1.
3
In thisIn this chachapterpter
3A Discount
3B Proﬁt and loss
3C Budgeting
3D Cost of services
3E Credit cards
3F Foreign exchange
syllabussyllabusrrefefererenceence
Strand:
Financial mathematics
Core topic:
Managing money 1
• Spending money
Spending
money
MQ Maths A Yr 11 - 03 Page 63 Wednesday, July 4, 2001 2:35 PM
2.
64 M a t h s Q u e s t M a t h s A Ye a r 1 1 f o r Q u e e n s l a n d
Introduction
Karla is now earning better money. Her ﬁrst fortnightly
pay of $985 was deposited into her bank account on
Friday, 24 January. Less than two weeks later her
account balance was $28. Karla could not believe that
she had spent over $950. Where did it all go? She sat
down and wrote out all the things she had spent
money on, and how she had parted with it. Much had
been spent at retail stores buying groceries, clothes,
books and CDs. She had paid for her
purchases in cash. Perhaps, she
thought, she should get a credit
card, but she found that there
were service charges for credit
cards, as well as interest.
Perhaps she could buy more
when there were discounts. She
wondered whether she should
have a budget. Clearly, she needed
a better understanding of the details
of handling her hard-earned money,
or it was just going to leak away.
Discounts, credit card charges, the costs of services
and budgeting are topics that affect us all and, like
Karla, we owe it to ourselves to understand how these
work so that we can make the best use of our money.
These and other related topics will be discussed in the following sections of this
chapter.
1 Calculate 7.5% of $450.
2 Increase $220 by 8%.
3 Reduce $360 by 15%.
4 After receiving a pay rise of 10%, Jaime’s wage was $396. What was her wage before
the pay rise?
5 Fifty-ﬁve litres of petrol cost $49. What will sixty litres of petrol cost?
SkillS
HEET 3.2
SkillS
HEET 3.3
SkillS
HEET 3.1
MQ Maths A Yr 11 - 03 Page 64 Wednesday, July 4, 2001 2:35 PM
3.
C h a p t e r 3 S p e n d i n g m o n e y 65
Discount
The ﬁrst thing that Karla decided to do was to get more for her money. Consequently,
she decided to buy discounted items wherever possible.
A discount is an amount of money by which the price of an item is reduced. If
expressed as a percentage of the original price, it is called a percentage discount.
Discount = Original price − Sale price
Percentage discount = × 100%
When the original price and the percentage discount are known, there are two methods
of ﬁnding the sale price.
Method 1
1. Find the discount in dollars (by ﬁnding the percentage of the original price).
2. Subtract the discount from the original price.
Sale price = Original price − percentage of the original price
Method 2
1. Treat the original price as 100%.
2. The sale price is then represented by (100% − % discount).
Sale price = (100% − percentage discount) of the original price
The choice of method depends on the problem. If the problem requires you to ﬁnd
the discount in dollars and hence the sale price, use method 1. If the actual amount of a
discount is not needed, use method 2 (which gives the sale price straight away).
Discount
Original price
---------------------------------
A vacuum cleaner is discounted
from $180 to $126.
Find the percentage discount.
THINK WRITE
Find the discount in dollars. Discount = Original price − Sale price
= $180 − $126
= $54
Write the formula for the percentage
discount.
% discount = × 100%
Substitute the values of the discount
and the original price into the formula
and evaluate.
% discount = × 100%
= 30%
Write the answer. The vacuum cleaner was discounted by 30%.
1
2
Discount
Original price
---------------------------------
3
54
180
---------
4
1WORKEDExample
MQ Maths A Yr 11 - 03 Page 65 Wednesday, July 4, 2001 2:35 PM
4.
66 M a t h s Q u e s t M a t h s A Ye a r 1 1 f o r Q u e e n s l a n d
Sometimes we are given a discount and the sale price and need to ﬁnd the original
price, as shown in the following example.
Find the sale price on a $42 kettle after a 12.5% discount has been applied.
THINK WRITE
Method 1
Find the discount in dollars. Discount = 12.5% of $42
= × 42
= $5.25
Find the sale price by subtracting the
discount amount from the original
price.
Sale price = Original price − Discount
= $42 − $5.25
= $36.75
Method 2
Express the sale price as a percentage
of the original price.
Original price = 100%, Discount = 12.5%
Sale price = 100% − 12.5%
= 87.5%
Find the sale price in dollars. Sale price = 87.5% of the original price
= × 42
= $36.75
1
12.5
100
----------
2
1
2
87.5
100
----------
2WORKEDExample
After a 20% discount, a kilogram of scotch ﬁllet steak costs $9.60. Find the original price
and the amount of money saved per kilogram.
THINK WRITE
Identify the unknown. Let the original price be x.
Express the sale price as a percentage
of the original price in terms of x.
Original price = 100%, Discount = 20%
Sale price = Original price − Discount
= 100% − 20%
= 80%
So sale price = 0.8x
Form an equation by equating an
expression for the sale price with the
sale price in dollars and solve for x.
0.8x = 9.60
x = 9.60 ÷ 0.8
= $12
Find the amount saved. Amount saved = Original price − Sale price
= $12 − $9.60
= $2.40
Write the answer. The price of 1 kg of scotch ﬁllet steak before
the sale was $12. The amount of money saved
per 1 kg is $2.40.
1
2
3
4
5
3WORKEDExample
MQ Maths A Yr 11 - 03 Page 66 Wednesday, July 4, 2001 2:35 PM
5.
