Chapter 11 Consumer Mathematics

1

• Chapter 11 Consumer Mathematics
• 11.1 Percent
• 11.2 Personal Loans and Simple
  Interest
• 11.3 Compound Interest
• 11.4 Installment Buying
• 11.5 Buying a House with a Mortgage

2

• Section 11.1 Percent
• Percents are everywhere. People come in contact
  with percents when going to the store, reading a
  newspaper, looking at bank statements, etc. This
  section will give you a better understanding of
  percents.

3

• What is Percent?
• Percent means per hundred.
• Percent is a ratio of some number to 100.
• So would be 17.

4

• What is Percent?
• Percent means per hundred.
• Percent is a ratio of some number to 100.
• So would be 17.
• Percents help us make comparisons between groups
  of different sizes. Which is a better test
  score, 12 out of 15 or 25 out of 30?

5

• What is Percent?
• Percent means per hundred.
• Percent is a ratio of some number to 100.
• So would be 17.
• Percents help us make comparisons between groups
  of different sizes. Which is a better test
  score, 12 out of 15 or 25 out of 30?
• Find the percent of correct answers for each
  test 12/15 80 and 25/30 83.3.

6

• What is Percent?
• Percent means per hundred.
• Percent is a ratio of some number to 100.
• So would be 17.
• Percents help us make comparisons between groups
  of different sizes. Which is a better test
  score, 12 out of 15 or 25 out of 30?
• Find the percent of correct answers for each
  test 12/15 80 and 25/30 83.3.
• Thus, 25 out of 30 is better.

7

• Changing Percents
• It is useful to know how to change between
  fractions, decimals, and percents. Depending on
  the type of word problem and how you choose to
  solve it, you will need to be able to find a
  fraction, decimal, or percent.

8

• Changing Percents
• It is useful to know how to change between
  fractions, decimals, and percents. Depending on
  the type of word problem and how you choose to
  solve it, you will need to be able to find a
  fraction, decimal, or percent.
• Look at the three procedures which are found in
  yellow boxes on pages 518 and 519 in the text.
  Also study Examples 1-4 on pages 518 and 519 in
  the text. These examples show how to change
  between the three different forms.

9

• Changing Percents Examples
• 1. Change 7/8 into a percent. To solve, divide
  7 by 8 and then multiply your answer by 100.
• 0.875 x 100 87.5.

10

• Changing Percents Examples
• 1. Change 7/8 into a percent. To solve, divide
  7 by 8 and then multiply your answer by 100.
• 0.875 x 100 87.5.
• 2. Change 0.6745 to a percent. To solve,
  multiply the decimal by 100. 0.6745 x 100
  67.5.

11

• Changing Percents Examples
• 1. Change 7/8 into a percent. To solve, divide
  7 by 8 and then multiply your answer by 100.
• 0.875 x 100 87.5.
• 2. Change 0.6745 to a percent. To solve,
  multiply the decimal by 100. 0.6745 x 100
  67.5.
• 3. Change 25.9 to a decimal. To solve, divide
  the percent by 100. (25.9 / 100) 0.259

12

• Changing Percents Examples
• 1. Change 7/8 into a percent. To solve, divide
  7 by 8 and then multiply your answer by 100.
• 0.875 x 100 87.5.
• 2. Change 0.6745 to a percent. To solve,
  multiply the decimal by 100. 0.6745 x 100
  67.5.
• 3. Change 25.9 to a decimal. To solve, divide
  the percent by 100. (25.9 / 100) 0.259
• 4. Change 3/8 to a decimal. To solve, divide
  the percent by 100. 3/8 0.375,
• thus 0.375/100 0.00375

13

• A Note About Rounding
• All answers from this section of the text are
  given to the nearest tenth of a percent. To do
  this, carry the division to four places after the
  decimal point (the ten-thousandths place) and
  then round to the nearest thousandth.

14

• Basic Percent Example
• Percent
• Read homework exercise 26 on page 524 in the
  text.

15

• Basic Percent Example
• Percent
• Read homework exercise 26 on page 524 in the
  text. To solve, we need to take the total sales
  for Crest toothpaste and divide it by the total
  sales of all toothpastes.

16

• Basic Percent Example
• Percent
• Read homework exercise 26 on page 524 in the
  text. To solve, we need to take the total sales
  for Crest toothpaste and divide it by the total
  sales of all toothpastes. Crests total sales
  was 370 million, and the total sales of all
  toothpaste was 1.5 billion or 1500 million.
  (We need to change total sales for all
  toothpastes to millions so the two sales will
  share the same unit.)

17

• Basic Percent Example
• Percent
• Read homework exercise 26 on page 524 in the
  text. To solve, we need to take the total sales
  for Crest toothpaste and divide it by the total
  sales of all toothpastes. Crests total sales
  was 370 million, and the total sales of all
  toothpaste was 1.5 billion or 1500 million.
  (We need to change total sales for all
  toothpastes to millions so the two sales will
  share the same unit.)
• Thus we calculate 370 / 1500 0.2466 24.7.

18

• Another Basic Percent Example
• Read homework exercise 28 on page 524 in the
  text. Here we are given the percent of children,
  and the total number of the children.

19

• Another Basic Percent Example
• Read homework exercise 28 on page 524 in the
  text. Here we are given the percent of children,
  and the total number of the children.
• Percent x Total Part, thus we change 18.6 into
  a decimal which would be 0.186, and we multiply
  this by the total number of children, which is
  10,398,000.
• 0.186 x 10398000 1,934,028

20

• Another Basic Percent Example
• Read homework exercise 28 on page 524 in the
  text. Here we are given the percent of children,
  and the total number of the children.
• Percent x Total Part, thus we change 18.6 into
  a decimal which would be 0.186, and we multiply
  this by the total number of children, which is
  10,398,000.
• 0.186 x 10398000 1,934,028
• Thus, in 1999, 1,934,028 children were cared for
  by their fathers while their mothers were at work.

