase that they did not make. A smaller, incorrect charge of $6 for
example, might go unnoticed unless the entire statement was checked
with a calculator. If one million credit card holders were each over-
charged $6 each month for fi ve years, what would be the total amount
that debtors were overcharged, not including the extra fi nance charges?
17. Naoko has these daily balances on his credit card for September’s
billing period. He paid his balance from the August billing in full.
two days @ $99.78
fi fteen days @ $315.64
eleven days @ $515.64
two days @ $580.32
a. His APR is 15.4%. How much is the fi nance charge on his
September bill?
b. Does the credit card company need to calculate his average daily
balance? Explain.
c. Naoko calculated his average daily balance to be $377.85. Is he
correct? If not, what was his average daily balance?
d. What mistake did Naoko make when calculating this average
daily balance?
CODE
NUMBER OR
DATE TRANSACTION DESCRIPTION
AMOUNT
PAYMENT
AMOUNT
DEPOSIT
$
$
BALANCE
12/3
12/6
12/7
12/11
12/12
Arloff’s Gifts
Bonnie’s Boutique
Gas
Cable TV
x
y
v
FEE
a.
b.
c.
d.
r
e.
12/14 Gas g
f.
Deposit
z
m
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200 Chapter 4 Consumer Credit
Objectives
To identify and use •
the various entries
in a credit card
statement.
debit/credit•
previous balance•
payments/credits•
new purchases•
late charge•
fi nance charge•
new balance•
minimum •
payment
Key Terms
billing cycle•
credit card •
statement
account number•
credit line•
available credit•
billing date•
payment due date•
transactions •
Credit Card Statement
4-5
Credit card companies pay college students generously to
stand outside dining halls, dorms, and academic buildings and
encourage their fellow students to apply for credit cards.
Louise Slaughter, American Congresswoman
What information does a credit
card statement give you?
Credit cards can be used when making purchases in person, by mail, by
phone, online, and more. In most situations you get a receipt for each
transaction, but it can be diffi cult to keep track of the transactions over a
billing cycle.
A
billing cycle is a predetermined amount of time set by the credit
card company that is used for calculating your credit card bill. This cycle
can be adjusted by the company based upon your credit worthiness. For
example, a college student with little or no track record of being able
to keep up credit card payments may initially be given a 21-day billing
cycle. A seasoned credit card holder who has proven to be fi nancially
responsible might get a longer billing cycle.
At the end of every cycle, the credit card company takes an account-
ing of your credits and debits and sends you that information in the
form of a
credit card statement. You should read the statement
carefully and verify the charges. All credit card companies have a pro-
cess through which the credit card holder can dispute errors on the
statement.
Jane Sharp has a FlashCard revolving credit card. At the end of a
30-day cycle, Jane receives her FlashCard statement listing all of her pur-
chases and the payments the company has received during that 30-day
cycle. Jane’s credit card statement is shown on the next page.
average daily •
balance
number of days •
in billing cycle
APR•
monthly •
periodic rate
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4-5 Credit Card Statement 201
Locate each of the terms explained below on Jane’s statement.
Account Number• Each credit card account has a unique number.
Credit Line• The maximum amount you can owe at any time.
Available Credit• The difference between the maximum amount
you can owe and the actual amount you owe.
Billing Date• The date the bill (statement) was written.
Payment Due Date• On this date the monthly payment must be
received by the creditor.
Transactions • Lists where purchases were made and the date. Some
companies use the date posted, which indicates when the creditor
received its notifi cation of the charge and processed it. Some compa-
nies list the date of transaction, which shows when purchases were
made or payments were received. Some companies list both the
posted and the transaction dates.
Debits/Credits• A debit is the amount charged to your account.
A credit is a payment made to reduce your debt. Credits are identi-
fi ed by a negative (−) sign.
Previous Balance• Any money owed before current billing period.
Payments/Credits• Total amount received by the creditor.
New Purchases• The sum of purchases (debits) on the current bill.
Late Charge• The penalty for late payments from a previous month.
Finance Charge• The cost of using the credit card for the current
billing period.
New Balance• The amount you currently owe.
Minimum Payment• This amount is the lowest payment the credit
card company will accept for the current billing period.
Average Daily Balance• The average amount owed per day
during the billing cycle.
Number of Days in Billing Cycle• The amount of time, in days,
covered by the current bill.
APR• The yearly interest rate.
Monthly Periodic Rate• The APR divided by 12.