C h a p t e r 3 S p e n d i n g m o n e y 67
Discount
1 Find the percentage discount for each of the following items.
a A dress, discounted from $80 to $60
b A watch, discounted from $365 to $185
c A clock, discounted from $47 to $34
d A lamp, discounted from $59 to $42
e A coffee table, discounted from $270 to $239
f A set of kitchen knives, discounted from $49 to $36
g A cordless phone, discounted from $119 to $89
h A tablecloth, discounted from $25 to $18
i A bookshelf, discounted from $70 to $63
j A scientiﬁc calculator, discounted from $30 to $24
2 Below are some items from a Home Shopper direct marketing brochure.
a b
c
d
Next to each item is the retail price and the Home Shopper’s price. For each item,
ﬁnd:
i the discount amount in dollars when the goods are purchased direct
ii the percentage discount.
remember
1. Discount = Original price − Sale price
2. Percentage discount = × 100%
3. Sale price = Original price − percentage of the original price
= (100% − percentage discount) of the original price
Discount
Original price
---------------------------------
remember
3A
WORKED
Example
1
MAGIC Blender
Blends drinks, sauces, grinds coffee, chops nuts.
12 Month Warranty. Retail $39.95
Home Shopper’s price $29.90Home Shopper’s price $29.90
SANDWICH Toaster
Toasted sandwiches to go. Easy clean.
12 Month Warranty. Retail $29.95
Home Shopper’s price $22.90Home Shopper’s price $22.90
TEFLON–Based Iron
Light weight, easy glide iron.
12 Month Warranty. Retail $39.95
Home Shopper’s price $22.90Home Shopper’s price $22.90
RETRO–Toaster
Your choice of colours, automatic, variable control.
12 Month Warranty. Retail $39.95
Home Shopper’s price $32.00Home Shopper’s price $32.00
MQ Maths A Yr 11 - 03 Page 67 Wednesday, July 4, 2001 2:35 PM
6.
68 M a t h s Q u e s t M a t h s A Ye a r 1 1 f o r Q u e e n s l a n d
3 This advertising brochure states that all
manchester (sheets and towels) is discounted
by up to 30%. Find the real percentage
discount for each item. Comment on your
ﬁndings.
a Single sheets
b Double sheets
c Queen sheets
d Single quilt cover
e Double quilt cover
f Queen quilt cover
g King quilt cover
4 Healthway is promoting savings
in its health and beauty products.
For each of the items shown
at right, ﬁnd:
i the original price
ii the percentage discount.
5 Copy and complete the following table.
Item
Original
price
($)
Discount
(%)
Discount
($)
Sale
price
($)
a Microwave oven 300 10%
b Furniture set 2030 5%
c Mirror 40 30%
d Necklace 1560 12.5%
e Refrigerator 760 20%
f Stereo system 480 33 %
g Washing machine 564 25%
h Car 7500 50%
Health & beauty
COSTS LESS at Healthway
Health & beauty
COSTS LESS at Healthway
HAIR
COLO
URCondtioner
Delight
Delight
&
Bright
Shampoo
Delight
Delight&
Bright
Hair Colour Varieties
$
957 Save
1.00
Hand cream
$
545 Save
46c
100s
$
399 Save
66c
50s
$
749 Save
86c
75s
$
1499 Save
2.00
200ml
$
399
Save up to 99c
Vitamin
CC
Multi
Vitamin
Horseradish
Garlic
&
a b c
d e f
WORKED
Example
2
1
3
---
MQ Maths A Yr 11 - 03 Page 68 Wednesday, July 4, 2001 2:35 PM
7.
C h a p t e r 3 S p e n d i n g m o n e y 69
6 A department store announced a 15% discount on every purchase for one day only.
Elena decided to use the opportunity to buy new clothes for her daughter. She bought
a dress normally priced at $29, a 3-piece shorts set (normally $30), pedal pushers
(normally $16), an embroidered top (normally $18) and sandals (normally $26). Find:
a the total cost of the clothes
b the amount she had to pay after the 15% discount was applied
c the amount of money Elena was able to save on these purchases by shopping on
that day.
7
The calculation that could not be used to ﬁnd the sale price of a $64 item after a dis-
count of 12.5% is:
8
The ring that will cost $78 after a discount of 33 % is:
A a friendship ring, normally $104
B a mother of pearl ring, normally $130
C a sapphire ring, normally $260
D a Russian band ring, normally $117
E a ruby ring, normally $234
9 After a discount of 15%, a jar of Kenya Gold coffee costs $10.15. Find:
a the original price
b the amount saved on each jar.
10 A Byer shareholder has a special card which allows a 5% discount on any purchase
made at Byer’s supermarkets (excluding items that are already on sale).
a What is the total cost of goods purchased by the shareholder who, after producing
the card, pays $166.25. (There are no sale items included.)
b What is the amount saved?
11 Before the beginning of a winter sale, a shop assistant was asked to reduce the prices
of all items in the store by 12.5%. She calculated the new prices and attached new tags
to the goods. At the end of the sale she was asked to put the old prices back. Unfortu-
nately, the shop assistant had thrown the old tags away as she did not think she would
need them again. She decided to add 12.5% to the sale prices. If the shop assistant
proceeds in this manner, will she get back to the original prices? Explain your answer.
A B C
D of 64 E 64 − × 64
mmultiple choiceultiple choice
12.5 64×
100
---------------------- 64
12.5 64×
100
----------------------–
87.5 64×
100
----------------------
7
8
---
1
8
---
mmultiple choiceultiple choice
1
3
---
WORKED
Example
3
MQ Maths A Yr 11 - 03 Page 69 Wednesday, July 4, 2001 2:35 PM
8.