21

• Percent Change
• The percent increase or decrease over a period of
  time is called percent change.
• The formula for percent change is found in a
  yellow box in the middle of page 520 in the text.
• This is a very useful formula and it will be used
  most often when completing your homework
  exercises. Study Example 6 on page 520, in the
  text, to see how to use this useful formula.

22

• Percent Change Example
• Here is another percent change example
• Read homework exercise 40 on page 525 in the
  text. Here we are given a graph and are asked to
  find percent increases and decreases.
• 40(a). To find the percent increase in the
  number of beds form 1966 to 1976, use the percent
  change formula.
• Percent change
• Which gives us a 0.5 increase in hospital beds.

23

• Percent Change Example
• Look at exercise 40(b). Find the percent
  decrease in the number of beds from 1976 to 1986.
  We solve this the same way as the other example.
  Expect to find a negative value for the answer
  since the question is asking for the percent
  decrease.
• Percent change
• Which gives us a 4.4 decrease in hospital beds
  from 1976 to 1986.

24

• Percent Markup on Cost
• Another formula given in the text is a formula
  for percent markup on cost. This can be found in
  a yellow box, in the middle of page 521.
• In form, it is very similar to the percent change
  equation. Study Example 8 on page 521 in the
  text. Make sure you can follow this example and
  can use the formula correctly.

25

• A Tricky Example?
• Read homework example 50 on page 526 in the text.
  We are looking for the original number of
  crewmembers.

26

• A Tricky Example?
• Read homework example 50 on page 526 in the text.
  We are looking for the original number of
  crewmembers.
• Let x the original number of crewmembers
• Let x 10 be the current number of crewmembers.
• Now use the percent change equation

,
,
,
27

• Three Basic Percent Equations
• A basic percent question can be asked three
  different ways.
• 1. What is 18 of 300?
• 2. What percent of 300 is 54?
• 3. 54 is 18 of what number?

28

• Three Basic Percent Equations
• A basic percent question can be asked three
  different ways.
• 1. What is 18 of 300?
• 2. What percent of 300 is 54?
• 3. 54 is 18 of what number?
• These problems can be solved easily by writing a
  simple equation from the words of the question.
  Remember that is means , and of means
  multiply. Also remember to write the percent as
  a decimal.

29

• Three Basic Percent Equations
• 1. What is 18 of 300?
• Rewrite the statement into an equation.

30

• Three Basic Percent Equations
• 1. What is 18 of 300?
• Rewrite the statement into an equation.

,
31

• Three Basic Percent Equations
• 1. What is 18 of 300?
• Rewrite the statement into an equation.
• 2. What percent of 300 is 54?

,
32

• Three Basic Percent Equations
• 1. What is 18 of 300?
• Rewrite the statement into an equation.
• 2. What percent of 300 is 54?

,
,
33

• Three Basic Percent Equations
• 1. What is 18 of 300?
• Rewrite the statement into an equation.
• 2. What percent of 300 is 54?
• 3. 54 is 18 of what number?

,
,
34

• Three Basic Percent Equations
• 1. What is 18 of 300?
• Rewrite the statement into an equation.
• 2. What percent of 300 is 54?
• 3. 54 is 18 of what number?

,
,
,
35

• Percent Problems
• With the percent change formula and the three
  percent equations, you can solve the homework
  exercises for this section.
• Find an large index card and write the percent
  formulas for this section on it. By the formula,
  write the page number in the text where it can be
  found. Each section in this chapter will have a
  few percent equations. Use this card when you do
  the homework examples. You will be allowed to
  use it on your chapter test too!

36

• Section 11.2 Personal Loans and Simple Interest
• This section is about money and how we spend and
  save it. When you understand what the actual
  cost of an item is, then you can determine if you
  really want to buy it right now. Determining the
  actual cost will also help you decide how you are
  going to pay for the item.

37

• Definitions
• The money a bank is willing to lend you is called
  the amount of credit extended or the principal of
  the loan.
• Security or collateral is anything of value that
  can be pledged by the borrower that the lender
  may keep if the borrower does not pay back the
  loan. If you do not have collateral, a bank may
  ask that you find a cosigner for the loan.
• A cosigner is a person who agrees to pay off the
  loan if you fail to pay it off.

38

• Definitions
• Types of loans discussed in this text
• 1. Secured loan a loan with collateral
• 2. Cosigner loan a loan with a cosigner
• 3. Installment loan (which is discussed in
  Section 11.4)
• What does it cost us to borrow money? Interest
  is the money that we pay the lender for the use
  of their money. Simple interest is based on the
  entire amount of the loan for the total period of
  time.

39

• Simple Interest

The variables Simple interest i p is the
principal, or amount of the loan r is the rate of
the loan expressed as a percent t is the number
of days, months, or years which the money is lent
40

• Simple Interest
• The most common type of simple interest is
  ordinary interest. For calculating ordinary
  interest, there are 12 months with 30 days each,
  and 360 days per year.
• Two types of notes with ordinary interest
• Simple interest note is a note in which the
  interest and the principal are due at the date of
  maturity.
• Discount note is a note in which the interest is
  paid at the time the borrower receives the loan.
  This interest is called the bank discount.

41

• Simple Interest Examples
• Study Examples 1, 2, 3, on pages 528 and 529 in
  the text. Notice how the simple interest formula
  is used to find the unknown in each case.
• These are pretty straight forward examples,
  nothing out of the ordinary.

42

• Simple Interest Examples
• Read homework exercise 18 on page 534 in the
  text. This one is a little out of the ordinary.
  Look at the interest rate. It is 0.055 per day.
  To solve this problem, we first need to
  calculate the yearly interest rate.