Previous
SUMMARY
$150.50
Balance
Payments
/ Credits
New
Late
Charge
Finance
Charge
New
Balance
Minimum
Payment
$75.00 $284.45 $0.00 $3.53 $363.48 $20.00
TRANSACTIONS
2 Jan Candida’s Gift Shop
3 Jan Skizza’s Pizzas
DEBITS / CREDITS (⫺)
$75.00
$31.85
5 Jan Beekman Department Store
10 Jan Festival Book Store
$139.10
$38.50
21 Jan Payment ⫺$75.00
Average
Daily
# Days
in Billing APR
Monthly
Periodic
Balance Cycle Rate
$235.10 30 18% 1.5%
ACCOUNT INFORMATION
Account Number 2653 8987 6098 Billing Date 23 Jan Payment Due 2 Feb
Total Credit Line
Total Available Credit
$ 8,000.00
$ 7,636.52
Jane Sharp 25 Main Street
Sunrise, NY
Purchases
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202 Chapter 4 Consumer Credit
Here you will learn how to read and verify entries on a credit card
statement.
EXAMPLE 1
The summary portion of Jane Sharp’s credit card statement shown on
the previous page looks as follows:
a. Explain how the new purchases amount was determined.
b. Explain how the new balance amount was determined.
SOLUTION
a. The new purchases amount is the sum of the purchases that
appear as debits. This sum must equal the amount $284.45 listed
in the New Purchases section of the statement summary.
New purchases = 75 + 31.85 + 139.10 + 38.50 = 284.45
b. The new balance amount is determined by using the formula given
below.
Previous − Payments + New + Finance + Late = New
Balance Purchases Charge Charge Balance
150.50 − 75 + 284.45 + 3.53 + 0 = 363.48
CHECK
■
YOUR UNDERSTANDING
Suppose you create the following spreadsheet that models the state-
ment summary and input the values in row 2. Write the spreadsheet
formula to compute the new balance in cell F2.
ABCDEF
1
Previous
Balance Payments
New
Purchases
Late
Charge
Finance
Charge
New
Balance
2
Previous
SUMMARY
$150.50
Balance
Payments
/ Credits
Late
Charge
Finance
Charge
New
Balance
Minimum
Payment
$75.00 $284.45 $0.00 $3.53 $363.48 $20.00
New
Purchases
TRANSACTIONS
2 Jan Candida’s Gift Shop
3 Jan Skizza’s Pizzas
DEBITS / CREDITS (⫺)
$75.00
$31.85
5 Jan Beekman Department Store
10 Jan Festival Book Store
$139.10
$38.50
21 Jan Payment ⫺$75.00
ACCOUNT INFORMATION
Account Number 2653 8987 6098 Billing Date 23 Jan Payment Due 2 Feb
Skills and Strategies
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4-5 Credit Card Statement 203
EXAMPLE 2
Pascual has a credit line of $15,000 on his credit card. His summary
looks as follows. How much available credit does Pascual have?
SOLUTION Pascual needs to determine his new balance and then sub-
tract that from his credit line in order to fi nd his available credit.
4,598.12 − 4,000.00 + 1,368.55 + 20.00 + 5.78 = $1,992.45
He has a new balance of $1,992.45. Subtracting this from his credit
line of $15,000 leaves him with an available credit of $13,007.55.
CHECK
■
YOUR UNDERSTANDING
Rhonda had a previous balance of $567.91 and made an on-time
credit card payment of $567.91. She has a credit line of x dollars and
made purchases totaling y dollars. Write an algebraic expression that
represents her current available credit.
EXAMPLE 3
Myrna is examining the summary section of her credit card statement.
Myrna has checked all the entries on her bill and agrees with every-
thing except the new balance. Determine where the error was made.
SOLUTION Add the amounts that show money Myrna must pay to
the credit card company.
$1,748.00
previous balance
800.00 purchases
9.15 fi nance charge
+ 19.00 late charge
$2,576.15 total to be paid
Subtract the $100 payment, and Myrna’s new balance will be
$2,476.16. It appears that Myrna was not credited for her payment.
Under the Fair Credit Billing Act, Myrna must notify her creditor in
writing within 60 days from the statement date on her bill.
CHECK
■
YOUR UNDERSTANDING
Determine the error that was made using the following summary
statement.
Previous
SUMMARY
$4,598.12
Balance
Payments
/ Credits
Late
Charge
Finance
Charge
$4,000.00 $1,368.55 $20.00 $5.78
New
Purchases
Previous
SUMMARY
$1,748.00
Balance
Payments
/ Credits
Late
Charge
Finance
Charge
New
Balance
$100.00 $800.00 $9.15 $19.00 $2,576.15
New
Purchases
Previous
SUMMARY
$850.00
Balance
Payments
/ Credits
Late
Charge
Finance
Charge
New
Balance
$300.00
$3.00 $4.78
$504.78
New
Purchases
$560.00
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