70 M a t h s Q u e s t M a t h s A Ye a r 1 1 f o r Q u e e n s l a n d
Proﬁt and loss
When an item is sold for more than it cost, the difference is said to be proﬁt. It is
customary to express proﬁt as a percentage of the cost price:
Proﬁt = Selling price − Cost price
Percentage proﬁt = × 100%
Loss = Cost price − Selling price
Percentage loss = × 100%
When the cost price and percentage proﬁt/loss are known and we need to ﬁnd the
selling price, there are two methods that can be used (see the following example).
Profit
Cost price
------------------------
Loss
Cost price
------------------------
Find the percentage proﬁt on an item that was bought for $30 and later sold for $38.
THINK WRITE
Identify the cost price (CP) and the selling
price (SP).
CP = $30; SP = $38
Write the formula for the proﬁt.
(SP > CP)
Proﬁt = SP − CP
Substitute the values of CP and SP into the
formula and evaluate.
Proﬁt = $38 − $30
= $8
Write the formula for the percentage proﬁt. Percentage proﬁt = × 100%
Substitute the values of proﬁt and CP into the
formula and evaluate.
Percentage proﬁt = × 100%
= 26.67%
1
2
3
4
Profit
CP
-------------
5
8
30
------
4WORKEDExample
Find the percentage loss if an item was bought for $220 and sold later for $180.
THINK WRITE
Identify the cost price (CP) and the selling
price (SP).
CP = $220; SP = $180
Write the formula for the loss.
(SP < CP)
Loss = CP − SP
Substitute the values of CP and SP into the
formula and evaluate.
Loss = $220 − $180
= $40
Write the formula for the percentage loss. Percentage loss = × 100%
Substitute the values of the loss and CP into
the formula and evaluate.
= × 100%
= 18.18%
1
2
3
4
Loss
CP
-----------
5
40
220
---------
5WORKEDExample
MQ Maths A Yr 11 - 03 Page 70 Wednesday, July 4, 2001 2:35 PM
9.
C h a p t e r 3 S p e n d i n g m o n e y 71
Finally, there are cases when the selling price and the percentage proﬁt (or loss) are
known and we need to ﬁnd the CP. The next example shows how to deal with such
problems.
A shopkeeper buys jumpers from a wholesaler for $22 each and wants to make a proﬁt of
20% per jumper. What should be the selling price of a jumper to provide this proﬁt?
THINK WRITE
Method 1
Find the proﬁt in dollars. Proﬁt = 20% of CP
= 20% of $22
= × 22
= $4.40
Find the selling price by adding the
proﬁt to the cost price.
SP = CP + Proﬁt
= $22 + $4.40
= $26.40
Method 2
Treating the cost price as 100%,
express the selling price as a percentage
of the CP.
CP = 100%; proﬁt = 20%
SP = (100 + 20)%
= 120% of CP
Substitute the values of the CP and
substitute.
SP = 120% of $22
= × 22
= $26.40
1
20
100
---------
2
1
2
120
100
---------
6WORKEDExample
A retailer sells a TV set for $732, making herself a proﬁt of 22%. Find the wholesale price
of the TV set.
THINK WRITE
Identify the unknown. Let the CP be x.
Express the SP as a percentage of the CP
in terms of x.
CP = 100%
Proﬁt = 22%
SP = (100 + 22)% = 122%
So SP = 122% of CP
= 1.22 × CP
= 1.22x
Form an equation by making the expression
for the selling price equal to $732.
1.22x = 732
Solve for x. x = 732 ÷ 1.22
x = 600
Write the answer. The wholesale price of the TV set was $600.
1
2
3
4
5
7WORKEDExample
MQ Maths A Yr 11 - 03 Page 71 Wednesday, July 4, 2001 2:35 PM
10.
72 M a t h s Q u e s t M a t h s A Ye a r 1 1 f o r Q u e e n s l a n d
Proﬁt and loss
1 Find the percentage proﬁt (to 2 decimal places) for each of the following items.
Item CP ($) SP ($)
a Tracksuit 80 139.95
b T-shirt 16 22.50
c Tennis shoes 49.95 89.95
d Tank top 6 9
e Swimsuit 38 59
f Short socks 2 5.95
g Training pants 20 29
h Tennis skirt 22 36
remember
1. Proﬁt = Selling price (SP) − cost price (CP)
2. Percentage proﬁt = × 100%
3. Loss = CP − SP
4. Percentage loss = × 100%
Profit
CP
-------------
Loss
CP
-----------
remember
3B
Mat
hcad
Profit
and
loss
WORKED
Example
4
MQ Maths A Yr 11 - 03 Page 72 Wednesday, July 4, 2001 2:35 PM
11.
C h a p t e r 3 S p e n d i n g m o n e y 73
2 The following goods were sold at a garage sale. Find the percentage loss for each of the
items, correct to 2 decimal places.
3 A shopkeeper buys 20 kg of cooking chocolate for $50 and sells it in 500 g packets at
$3 each. Find the proﬁt made and express it as a percentage of the cost price.
4 Alex had a collection of 5 Betallica CDs, which he
purchased over a period of time at $29.95 each.
A friend offered to pay $70 for the whole set.
Find the loss in dollars and express it as a
percentage of the cost price.
5 A shopkeeper at the Southbank Markets
buys sheepskin moccasins from the
wholesaler at the following prices: chil-
dren’s sizes — $12 per pair; adults’
sizes — $17 per pair, and extra-large
sizes — $19 per pair. If the shopkeeper
wants to make a 20% proﬁt, what should be
the sale price for each type?