43

• Simple Interest Examples
• Read homework exercise 18 on page 534 in the
  text. This one is a little out of the ordinary.
  Look at the interest rate. It is 0.055 per day.
  To solve this problem, we first need to
  calculate the yearly interest rate.
• Calculate 0.055 x 360 (days per year) 19.8
• So the annual interest rate is 19.8. Now we can
  use our simple interest formula

44

• Simple Interest Examples
• Read homework exercise 20 on page 534 in the
  text. We are supposed to use the simple interest
  formula to find the missing value.

45

• Simple Interest Examples
• Read homework exercise 20 on page 534 in the
  text. We are supposed to use the simple interest
  formula to find the missing value.
• Calculate the principal of the loan

,
,
The principal of the loan is 600.00.
46

• Bank Discount Note Example
• Read homework exercise 28 on page 535 in the
  text. This is an example involving a discounted
  loan. Remember with this type of loan, the
  interest is paid at the time the borrower
  receives the loan. Basically, you calculate the
  interest, and subtract it from the principal to
  find out how much the person actually received
  from the bank.

47

• Discount Note Example
• Homework exercise 28 page 535
• Part (a) How much interest did he pay the bank?
• To solve this use the simple interest formula.

48

• Discount Note Example
• Homework exercise 28 page 535
• Part (a) How much interest did he pay the bank?
• To solve this use the simple interest formula.

49

• Discount Note Example
• Homework exercise 28 page 535
• Part (a) How much interest did he pay the bank?
• To solve this use the simple interest formula.

(b) What did he receive from the bank?
50

• Discount Note Example
• Homework exercise 28 page 535
• Part (a) How much interest did he pay the bank?
• To solve this use the simple interest formula.

(b) What did he receive from the bank?
51

• Discount Note Example
• Homework exercise 28 page 535
• Part (c) What was the actual rate of interest
  paid? Since he only received 2416.67 from the
  bank (not the whole 2500), the interest rate is
  actually a little higher than 8. Use the simple
  interest formula, and use 2416.67 as the
  principal. Find the rate.

,
,
So, the actual rate of interest is ? 8.3.
52

• Discount Note Example
• Study Example 4 on page 530 in the text. This is
  another example involving a discount note.
  Notice how, once again, the actual interest rate
  is a little higher than the interest rate.

53

• United States Rule
• A loan has a date of maturity, at which time the
  principal and the interest are due. A person can
  make payments on a loan before the date of
  maturity. The Supreme Court specified a method
  by which these early payments are credited to the
  loan. The procedure that is followed for
  crediting these early payments is called the
  United States Rule.

54

• United States Rule
• The United States rule states that if a partial
  payment is made on a loan, interest is computed
  on the principal from the first day of the loan
  to the date of the partial (early) payment. This
  payment is used to pay off the interest first,
  and then the rest of the payment goes towards the
  principal of the loan.
• If another partial payment is made, the interest
  is calculated from the date of the previous
  partial payment. Once again the payment is used
  to pay off the interest first, then the rest goes
  towards the principal.

55

• United States Rule
• This procedure is repeated for each partial
  payment. The balance due at the date of maturity
  is found by calculating the interest due since
  the last partial payment and adding this interest
  to the unpaid principal.
• Since the partial payments are used to lower the
  principal of the loan during the period of the
  loan, the total amount of interest paid over the
  period of the loan is lowered.

56

• United States Rule
• The Bankers Rule is used to calculate simple
  interest when applying the United States rule.
• The Bankers rule considers a year to have 360
  days, and any fractional part of a year is the
  exact number of days of the loan.
• To determine the exact number of days of a loan,
  we use a table.

57

• Exact Number of Days
• Look at Table 11.1 on page 532 in the text. This
  table is used to find the exact number of days of
  a period, it can also be used to determine the
  due date of a loan.
• Notice the table has a column for each month, and
  a row for each day of the month. The number
  located at the intersection of the month and the
  date is the number of the day in the year. For
  example, May 15th is the 135th day of the year
  (look down the May column, until you find Day
  15).

58

• Exact Time Examples
• 1. Find the exact time from May 19th to
  September 17th.

59

• Exact Time Examples
• 1. Find the exact time from May 19th to
  September 17th.
• September 17th is day 260.
• May 19th is day 139.
• Subtract the two values 260 139 121 days.

60

• Exact Time Examples
• 1. Find the exact time from May 19th to
  September 17th.
• September 17th is day 260.
• May 19th is day 139.
• Subtract the two values 260 139 121 days.
• 2. Find the exact time from December 21st to
  April 28th.

61

• Exact Time Examples
• 1. Find the exact time from May 19th to
  September 17th.
• September 17th is day 260.
• May 19th is day 139.
• Subtract the two values 260 139 121 days.
• 2. Find the exact time from December 21st to
  April 28th.
• December 21st is day 355, April 28th is day 118.
• (365 355) 118 10 118 128 days.

62

• Exact Time Examples
• 1. Find the exact time from May 19th to
  September 17th.
• September 17th is day 260.
• May 19th is day 139.
• Subtract the two values 260 139 121 days.
• 2. Find the exact time from December 21st to
  April 28th.
• December 21st is day 355, April 28th is day 118.
• (365 355) 118 10 118 128 days.
• Notice we used 365 355. Do you know why?

63

• Exact Time Examples
• 3. Determine the due date of a 120 day loan that
  is made on June 8th.

64

• Exact Time Examples
• 3. Determine the due date of a 120 day loan that
  is made on June 8th.
• June 8th is day 159.
• 159 120 279.

65

• Exact Time Examples
• 3. Determine the due date of a 120 day loan that
  is made on June 8th.
• June 8th is day 159.
• 159 120 279.
• Look up day 279 in the body of the table.
• Day 279 is October 6th, so the loan is due on
  October 6th.

66

• Exact Time Examples
• 3. Determine the due date of a 120 day loan that
  is made on June 8th.
• June 8th is day 159.
• 159 120 279.
• Look up day 279 in the body of the table.
• Day 279 is October 6th, so the loan is due on
  October 6th.
• Example 6 on page 531 and 532 also uses the table
  to find exact time and the due date of a loan.
  Read this example for more information on these
  topics.

