This document discusses credit cards and mortgages. It provides examples of calculating average daily balances and interest on credit cards. It also discusses different types of mortgages, calculating monthly mortgage payments, determining loan eligibility based on income ratios, and estimating upfront costs for home purchases.

1. © The McGraw-Hill Companies, Inc., 2008
McGraw-Hill/Irwin
10-1
Chapter 8
Consumer Mathematics

2. 10-2
10.1 Credit Cards
• It’s no secret that credit cards can be useful to
both businesses and individual consumers.
• It’s also no secret that letting things get out of
control with credit cards can be disastrous to
your financial well-being.
• Given these facts, it’s worthwhile to have a solid
understanding of the mathematics involved in
their use.

3. 10-3
10.1 Credit Cards
• Since using a credit card means borrowing money, it
also means interest.
• One common complaint about credit cards is that their
interest rates are often very high compared to the
rates on other loans, such as car loans or home loans.
• With those sorts of loans, the lender has collateral.
This means that if you do not repay the loan as
promised, the lender has the right to take the property
for which you borrowed the money.
• Credit cards, on the other hand, are normally
unsecured loans, meaning they are issued without
any collateral.

4. 10-4
10.1 Credit Cards
• Debit cards present an alternative for those who
really don’t want to borrow.
• Purchases made with a debit card are paid out
of a checking, savings, or a similar account
immediately, so you are not borrowing any
money.

5. 10-5
10.1 Credit Cards
• Another similar type of card is sometimes known
as a travel and entertainment card (T&E).
• Payments for purchases made with these cards
are handled in much the same way as with credit
cards.
• However, while a credit card allows you flexibility
in when you pay the money back, with a T&E
card you are normally required to pay off the
charges in full each month. Therefore, there is
usually no interest charged on these cards.

6. 10-6
10.1 Credit Cards
• The calculation of credit card interest poses a bit
of a challenge. On the one hand, since
statements are produced and payments are due
monthly, it makes sense that interest should be
computed and charged to the account monthly.
• On the other hand, since the balance changes
from day to day, it seems that interest should be
calculated daily.

7. 10-7
10.1 Credit Cards
• The most common method of calculating interest
on the credit card is known as the average daily
balance (ADB) method.
• The interest is computed and added to the
account monthly.

8. 10-8
10.1 Credit Cards
Example 10.1.1
• Problem
– Joanna has a credit card whose billing period
begins on the 17th day of each month. On July
17 her balance was $815.49. She made a $250
payment on July 28. She also made new
charges of $27.55 on July 21, $129.99 on August
5, and $74.45 on August 8.
– Find her average daily balance.
• Solution
– See table on the next slide.
– ADB = $23,253.97/31 = $750.13

9. 10-9
10.1 Credit Cards
Example 10.1.1 Cont.
• Solution
Effective Date Activity Balance
Days at
Balance
(Balance)(Days)
July 17 Start $815.49 4 $3,261.96
July 21 +$27.55 $843.04 7 $5,901.28
July 28 -$250.00 $593.04 8 $4,744.32
August 5 +$129.99 $723.03 3 $2,169.09
August 8 +$74.45 $797.48 9 $7,177.32
Totals: 31 $23,253.97

10. 10-10
10.1 Credit Cards
• Most credit cards offer a feature known as a
grace period, which adds an interesting wrinkle
to the matter of interest.
• It’s a period of time, typically 20 to 25 days,
beginning on the card’s billing date. If you pay
the entire balance within a grace period, and if
you paid your previous month’s balance off in
full, you pay no interest at all.

11. 10-11
10.1 Credit Cards
• Although the main source of profit for credit
card issuers is interest, two other sources are
annual fees and commissions.
• An annual fee is a fee paid by the cardholder
simply for having the credit card.
• Commissions are not paid by the cardholder
but by a merchant who accepts credit card
payments. These fees may be a percent of
the amount charged, a flat amount per
transaction, or a combination of the two.

12. 10-12
10.1 Credit Cards
Example 10.1.5
• Problem
– Travis 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?
• Solution
$107.79 x 1.25% = $1.35
$1.35 + $0.45 = $1.80
$107.79 -- $1.80 = $105.99

13. 10-13
10.1 Credit Cards
• The credit card industry is highly competitive, with
literally hundreds of different card issuers competing
for each potential card holder.
• 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.
• Ideally, as a consumer, you would want to choose
the card that has both the lowest interest rate and
the lowest annual fee.
• What if, though, the card with the lowest annual fee
carries a higher interest rate, while the card with the
lowest interest rate has a low annual fee?