6 Michael buys a car for $12 000. It depreciates
at a rate of $900 per year. If Michael wants his
losses to be no more than 30% of the cost price,
after how many years from the purchase does
he have to sell the car?
7 By selling a collection of coins for $177, Igor
makes a proﬁt of 18%. What was the original
cost of the collection?
8 A retailer has purchased a particular style of
jumper which is proving to be unpopular. After
attempting to sell them for two consecutive sea-
sons, the retailer decides to put them on sale at
$15 each to recover part of the cost. Find the
wholesale price of each jumper if the retailer suf-
fers a 40% loss.
Item CP ($) SP ($)
a Cutlery 40 8
b Two bedside lamps 100 22
c Vase 35 5
d Toaster 19.95 1.50
e Electric kettle 42 6
f Set of golf clubs 150 45
g Set of building blocks 16 4
h Five paperback books
by Sydney Sheldon
60 2.50
WORKED
Example
5
WORKED
Example
6
WORKED
Example
7
MQ Maths A Yr 11 - 03 Page 73 Wednesday, July 4, 2001 2:35 PM
12.
74 M a t h s Q u e s t M a t h s A Ye a r 1 1 f o r Q u e e n s l a n d
1 A tennis racquet is discounted from $240 to $180. Calculate the percentage discount.
2 A pair of running shoes is advertised at $140. What does a customer pay if a 25%
discount is applied.
3 After bargaining with the salesperson, Sue has the price of a computer reduced from
$1200 to $1050. Express this reduction as a percentage of the original price.
4 A carton of drinks is marked at $28. If all stock is reduced by 15%, calculate the cost
of the drinks.
5 A shopkeeper buys a 12-kg case of tomatoes for $20. If he sells all of the tomatoes for
$2.50 per kg, calculate the percentage proﬁt.
6 Karen pays $12 each for fake name brand watches. When she sells them she wants to
make an 80% proﬁt. What price should she sell these watches for?
7 Michelle buys and sells second-hand skateboards. She makes a 40% proﬁt on each
sale. If she sells a skateboard for $56, what did she originally pay for the skateboard?
8 John paid $50 for a dozen trophies. If he sells them for $14 each, calculate the per-
centage proﬁt.
9 P-Mart make 30% on all their sales. If they pay $600 for a dining suite, what price
should they sell it for to make the desired proﬁt?
10 Hans sells a restaurant for $198 000. He calculates that he has made a 10% proﬁt on
the buying price. What did he pay for the restaurant originally?
Dealing in diaries
Just before Christmas a shopkeeper purchased a box of 50 diaries for $120.
1 Find the cost price of each diary.
2 If he sold 30 diaries before Christmas at $5 each, calculate the proﬁt that he
would make.
3 Find the percentage proﬁt.
4 If, after Christmas, the shopkeeper sold the remaining diaries for $1 each, ﬁnd
the percentage loss on each of these diaries.
5 After the shopkeeper had sold the leftover diaries (at $1 each), ﬁnd the total
proﬁt that he made.
6 Express the total proﬁt as a percentage of the cost price.
7 Find the proﬁt that the shopkeeper could have made had he managed to sell all
of the diaries before Christmas (at $5 each).
8 What was his loss (in dollars) by not selling all of his diaries before Christmas?
9 Express the loss as a percentage of the potential proﬁt.
1
inv
estigat
ioninv
estigat
ion
MQ Maths A Yr 11 - 03 Page 74 Friday, July 6, 2001 1:56 PM
13.
C h a p t e r 3 S p e n d i n g m o n e y 75
Budgeting
Karla wants to go to New Zealand for her holidays next year;
but if she saves only $28 each pay, she will certainly not
have enough money to go. Although she is to receive a pay
rise, she realises that she still does not know how much
she will need to save. She understands that a budget will
help her, so decides to look into the principles of
budgeting in more detail.
A budget is a table containing an estimate of income
and expenditure. A personal (or family) budget can help
you to:
1. ensure that you do not spend more than you earn
2. estimate the amount of money that you can save
3. control your expenses and perhaps cut some of them
in order to save more
4. decide what you can and what you can’t afford.
A personal budget helps you to make various ﬁnancial
decisions. The expenses in the personal (or family) budget can
be divided into two major categories: ﬁxed (or unavoidable) expenses and variable
expenses. Fixed expenses may include rent or mortgage, medical insurance, car regis-
tration and other regular payments that must be paid and can’t be varied. Variable
expenses include food, entertainment, clothing and other items that can be controlled or
varied. To reduce some expenses in order to save more money, one would look into
variable expenses.
A weekly, monthly or yearly budget can be prepared. Expenses may be weekly (such
as food), monthly (health insurance), quarterly (electricity bills) or yearly (car
registration). Depending on the budget duration, all expenses should be converted to
weekly, monthly or yearly amounts. The following table of conversion is helpful in
budget preparation.
It should be understood that budgets give only an approximation of the real-life
situation, as they are based on estimates and do not include unexpected expenses.
Purpose Convert from Convert to Operation
Weekly budget Monthly cost Weekly cost × 12, then ÷ 52
Yearly cost Weekly cost ÷ 52
Monthly budget Weekly cost Monthly cost × 52, then ÷ 12
Yearly cost Monthly cost ÷ 12
Yearly budget Weekly cost Yearly cost × 52
Monthly cost Yearly cost × 12
MQ Maths A Yr 11 - 03 Page 75 Wednesday, July 4, 2001 2:35 PM
14.