67

• Using the United States Rule
• Carefully study Example 8 on page 533 in the
  text. This example relates to partial payments,
  due dates of loans, and using the United States
  Rule. Note that in part (b) they subtract from
  365 since the due date extends into another year.
  Also note that when using the interest formula,
  we are dividing the number of days of the loan by
  360.
• This example is quite involved, but be forewarned
  that there is one of these assigned in the
  homework exercises.

68

• Remember
• Remember to write the Simple Interest Formula on
  your index card. You will want that formula
  handy for your homework and test.
• Note The formula is found on page 528.

69

• Section 11.3 Compound Interest
• This section covers the compound interest
  formula. This formula is used to calculate the
  value of an investment. A form of this formula
  is also used when working with present value.

70

• Investments
• An investment is the use of money or capital for
  income or profit. There are two classes of
  investments fixed and variable.
• Fixed investment the amount invested as
  principal is guaranteed, and interest is computed
  at a fixed rate. The exact amount invested and
  the accumulated interest will be paid back to the
  investor.
• Examples of fixed investments are savings
  accounts and certificates of deposit.

71

• Investments
• Variable investment the amount invested (the
  principal) nor the interest is guaranteed.
• Examples of variable investments are stocks and
  mutual funds.

72

• Background
• Earlier we studied simple interest, where the
  interest is calculated once for the period of the
  loan. This is not the way banks calculate
  interest. Banks calculate the interest
  periodically (i.e., monthly, daily). This
  interest is then added to the original principal.
  The next time interest is calculated, it is
  calculated on the new principal (which is the
  original principal plus the interest). This type
  of interest is called compound interest.

73

• Compound Interest
• Read Example 1 on page 537 and 538 in the text.
  Notice that they use the simple interest formula
  four times since the interest is compounded
  quarterly. Each time the interest is calculated,
  it is added to the principal. Thus, the
  principal goes up every time, and the amount of
  interest goes up every time.

74

• Compound Interest
• Read Example 1 on page 537 and 538 in the text.
  Notice that they use the simple interest formula
  four times since the interest is compounded
  quarterly. Each time the interest is calculated,
  it is added to the principal. Thus, the
  principal goes up every time, and the amount of
  interest goes up every time.
• What if we would have wanted to know the amount
  the 1000 would grow in 4 years?
• We would have had to do that calculation 4x416
  times! There must be an easier way.

75

• Compound Interest Formula
• There is. Instead of computing with the simple
  interest formula 16 times, we use the
• compound interest formula.

A amount p principal n number of periods
per year t number of years r annual interest
rate
76

• Compound Interest Example
• Use the compound interest formula to find the
  total amount and the interest earned on an
  investment of 3000 for 2 years at 6.25
  compounded monthly.

77

• Compound Interest Example
• Use the compound interest formula to find the
  total amount and the interest earned on an
  investment of 3000 for 2 years at 6.25
  compounded monthly.

78

• Compound Interest Example
• Use the compound interest formula to find the
  total amount and the interest earned on an
  investment of 3000 for 2 years at 6.25
  compounded monthly.

79

• Compound Interest Example
• Use the compound interest formula to find the
  total amount and the interest earned on an
  investment of 3000 for 2 years at 6.25
  compounded monthly.

So the total amount is 3398.34, and the interest
earned is 398.34.
80

• Compound Interest
• Study Example 3 on page 539 in the text. This is
  another example of compound interest. Note that
  this is compounded semi-annually, so n 2.

81

• Effective Annual Yield
• The effective annual yield ( or effective yield)
  is a percent that is calculated by substituting
  p 1 in the compound interest formula and
  then subtracting 1 from the amount.
• Look below Example 3 on page 539 in the text.
  This shows how to find the effective annual yield
  using the interest information stated in Example
  3. Note that the effective annual yield is 8.16
  which is actually higher than the 8 interest
  rate given in the example.

82

• Effective Annual Yield - Example
• Determine the effective annual yield for 1
  invested for 1 year at 6.5 compounded quarterly.

83

• Effective Annual Yield - Example
• Determine the effective annual yield for 1
  invested for 1 year at 6.5 compounded quarterly.
• Use the compound interest formula

84

• Effective Annual Yield - Example
• Determine the effective annual yield for 1
  invested for 1 year at 6.5 compounded quarterly.
• Use the compound interest formula

85

• Effective Annual Yield - Example
• Determine the effective annual yield for 1
  invested for 1 year at 6.5 compounded quarterly.
• Use the compound interest formula

So the effective annual yield is 6.66.
86

• Effective Annual Yield
• Example 4 on page 540 in the text is another
  example of determining the effective annual
  yield.
• One more thing to note when a bank compounds
  interest daily, use 360 for the number of periods
  in a year, when computing the effective annual
  yield.

87

• Present Value
• People often wonder what amount of money they
  would need to deposit today to have enough money
  for their children to go to college at some date
  in the future. For example, how much must you
  deposit in an account today at a given rate of
  interest so it will accumulate to 25,000 to pay
  your childs college costs in 4 years.
• The principal, p, that would have to be invested
  now is called the present value.

88

• Present Value
• Present Value Formula

p the principal that would have to be invested
now A amount needed at the end of specified
number of years n number of periods per year t
number of years r annual interest rate
89

• Present Value
• Present Value Formula

p the principal that would have to be invested
now A amount needed at the end of specified
number of years n number of periods per year t
number of years r annual interest rate
Notice that this formula is a variation of the
compound interest formula.
90

• Present Value - Example
• Read homework exercise 20 on page 542 in the
  text, saving for a tractor.