14. 10-14
10.1 Credit Cards
Example 10.1.6
• Problem
– Jerome expects that
he will normally carry
a credit card balance
of around $800.
Which of the three
options in the table
would be the lowest-
cost option for him?
Card
Issuer
APR
Annual
Fee
Bank A 9% $80
Bank B 15% $25
Bank C 23.99% None

15. 10-15
10.1 Credit Cards
Example 10.1.6 Cont
• Solution
– Bank A
I = PRT
I = $800 x 9% x 1 = $72
Total = $72 + $80 = $152
– Bank B
I = $800 x 15% x 1 = $120
Total = $120 + $25 = $145
– Bank C
I = $800 x 23.99% = $191.92

16. 10-16
10.2 Mortgages
• A mortgage is a loan that is secured by real estate.
• If the borrower fails to pay back the loan as promised,
the lender has the right to take the real estate through a
legal process known as foreclosure.
• Another way of saying that the lender has the right to do
this is to say that the lender has a lien on the property.
• With few exceptions, the amount borrowed with a
mortgage loan must be less than the value of the
property. This is sometimes called the maximum loan
to value percentage.
• The difference between the value of a property and the
amount that is owed against it is called the homeowner’s
equity.

17. 10-17
10.2 Mortgages
Example 10.2.1
• Problem
– Les and Rhonda own a house worth $194,825.
The balance they owe on their first mortgage is
$118,548. They want to take out a second
mortgage and all of the lenders they have spoken
with require a minimum equity of 5%.
– Find (a) their equity now, (b) the maximum they
can borrow with the second mortgage, and (c)
their equity if they borrow the maximum.

18. 10-18
10.2 Mortgages
Example 10.2.1 Cont.
• Solution
(a) $194,825 -- $118,548 = $76,277
(b) The maximum they can owe:
95% x $194,825 = $185,084
Since they already owe $118,548, they can borrow
$185,084 -- $118,548 = $66,536
(c) If they borrow the maximum, they will have only 5%
equity left or 5% x $194,825 = $9,741

19. 10-19
10.2 Mortgages
• However, second mortgages are not to be confused with
a similar financial product called a home equity line of
credit.
• The difference between the two is that, with a home
equity line, instead of being lent a set amount up front,
the borrowers are given a checkbook or debit card that
they can use to borrow money as needed against their
home equity up to a set limit.
• Occasionally, some finance companies will offer
mortgage loans for more than the value of the property.
In those cases, it’s actually possible to have negative
equity.

20. 10-20
10.2 Mortgages
• A fixed (or fixed-rate) mortgage has an interest rate
that is set at the beginning and never changes over the
entire term of the loan.
• If mortgage rates drop, a borrower can often take an
advantage of this by refinancing.
• An adjustable-rate mortgage (or ARM) is a more
complicated type of a loan. It will usually have some
initial period of time for which the rate is fixed. After that,
the rate can change.
• Adjustable-rate mortgages will usually carry better
interest rates up front.

21. 10-21
10.2 Mortgages
Example 10.2.3
• Problem
– Chantal took out a $142,000 mortgage with a 30-year, fixed-rate
loan at 7.2%. Find her monthly mortgage payment
• Solution
– PV = PMTan/i
$142,000 = PMTa360/0.006
PMT = $963.88

22. 10-22
10.2 Mortgages
• When deciding whether to approve someone for a
mortgage loan, the lenders consider the following:
– Your Credit History
– Employment Stability
– Income
• How does a lender determine whether or not your
income is adequate for a loan?
• Most lenders decide this by using ratio tests, comparing
the total monthly PITI for the loan to a percentage of
your gross monthly income.

23. 10-23
10.2 Mortgages
• In addition to the monthly PITI payments, buying real
estate usually involves a significant cash outlay up front.
Some of the many expenses involved include:
– Down payment
– Legal fees
– Appraisal
– Title search and insurance
– Inspections
– Flood check
– Recording fees
– Mortgage taxes
– Application and origination fees

24. 10-24
10.2 Mortgages
Example 10.2.9
• Problem
– Drew and Joanne are buying a house for $128,550. They will
make a minimum 3% down payment, and closing costs will total
$2,100. Annual property taxes are $2,894 and homeowners’
insurance is $757 annually. How much money will they need up
front?
• Solution
– Their down payment will be 3% x $128,550 = $3,856.50
Total = $3,856.50 + $2,100 + $2,894 + $757 = $9,607.50