76 M a t h s Q u e s t M a t h s A Ye a r 1 1 f o r Q u e e n s l a n d
Karla’s monthly budget.
Use the table to resolve each of the following.
a Calculate the total of the ﬁxed expenses. Note that Karla views health insurance, house
contents insurance and car insurance as important expenses, and their regular pay-
ments are ﬁxed.
b Calculate the total of the variable expenses.
c Calculate the amount available for saving.
d If Karla wishes to take a vacation and travel to New Zealand (estimated cost $3500),
for how long does she have to save?
e Suggest some possibilities for cutting expenses in order to save enough money for the
New Zealand holiday one month sooner.
Income Expenses
Salary after tax $2050
Dividends from shares $23
Rent of 1-bedroom ﬂat $520
Electricity $70
Phone $40
Health insurance $30
House contents insurance $10
Car registration $27
Car insurance $42
Petrol $35
Food $110
Clothing $150
Entertainment $150
Sport $100
Miscellaneous $40
Total: $2073 Total: $1324
THINK WRITE
a Identify the ﬁxed expenses and add them
up.
a Fixed expenses:
Rent $520
Health insurance $30
House contents insurance $10
Car registration $27
Car insurance $42
Total = 520 + 30 + 10 + 27 + 42 = $629
b Calculate the total of variable expenses
by subtracting ﬁxed expenses from the
total.
b Total of variable expenses
= total expenses − total of ﬁxed expenses
= 1324 − 629
= $695
c Calculate monthly savings by
subtracting expenses from the income.
c Monthly savings
= monthly income − monthly expenses
= 2073 − 1324
= $749
8WORKEDExample
MQ Maths A Yr 11 - 03 Page 76 Wednesday, July 4, 2001 2:35 PM
15.
C h a p t e r 3 S p e n d i n g m o n e y 77
The Australian budget
Budgets can be prepared for individuals, families and small organisations. However,
there is also a budget for each country. Investigate the last Australian budget.
1 Who prepares the budget?
2 What is the budget’s period?
3 What is/are the source/s of income?
4 What are the items in the expenditure section (that is, where does the money go)?
5 Was there any deﬁcit in the last budget?
THINK WRITE
d Calculate the number of months required
to save for the holiday.
d To save $3500 at the rate of $749 per month:
3500 ÷ 749 = 4.67 or approximately
5 months
e Identify the number of months
within which the money is to be
saved.
e To save one month sooner than
calculated in part d means 5 − 1 = 4
months
Calculate the amount required to be
saved monthly.
Monthly savings needed = 3500 ÷ 4
Monthly savings needed = $875
Calculate the extra amount which is
to be saved per month.
Extra monthly savings needed
= $875 − $749
= $126
Suggest cuts in variable expenses. Cuts could be made as follows:
Phone bills: cut from $40 to $30 gives
$10
Clothing: cut from $150 to $80 gives
$70
Entertainment: cut from $150 to
$104
gives $46
This gives 10 + 70 + 46 = $126, which is
the required extra saving.
1
2
3
4
inv
estigat
ioninv
estigat
ion
remember
1. A budget is a table that contains an estimate of income and expenditure.
2. The two major categories of expenses are ﬁxed and variable expenses.
3. Both budget and expenses can be calculated weekly, monthly, quarterly or
yearly. Depending on the budget, all expenses should be recalculated for the
same time interval.
remember
MQ Maths A Yr 11 - 03 Page 77 Wednesday, July 4, 2001 2:35 PM
16.
78 M a t h s Q u e s t M a t h s A Ye a r 1 1 f o r Q u e e n s l a n d
Budgeting
1 The table below shows the monthly budget for a couple with one school-aged child.
Use the table to calculate the following:
a the total of ﬁxed expenses
b the total of variable expenses
c the total monthly savings
d the time needed for the family to save enough for a trip to Bali (estimated cost $3000).
2 List as many variable expenses as you can that are missing from the budget in question 1.
3 A university student who lives with her parents has the following expenses: she pays
her parents $50 per week for board and food; a monthly ticket for public transport costs
her $63; she spends on average $40 a month on books and stationery; her single health
insurance premium is $24 a month; entertainment and snacks cost her about $55 a
month; the university enrolment fee takes $300 a year and she also needs clothes and
accessories which cost approximately $15 per week.
a Prepare a monthly budget if the student’s income consists of Austudy (which is
$116 per week) plus birthday and Christmas presents ($250 a year).
b Calculate the amount of money that she can save per month.
Income Expenses
Combined monthly salary
after tax $3800
Mortgage repayments $1200
Rates $75
Building insurance $20
Contents insurance $15
Electricity $120
Gas $25
Telephone $50
Car registration $35
Car insurance $50
Health insurance $60
School fees $110
Food $160
Clothing $60
Entertainment $100
Sport $75
Miscellaneous $120
Household needs and repairs $20
Petrol $55
Total: $3800 Total: $2350
3C
WORKED
Example
8
MQ Maths A Yr 11 - 03 Page 78 Wednesday, July 4, 2001 2:35 PM
17.
C h a p t e r 3 S p e n d i n g m o n e y 79
4 Using the ﬁgures in the table below, prepare an expenditure side of a weekly budget.
5 The student in question 3 is offered a part-time job in the university cafeteria, where
she will be able to earn $66 per week.
a Calculate her total monthly savings if she accepts this position.
b Our student is considering moving in with her friends. By doing so she will save the
$50 per week that she is paying to her parents in board and food, but she will have
to pay $100 per month for her share of the rent. She will also have to contribute
$45 per month for electricity and phone bills and $60 per week for food. With the
new job can the student afford to move out of home? Support your answer with
appropriate calculations.