91

• Present Value - Example
• Read homework exercise 20 on page 542 in the
  text, saving for a tractor.
• We need to use the present value formula

92

• Present Value - Example
• Read homework exercise 20 on page 542 in the
  text, saving for a tractor.
• We need to use the present value formula

93

• Present Value - Example
• Read homework exercise 20 on page 542 in the
  text, saving for a tractor.
• We need to use the present value formula

94

• Present Value - Example
• Read homework exercise 20 on page 542 in the
  text, saving for a tractor.
• We need to use the present value formula

He needs to invest 23,202.23 now in the
specified CD.
95

• Present Value
• Example 5 on page 541 in the text is another
  example of present value. Observe how the
  different values are substituted into the present
  value formula. Work through the calculations
  with your calculator to see if you can come up
  with the same answer.
• Do not forget to write the compound interest
  formula (page 538) and the present value formula
  (page 541) on your index card.

96

• Section 11.4 Installment Buying
• This section covers installment loans, which are
  loans that the borrower makes payments on a
  weekly or monthly basis. In certain instances,
  these loans can be more convenient than paying
  off the entire loan at the end of the specified
  time period.

97

• Installment Loans
• There are two types of installment loans fixed
  installment loans and open-end installment loans.
• Fixed installment loans are loans in which you
  pay a fixed amount of money for a set amount of
  payments (normally, monthly payments). Example
  College loans car loans
• Open-end installment loans are loans in which the
  borrower makes variable payments each month.
  Example Credit cards

98

• Important Definitions
• APR (annual percentage rate) is the true rate of
  interest charged for a loan. The text uses
  tables to determine APR.
• The total installment price is the sum of all the
  monthly payments and any down payment.
• A Finance charge is the total amount of money the
  borrower must pay for its use. This could be
  interest, service charges, etc. The finance
  charge can be calculated by subtracting the total
  installment price and the cash price.

99

• APR Table
• Look at Table 11.2 on page 546 in the text. This
  table lists the annual percentage rates for
  monthly payment plans. The column headings are
  different annual percentage rates, the rows are
  the number of payments, and the cells of the
  table are the finance charges per 100 of amount
  financed.
• Study Examples 1 2 on pages 546 and 547 in the
  text. These examples will help clarify how to
  use the table properly. Notice in Example 2 (b)
  the amount financed is 3000, not 3600.
• Do you know why?

100

• Fixed Installment Loan Example
• Read homework exercise 12 on page 554 in the text
  Financing Eye Surgery.

101

• Fixed Installment Loan Example
• Read homework exercise 12 on page 554 in the text
  Financing Eye Surgery.
• (a) Determine the total finance charge.

102

• Fixed Installment Loan Example
• Read homework exercise 12 on page 554 in the text
  Financing Eye Surgery.
• (a) Determine the total finance charge. First
  we need to look up the finance charge per 100 in
  Table 11.2 on page 546. Follow the row for 48
  payments and the column for 9.5 until they
  intersect. They intersect at 20.59.

103

• Fixed Installment Loan Example
• Read homework exercise 12 on page 554 in the text
  Financing Eye Surgery.
• (a) Determine the total finance charge. First
  we need to look up the finance charge per 100 in
  Table 11.2 on page 546. Follow the row for 48
  payments and the column for 9.5 until they
  intersect. They intersect at 20.59.
• So our calculation is

The total finance charge is 864.78.
104

• Fixed Example Continued
• (b) Determine Tigers monthly payment.

105

• Fixed Example Continued
• (b) Determine Tigers monthly payment.
• We need to find the total installment price
• 4200 864.78 5064.78

106

• Fixed Example Continued
• (b) Determine Tigers monthly payment.
• We need to find the total installment price
• 4200 864.78 5064.78
• Then we need to divide this by 48 monthly
  payments

So each of his monthly payments is 105.52.
107

• Fixed Example with a Down Payment
• Read homework exercise 14 on page 554 in the text
  Financing a Computer.

108

• Fixed Example with a Down Payment
• Read homework exercise 14 on page 554 in the text
  Financing a Computer.
• (a) Determine the total finance charge.

109

• Fixed Example with a Down Payment
• Read homework exercise 14 on page 554 in the text
  Financing a Computer.
• (a) Determine the total finance charge.
• First find the total installment price.

110

• Fixed Example with a Down Payment
• Read homework exercise 14 on page 554 in the text
  Financing a Computer.
• (a) Determine the total finance charge.
• First find the total installment price.
• 24 payments x 85.79 2058.96.

111

• Fixed Example with a Down Payment
• Read homework exercise 14 on page 554 in the text
  Financing a Computer.
• (a) Determine the total finance charge.
• First find the total installment price.
• 24 payments x 85.79 2058.96.
• Next find the amount financed.

112

• Fixed Example with a Down Payment
• Read homework exercise 14 on page 554 in the text
  Financing a Computer.
• (a) Determine the total finance charge.
• First find the total installment price.
• 24 payments x 85.79 2058.96.
• Next find the amount financed.
• 2350 - 500 (down payment) 1850.

113

• Fixed Example with a Down Payment
• Read homework exercise 14 on page 554 in the text
  Financing a Computer.
• (a) Determine the total finance charge.
• First find the total installment price.
• 24 payments x 85.79 2058.96.
• Next find the amount financed.
• 2350 - 500 (down payment) 1850.
• So the total finance charge is

114

• Down Payment Example - Continued
• (b) What is the APR to the nearest half a
  percent?

115

• Down Payment Example - Continued
• (b) What is the APR to the nearest half a
  percent?

116

• Down Payment Example - Continued
• (b) What is the APR to the nearest half a
  percent?

11.30 is the finance charge per 100 of amount
financed. Follow the 24 payments row until you
find 11.30 in one of the table cells. This lies
in the 10.5 column.
117

• Down Payment Example - Continued
• (b) What is the APR to the nearest half a
  percent?

11.30 is the finance charge per 100 of amount
financed. Follow the 24 payments row until you
find 11.30 in one of the table cells. This lies
in the 10.5 column. Thus, the APR is 10.5.
118

• Early Pay Off
• There are two methods to find the finance charge
  if an installment loan is paid off early. They
  are the Actuarial method and the Rule of 78s.
  You should read through the examples that cover
  these methods (Examples 4 5 on pages 548 and
  549). These two methods are interesting to know,
  but you will not be tested on them.

119

• Open-End Installment Loan
• Remember that an open-end installment loan is
  something most people are already familiar with
  it is a typical credit card/charge account.
• Read about credit card statements on page 550 in
  the text. Note that the minimum monthly payment
  is oftentimes determined by dividing the balance
  due by 36 months and rounding the answer up to
  the nearest whole dollar. This ensures repayment
  within 36 months. If the balance due for a month
  is less than 360, the monthly payment is
  typically 10.

120

• Credit Card Examples
• Study Example 6 on page 550 in the text. It
  covers determining the minimum payment on a
  credit card, and determining the balance due.

121

• Another Credit Card Example
• Read homework exercise 26 on page 556 in the text
  College Expenses.

122

• Another Credit Card Example
• Read homework exercise 26 on page 556 in the text
  College Expenses.
• (a) What is the minimum payment due September
  1st?

123

• Another Credit Card Example
• Read homework exercise 26 on page 556 in the text
  College Expenses.
• (a) What is the minimum payment due September
  1st?
• To find the minimum payment due, we need to find
  the balance due on September 1st and divide the
  answer by 36.

124

• Another Credit Card Example
• Read homework exercise 26 on page 556 in the text
  College Expenses.
• (a) What is the minimum payment due September
  1st?
• To find the minimum payment due, we need to find
  the balance due on September 1st and divide the
  answer by 36.
• 425 175 450 125 1175

125

• Another Credit Card Example
• Read homework exercise 26 on page 556 in the text
  College Expenses.
• (a) What is the minimum payment due September
  1st?
• To find the minimum payment due, we need to find
  the balance due on September 1st and divide the
  answer by 36.
• 425 175 450 125 1175

Which we round up to the nearest dollar to get a
minimum payment of 33.00.
126

• Credit Card Example - Continued
• (b) What is the balance due on October 1st?

127

• Credit Card Example - Continued
• (b) What is the balance due on October 1st?
• With no more purchases and a payment of 650, the
  balance on October 1st is
• 1175-650525.
• But interest must also be added

128

• Credit Card Example - Continued
• (b) What is the balance due on October 1st?
• With no more purchases and a payment of 650, the
  balance on October 1st is
• 1175-650525.
• But interest must also be added
• 525 x 0.012 6.30 in interest.
• 525 6.30 531.30
• So 531.30 is the balance on October 1st.

129

• Calculating Finance Charges
• In the past example and Example 6 in the text,
  there were no additional charges for the period.
  When there are additional charges during the
  period, the finance charges are calculated by
  either the unpaid balance method, or the average
  daily balance method.

130

• Unpaid Balance Method
• Following the unpaid balance method, the borrower
  is charged interest (finance charge) on the
  unpaid balance from the previous charge period.
  The finance charge is calculated using the simple
  interest formula ( i prt ) with a time of one
  month on the financed amount.
• Study Example 7 on page 551 in the text. This
  example demonstrates the use of the unpaid
  balance method.

131

• Unpaid Balance Method Example
• Read homework exercise 30 on page 556 in the
  text.

132

• Unpaid Balance Method Example
• Read homework exercise 30 on page 556 in the
  text.
• (a) Find the finance charge on October 5th
  assuming the interest rate is 1.40 per month.

133

• Unpaid Balance Method Example
• Read homework exercise 30 on page 556 in the
  text.
• (a) Find the finance charge on October 5th
  assuming the interest rate is 1.40 per month.
• The finance charge is based on the balance due
  which was 385.75, so we calculate

134

• Unpaid Balance Method Example
• Read homework exercise 30 on page 556 in the
  text.
• (a) Find the finance charge on October 5th
  assuming the interest rate is 1.40 per month.
• The finance charge is based on the balance due
  which was 385.75, so we calculate
• 385.75 x 0.0140 5.40

135

• Unpaid Balance Method Example
• Read homework exercise 30 on page 556 in the
  text.
• (a) Find the finance charge on October 5th
  assuming the interest rate is 1.40 per month.
• The finance charge is based on the balance due
  which was 385.75, so we calculate
• 385.75 x 0.0140 5.40
• Thus, the finance charge on October 5th is 5.40.

136

• Unpaid Balance Method - Continued
• (b) Find the new balance on October 5th.

137

• Unpaid Balance Method - Continued
• Find the new balance on October 5th.
• We need to take the balance due on September 5th,
  and add to it any additional purchases and
  finance charges, and subtract any payments or
  credits.

138

• Unpaid Balance Method - Continued
• Find the new balance on October 5th.
• We need to take the balance due on September 5th,
  and add to it any additional purchases and
  finance charges, and subtract any payments or
  credits.
• 385.75 330 190.80 84.75 5.40 275
  721.70.

139

• Unpaid Balance Method - Continued
• Find the new balance on October 5th.
• We need to take the balance due on September 5th,
  and add to it any additional purchases and
  finance charges, and subtract any payments or
  credits.
• 385.75 330 190.80 84.75 5.40 275
  721.70.
• Thus, the new balance on October 5th is 721.70.

140

• Average Daily Balance Method
• What if you bought a lot of expensive items at
  the end of your billing period. Should your
  finance charge be based on the higher amount,
  even though you were not using that money for
  the entire billing period?
• Some lending institutions use the average daily
  balance method because it seems to be fairer to
  the customers. The calculations are longer than
  the unpaid balance method, but they are important
  to understand.

141

• Average Daily Balance Method
• Study Example 8 on page 551 and 552 in the text.
  It shows how to determine charges using the
  average daily balance method. Pay close
  attention to how the number of days the balance
  did not change is calculated.
• The following slide shows another example of the
  average daily balance method.

142

• Average Daily Balance Method
• Lets solve homework exercise 30 on page 556 in
  the text. This time, use the average daily
  balance method.