6 Prepare your personal monthly budget (or your family budget if you do not have any
income). Are there any possibilities for cutting some of the expenses?
7 Members of a welfare group are discussing the budget for the next year. Their income
will come from three sources: a government subsidy of $4200; annual membership fees
of $25 per person and proﬁts from the various events. They estimate that the auction
will bring in $400, proﬁts from the food stalls (at the picnic and the three local fairs)
will be $230 each time and proﬁts from the two concerts will yield about $1800 each.
They also estimate that about 650 people will renew their membership. The money will
be spent as follows: rent of the premises at $500 a month; publishing the newsletter
$240 per quarter; expenses of $180 associated with each Sunday School for 40 weeks a
year; electricity and phone bills at $220 a month; public liability and contents insur-
ance, $1860 per year. Advertising will cost $30 per month and stationery $250 per year.
After buying a new computer (for about $3500) and allowing $2000 for unexpected
expenses, the rest of the money will be spent on charity.
a Prepare a yearly budget for the welfare group.
b Calculate the amount of money left to use for charity.
c Express your answer to b as a percentage of the annual income.
Item Cost and period
Rent $600 per month
Food $90 per week
Electricity $420 per 3 months
Gas $40 per 2 months
Phone $360 per 3 months
Car registration $430 per year
Car insurance $500 per year
Health insurance $175 per 3 months
Contents insurance $125 per year
Clothes $100 per month
Entertainment $80 per month
Work
SHEET 3.1
MQ Maths A Yr 11 - 03 Page 79 Wednesday, July 4, 2001 2:35 PM
18.
80 M a t h s Q u e s t M a t h s A Ye a r 1 1 f o r Q u e e n s l a n d
Cost of services
An important part of being able to prepare a personal budget is to understand how
various organisations charge for their services.
The following questions are designed to help you investigate the cost of services,
such as electricity and gas charges, water and council rates and the costs of using a
telephone.
The club’s end-of-season break-up
Work in groups of three.
Karla is a member of the committee of her local netball
club and she has been asked to organise food and drinks
for the club’s breakup. It is to be a BBQ held at the
club grounds. Everyone who attends will be asked
to pay a certain amount and the club will supply
food and drinks.
Last year about 100 people attended and the
number is expected to be the same this year.
Your task:
1 Help Karla plan a menu, indicating what
each person could be expected to eat and
drink.
2 Prepare a shopping list with
deﬁnite, speciﬁc quantities and
prices.
3 Suggest to the committee a
cost per person that should cover
expenses plus 10%.
investigat
ioninv
estigat
ion
MQ Maths A Yr 11 - 03 Page 80 Wednesday, July 4, 2001 2:35 PM
19.
C h a p t e r 3 S p e n d i n g m o n e y 81
Cost of services
Study the electricity bill shown below and answer the following questions.
1 a What is the total amount to be paid?
b When should this bill be paid?
c How does this bill compare with the bill from the previous quarter?
d On what dates were the meter readings taken?
e What is the average daily cost of electricity?
f If the Beales want to prepare a weekly budget, what amount should they allocate
to the cost of electricity?
g How does the average daily kWh usage compare with the same period last year?
2 The bill records two different types of consumption — Tariff 11 (used for lights,
toasters etc.) and Tariff 33 (used for hot water systems and other devices whose power
consumption can be restricted to off-peak times).
3D
MQ Maths A Yr 11 - 03 Page 81 Wednesday, July 4, 2001 2:35 PM
20.
82 M a t h s Q u e s t M a t h s A Ye a r 1 1 f o r Q u e e n s l a n d
a How many kWh in Tariff 11 were used in the quarter?
b What was the most recent Tariff 11 meter reading?
c What GST was charged on the Tariff 11 consumption?
d What is the cost of the Tariff 11 supply before GST is added?
e Calculate the cost of Tariff 11 supply (in cents per kWh) if it is charged at a ﬂat rate.
3 a Estimate the consumption, in kWh, of Tariff 11 supply for the February quarter
account last year.
b Estimate the consumption, in kWh, of Tariff 33 supply for the February quarter
account last year.
c Estimate the cost of last year’s bill, if the rates charged were the same as those
charged this year. (Include GST.)
4 Study the gas bill shown below for the February quarter and answer the following
questions.
MQ Maths A Yr 11 - 03 Page 82 Wednesday, July 4, 2001 2:35 PM
21.
C h a p t e r 3 S p e n d i n g m o n e y 83
a What is the value of the bill?
b How does this bill compare with last quarter’s?
c How does this bill compare with the bill for the same quarter last year?
d What is the average daily cost of gas consumption?
e What would you estimate the yearly cost of gas consumption?
f If Jane is to make a monthly budget, how much should she allow for gas?
5 The following ﬁgure shows the reverse side of the gas bill.
You will notice that the amount of gas consumed is given in Megajoules (MJ) and is
calculated indirectly from the meter readings. An ‘MJ factor’, which depends on
quantities such as temperature and pressure, is used to convert from the meter read-
ings to Megajoules.
a What is the difference between the meter readings?
b Explain how the consumption, in MJs, is calculated from the difference between
meter readings.
c How much GST is charged in this bill?
d What is the rate, in cents per MJ, of
the cost of the ﬁrst 1710 MJ?
e Using the rates given in the bill,
calculate the cost of 6000 MJ
(excluding GST).