143

• Average Daily Balance Method
• Lets solve homework exercise 30 on page 556 in
  the text. This time, use the average daily
  balance method.
• We need to make a table which includes important
  dates, balance due, and days balance did not
  change.

144

• Average Daily Balance Method

First write in the dates and the balance due.
145

• Average Daily Balance Method

146

• Average Daily Balance Method

Balance due goes down because of 275.00 payment.
147

• Average Daily Balance Method

Balance due goes up because of 330.00 purchase.
148

• Average Daily Balance Method

Balance due goes up because of 190.80 purchase.
149

• Average Daily Balance Method

Balance due goes up because of 84.75 purchase.
150

• Average Daily Balance Method

Now calculate the days balance unchanged.
151

• Average Daily Balance Method

From Sept 5 to Sept 8.
152

• Average Daily Balance Method

From Sept 8 to Sept 21.
153

• Average Daily Balance Method

From Sept 21 to Sept 27.
154

• Average Daily Balance Method

From Sept 27 to Oct 2.
155

• Average Daily Balance Method

From Oct 2 to end of billing Oct 5.
156

• Average Daily Balance Method

Now multiply each balance due by its days balance
unchanged, find the sum, and divide by 30 days.
157

• Average Daily Balance Method

158

• Average Daily Balance Method

So, the average daily balance was 351.61.
159

• Average Daily Balance Method
• (b) Find the finance charge to be paid on
  October 5th.

160

• Average Daily Balance Method
• (b) Find the finance charge to be paid on
  October 5th.
• Use the average daily balance in the simple
  interest formula using t 1 month, and the given
  interest rate.

161

• Average Daily Balance Method
• (b) Find the finance charge to be paid on
  October 5th.
• Use the average daily balance in the simple
  interest formula using t 1 month, and the given
  interest rate.

162

• Average Daily Balance Method
• (c) Find the balance due on October 5th.

163

• Average Daily Balance Method
• (c) Find the balance due on October 5th.
• Take the balance due on October 2nd (from the
  table), and add the finance charge.

164

• Average Daily Balance Method
• (c) Find the balance due on October 5th.
• Take the balance due on October 2nd (from the
  table), and add the finance charge.
• 716.30 4.92 721.22

165

• Comparison of Methods
• Compare this answer - 721.22 using the average
  daily balance method to the 721.70 found using
  the unpaid balance method (slide 139).
• The balance due using the average daily balance
  method was 48 cents lower.

166

• Examples 9 10
• We will not be covering cash advances and
  comparing loan sources Examples 9 10 on pages
  552 and 553 in the text. You will not be tested
  on these types of problems.

167

• Section 11.5 Buying a House with a Mortgage
• Most likely, at some point, everyone will
  purchase a house. It is possibly the largest
  purchase we will ever make. This section covers
  mortgages, interest, and how much house can a
  person really afford?

168

• Definitions
• The down payment is the amount of cash the buyer
  must pay to the lending institution before the
  lender will grant the mortgage.
• A homeowners mortgage is a long term loan in
  which the property is pledged as security for
  payment of the difference between the down
  payment and the sales price.
• The two most popular mortgage loans are the
  conventional loan and the adjustable (variable)
  rate loan.

169

• Definitions
• A conventional loan is a loan in which the
  interest rate is fixed for the duration of the
  loan.
• An adjustable-rate loan (also called a
  variable-rate loan) is a loan in which the
  interest may change every period, as specified in
  the loan.
• Most lending institutions require buyers to pay
  points. One point amounts to 1 of the amount
  being borrowed. Points are paid at the time of
  closing.

170

• Down Payment and Points Example
• Study Example 1 on page 559 in the text. Notice
  that the cost of a point (1), is based on the
  amount of the mortgage, not the selling price of
  the house.
• In this case, the amount of the mortgage was the
  selling price less the amount of the down
  payment.
• Also notice that the amount of the point is
  paid to the bank.

171

• Another Example
• Read homework exercise 14 on page 567.

172

• Another Example
• Read homework exercise 14 on page 567.
• (a) What is the required down payment?

173

• Another Example
• Read homework exercise 14 on page 567.
• (a) What is the required down payment?
• Multiply the selling price by the down payment
  percent

174

• Another Example
• Read homework exercise 14 on page 567.
• (a) What is the required down payment?
• Multiply the selling price by the down payment
  percent

So, the down payment is 9750.00
175

• Another Example
• Read homework exercise 14 on page 567.
• (b) With the down payment, what is the amount of
  the mortgage?

176

• Another Example
• Read homework exercise 14 on page 567.
• (b) With the down payment, what is the amount of
  the mortgage?
• Take the selling price and subtract the down
  payment

177

• Another Example
• Read homework exercise 14 on page 567.
• (b) With the down payment, what is the amount of
  the mortgage?
• Take the selling price and subtract the down
  payment

Thus, the amount of the mortgage is 55,250.00
178

• Another Example
• Read homework exercise 14 on page 567.
• (c) What is the cost of 2 points on the mortgage?

179

• Another Example
• Read homework exercise 14 on page 567.
• (c) What is the cost of 2 points on the
  mortgage?
• Take the amount of the mortgage and multiply by
  2

180

• Another Example
• Read homework exercise 14 on page 567.
• (c) What is the cost of 2 points on the
  mortgage?
• Take the amount of the mortgage and multiply by
  2

So, the cost of 2 points is 1105.00
181

• Another Example
• Read homework exercise 12 on page 566.
• (a) Determine the amount of the required down
  payment.

182

• Another Example
• Read homework exercise 12 on page 566.
• (a) Determine the amount of the required down
  payment.
• This is similar to the last example

183

• Another Example
• Read homework exercise 12 on page 566.
• (a) Determine the amount of the required down
  payment.
• This is similar to the last example

So, the required down payment is 19,400.00
184

• Another Example
• Read homework exercise 12 on page 566.
• (b) Determine the monthly mortgage payment for a
  30 year loan with the down payment calculated in
  the last example.

185

• Another Example
• Read homework exercise 12 on page 566.
• (b) Determine the monthly mortgage payment for a
  30 year loan with the down payment calculated in
  the last example.
• 30 years at 8.5. Look at Table 11.4 on page 561
  in the text.

186

• Another Example
• Read homework exercise 12 on page 566.
• (b) Determine the monthly mortgage payment for a
  30 year loan with the down payment calculated in
  the last example.
• 30 years at 8.5. Look at Table 11.4 on page 561
  in the text. 30 years and 8.5 intersect at
  7.69, the monthly payment per 1000 of mortgage.

187

• Another Example
• Read homework exercise 12 on page 566.
• (b) Determine the monthly mortgage payment for a
  30 year loan with the down payment calculated in
  the last example.
• 30 years at 8.5. Look at Table 11.4 on page 561
  in the text. 30 years and 8.5 intersect at
  7.69, the monthly payment per 1000 of mortgage.

77600 is the amount of the mortgage, and 596.74
is the monthly payment.
188

• Ability to Pay?
• Lending institutions decide how much they believe
  the purchaser can pay a month for their mortgage
  payment. If the mortgage is too high, then the
  lender will not agree to the mortgage.
• A mortgage loan officer calculates the buyers
  adjusted monthly income (which is their gross
  income less any monthly payments with more than
  10 payments remaining). Though this varies by
  location, most lending institutions will allow
  somewhere around 28 of the buyers adjusted
  monthly income.

189

• Ability to Pay?
• The 28 of the adjusted monthly income must be
  more than the sum of the principal, interest,
  property taxes and insurance.
• Study Example 2 on page 560 in the text. It show
  how a bank determines whether a prospective buyer
  qualifies for a mortgage. Notice how the
  adjusted monthly income is calculated (gross
  income less car and appliance loan payments).

190

• Total Cost of a House
• Study Example 3 on page 561 in the text. It
  covers how to calculate the total amount a person
  actually pays for the 85000 house. It also
  covers how much of the cost is interest, and how
  much of the first payment is interest.
• Are you surprised just how much of the cost is
  interest? Table 11.5 is an amortization
  schedule. These schedules are typically
  generated by computers. They contain information
  on the payment number, payment on interest,
  payment on principal, and balance of the loan.
  Interesting!

191

• How Much?
• Read homework exercise 18 on page 567.
• (a) Determine the total amount paid for the
  house.

192

• How Much?
• Read homework exercise 18 on page 567.
• (a) Determine the total amount paid for the
  house.
• First find the down payment

193

• How Much?
• Read homework exercise 18 on page 567.
• (a) Determine the total amount paid for the
  house.
• First find the down payment

Then find the total of the monthly payments and
add the down payment.
194

• How Much?
• Read homework exercise 18 on page 567.
• (a) Determine the total amount paid for the
  house.
• First find the down payment

Then find the total of the monthly payments and
add the down payment.
187,736.40 for a 75,000 house.
195

• How Much?
• Read homework exercise 18 on page 567.
• (b) How much of the cost will be interest?

196

• How Much?
• Read homework exercise 18 on page 567.
• (b) How much of the cost will be interest?
• Subtract the purchase price and any points from
  the total cost.

197

• How Much?
• Read homework exercise 18 on page 567.
• (b) How much of the cost will be interest?
• Subtract the purchase price and any points from
  the total cost.

Notice that this example did not include any
points.
198

• How Much?
• Read homework exercise 18 on page 567.
• (c) How much of the first payment on the
  mortgage is applied to the principal?

199

• How Much?
• Read homework exercise 18 on page 567.
• (c) How much of the first payment on the
  mortgage is applied to the principal?
• Use the simple interest formula to find the
  interest on the first payment. Then subtract
  that interest from the monthly payment.

200

• How Much?
• Read homework exercise 18 on page 567.
• (c) How much of the first payment on the
  mortgage is applied to the principal?
• Use the simple interest formula to find the
  interest on the first payment. Then subtract
  that interest from the monthly payment.

38.68 of the first payment is applied to the
principal.
201

• Adjustable-Rate Mortgages
• Adjustable-rate mortgages (ARMs) vary from state
  to state and from bank to bank, but in general
• The monthly mortgage payment remains the same for
  1, 2, or 5 year periods even though the interest
  rate may change.
• The interest rate for the mortgage changes every
  3 to 6 months.
• The interest rate may be based on the Treasury
  Bill rate, plus some add on rate or margin
  (typically 3 3 ½ ).

202

• Adjustable-Rate Mortgages
• Remember the interest rate is changing every 3
  to 6 months, but the monthly mortgage payment is
  adjusted only every 1, 2, or 5 years depending on
  the terms of the mortgage.
• So, if the interest rate for the mortgage goes
  down, the extra money in the payments goes to the
  principal. If the interest rate for the mortgage
  goes up, the entire payment may go to interest.
  If this happens too long, the length of the
  mortgage may have to be increased.

203

• Adjustable-Rate Mortgages
• Study Example 4 on page 564 in the text. Notice
  how in this example, the interest rate is tied to
  the Treasury bill rate.

204

• Adjustable-Rate Mortgages - Safeguards
• There are some safeguards for the borrower that
  prevent the interest rates from increasing too
  rapidly. A rate cap limits the maximum amount
  the interest rate may change. A periodic rate
  cap limits the maximum amount the interest rate
  may change per period. An aggregate rate cap
  limits the interest rate increase or decrease
  over the life of the loan. A payment cap limits
  the amount the monthly payment may change but
  does not limit changes in interest rates.

205

• Other Types of Mortgages
• There are other types of mortgages discussed on
  pages 565 and 566 in the text. Read about these
  mortgages so you have an idea of what they are
  all about.

206

• Congratulations!
• You have now completed the