6 In the May quarter last year the average
daily consumption of gas was 70 MJ.
If there were 91 days in this quarter,
calculate the:
a total gas consumption for the quarter
b total cost of this gas (excuding GST)
c GST payable on this cost of gas
d total cost of gas for this quarter.
7 In the August quarter last year the
average daily consumption of gas was
85 MJ. If there were 93 days in this
quarter, determine the total cost of gas
for this quarter, including GST.
MQ Maths A Yr 11 - 03 Page 83 Wednesday, July 4, 2001 2:35 PM
22.
84 M a t h s Q u e s t M a t h s A Ye a r 1 1 f o r Q u e e n s l a n d
Questions 8 to 11 refer to the Brisbane City Council Rates notice shown below.
MQ Maths A Yr 11 - 03 Page 84 Wednesday, July 4, 2001 2:35 PM
23.
C h a p t e r 3 S p e n d i n g m o n e y 85
8 a What amount is to be paid, if the bill is paid before 13th June?
b What amount is to be paid, if the bill is paid after 13th June?
c Why is Mr Ratepayer’s bill subsidised?
d Calculate the bill to be paid if the subsidies and remissions were not given.
e Estimate Mr Ratepayer’s yearly rates bill.
f If he is planning a monthly budget, how much should he allocate for rates?
9 a How much water is used in the quarter?
b What is the cost, in cents per kL, of water?
c How much water would he expect to use in a year?
MQ Maths A Yr 11 - 03 Page 85 Wednesday, July 4, 2001 2:35 PM
24.
86 M a t h s Q u e s t M a t h s A Ye a r 1 1 f o r Q u e e n s l a n d
10 If Mr Ratepayer’s water meter readings were
845 987
calculate his water bill for this period. Include the water service charge.
11 a What was the increase in the valuation of the property from 01 July 1998 to 01
July 1999?
b Express this increase as a percentage of the original valuation.
12 The ﬁrst page of a telephone bill issued by Telstra is shown below.
a Explain how the total of this
bill was calculated from the
components shown.
b What percentage of the total
bill does the service charge
represent?
c Is there any concession
available for the telephone
bill?
d If the service charge is
always constant, what was
the total of the previous bill,
assuming that the Flexi-Plan
was not yet introduced?
Telstra Bill
Telstra Corporation Limited
ACN 051 775 556
Account number
Opening Balance We received
93 G Flexi-Plan balance 8.40cr
91 G Call charges to 23 June 116.51
92 G Service and equipment to 23 June 42.45
Total of this bill $150.56
Item Account Summary Your Reference 07 5551 0000 $
Balance Total of this bill
Bill number Date of issue Bill enquiries
Total amount payable
$150.55
30 Jun 01
Payment to be made by
T 000 123 123-2
$0.00
MS A SAMPLE
10 SAMPLE STREET
SAMPLEVILLE 0000
$0.00 $0.00 $150.56
000 0000 034 25 June 01 13 20 00
Calling Patterns Compared With Last Bill
Local Calls up by $8.75
STD Calls up by $4.06
Calls to Mobiles up by $2.00
June-00 Oct-00 Mar-01 June-01
$200
$160
$120
$80
$40
$0
Same Time
Last year
Total Bill
MQ Maths A Yr 11 - 03 Page 86 Wednesday, July 4, 2001 2:35 PM
25.
C h a p t e r 3 S p e n d i n g m o n e y 87
13 Page 3 of the Telstra bill is shown below.
a According to the service summary, how many metered calls were made and what
was the cost of each call?
b What percentage of the service and equipment charge does the rent of the telephone
represent?
c If a family buys a telephone valued at $89 and hence stops renting one from
Telstra, in how many months will the savings from not paying rental cover the cost
of the new phone?
d Use the itemised STD Calls section to ﬁnd the afternoon rate for calling Marysville.
e Study the Calls Direct to Mobiles itemised section and complete the following
statement: ‘Judging from the bill it is reasonable to assume that the off peak rate is
applied to any calls to mobiles made after pm.’
Local Call Saver 15
69 Plan fee 23 Mar to 23 June 0.00
71 Discount 8.40 cr
Plan balance $8.40 cr
Total Flexi-Plan balance $8.40 cr
Item Flexi-Plan Details $
Telephone Service 07 5551 0000
Flexi-Plan/Concession discounts $8.40 cr
Call charges
51 Metered calls 23 Mar to 23 June 404 units at $0.25 each 101.00
57 STD to 23 June 8 calls 6.51
58 Calls direct to Mobiles to 23 June 9 calls 9.00
Service and equipment
2 1 Telephone Handset Rental
Rent in advance 23 Mar to 23 June 2.50 7.50
1 1 Telephone Line Rental
Rent in advance 23 Mar to 23 June 11.65 34.95
Total for 07 5551 0000 $150.56
Item Service Summary $
STD Calls
Date Time Place Number Rate Min:Sec $
Telephone Service 07 5551 0000
27 23 Mar 02:54 pm Marysville 03596 Afternoon 2:30 0.57
25 23 Mar 08:13 pm Warburton 03585 Economy 1:51 1.28
26 23 Mar 06:54 pm Marysville 03596 Economy 1:05 0.23
24 02 Apr 03:32 pm Marysville 03596 Economy 1:35 0.28
21 03 Apr 01:04 pm Warburton 03585 Afternoon 2:39 1.48
22 02 May 10:01 pm Marysville 03596 Economy 1:09 0.24
19 07 May 02:17 pm Warburton 03585 Economy 4:12 1.54
20 09 May 10:34 am Marysville 03596 Economy 7:42 0.89
STD Calls
Date Time Place Number Rate Min:Sec $
Telephone Service 07 5551 0000
45 23 Mar 08:13 pm Mobile 0411309 Off Peak 0:17 0.50
46 23 Mar 04:39 pm Mobile 0411309 Peak 0:47 1.25
48 06 Apr 12:33 pm Mobile 0411309 Peak 0:42 1.00
47 10 May 02:59 pm Mobile 0411309 Peak 0:43 1.00
50 07 May 01:33 pm Mobile 0411309 Peak 1:44 1.25
44 08 May 12:35 pm Mobile 0411834 Peak 4:19 2.25
49 21 May 08:37 am Mobile 0411309 Off Peak 0:07 0.50
37 23 Mar 06:42 am Mobile 0411309 Peak 0:20 0.50
43 03 May 07:36 pm Mobile 0411690 Off Peak 0:36 0.75
Item
Item
STD Calls - Itemised $
Calls To Mobiles - Itemised $
Page 3
MQ Maths A Yr 11 - 03 Page 87 Wednesday, July 4, 2001 2:35 PM
26.
88 M a t h s Q u e s t M a t h s A Ye a r 1 1 f o r Q u e e n s l a n d
Credit cards
Karla has decided that it is time for her to obtain a credit card.
A credit card will allow her to purchase goods and services without
paying for them on the spot. They can also be used for obtaining cash
advances, paying bills and making purchases over the phone or on the
Internet.
Common credit cards used in Australia include MasterCard, Visa,
Bankcard, Diners Club and American Express.
When applying for a MasterCard, Visa or Bankcard, a customer is
given a choice of having either an interest-free period
(usually up to 55 days) for a small annual fee (around
$22), or no fee payable and no interest-free period
(with the interest rate usually being lower for the
second option). Each cardholder is offered a certain
limit of credit.
A monthly statement showing all transactions for the
previous month is issued for every cardholder. Upon
receiving a monthly statement, a customer may decide to pay the bank in full by the
due date indicated on the statement and hence not have to pay any interest with an
interest-free period card. Alternatively, the customer may choose to make the minimum
payment only. In this case interest will be charged on the unpaid balance. The
minimum payment is usually a certain percentage of the unpaid balance or a certain
ﬁxed amount — whichever is larger. Variations in interest rates occur from time to time
and cardholders are notiﬁed of these changes in advance.
Below are two extracts from Commonwealth Bank brochures outlining part of their
credit policy.
Source: Commonwealth Bank. Credit Cards — Check Out Our Credit Card
Advantages. Valid as at 10 May 2001.
Statement of the cost of credit: In accordance with
section 158(1)(b) of the Consumer Credit Code, we make
the following statement of the cost of credit for the
purposes of section 140(3) of that Code:
As at 10 May 2001, the annual percentage rates for our
standard credit cards are:
MasterCard/Visa/Bankcard 15.90%
(up to 55 interest free days with an annual fee)
MasterCard/Visa/Bankcard 14.25%
(no interest free days with no annual fee)
Fees and charges are payable.
The above annual percentage rates may change.
Please call us on 13 2221 from 8am to 8pm, Monday to
Friday, or ask at any branch for our up-to-date rates.
MQ Maths A Yr 11 - 03 Page 88 Wednesday, July 4, 2001 2:35 PM
27.
C h a p t e r 3 S p e n d i n g m o n e y 89
Source: Commonwealth Bank. Credit Cards — Conditions of Use — Valid as at 04/01. Subject to change.
For the ‘No interest-free period’ option the interest charged on the outstanding amount
of each purchase and cash advance is charged from the date of the purchase (or cash
Gold MasterCard, Visa Gold
On some Gold card accounts we may require a
minimum payment each month whilst on others
we may require a minimum payment once
each six months.
Monthly minimum payments
If a statement of your card account shows a
closing balance of less than $25, the minimum
payment is the closing balance.
Otherwise, the minimum payment you must
make is the greatest of:
• the excess of the closing balance over the
credit limit on your card account;
• 1.5% of the closing balance (rounded down
to the nearest dollar if the closing balance
of your card account is $1,700 or more); or
• $25.
Find the minimum payment due for each of the following balances using the information
supplied previously.
a $23.40 b $1236.25 c $280.10 d $1560 with the credit limit being $1500
THINK WRITE
a Since the closing balance is under $25, it
should be paid in full.
a As $23.40 < $25, the amount due = $23.40
b Since the closing balance is over
$1000, calculate 2.5% of it.
b Amount due = 2.5% of $1236.25
= × 1236.25
= $30.91
Round down to the nearest dollar. Rounded down to the nearest dollar, the
amount due is $30.
c Since the closing balance is above $25
but below $1000, the minimum payment
is $25.
c $25 < $280.10 < $1000
Therefore payment due = $25
d Since the closing balance is above
$1000, calculate 2.5% of it and round
down to the nearest dollar.
d 2.5% of $1560 = × 1560
= 39
Calculate the excess of the closing
balance above the credit limit.
The excess of the closing balance above
the credit limit = $1560 − $1500
= $60
Select the greater of the two amounts. As $60 > $39, the amount due is $60.
1
2.5
100
---------
2
1
2.5
100
---------
2
3
9WORKEDExample
MQ Maths A Yr 11 - 03 Page 89 Wednesday, July 4, 2001 2:35 PM
28.
90 M a t h s Q u e s t M a t h s A Ye a r 1 1 f o r Q u e e n s l a n d
advance) and until the purchase (or cash advance) is repaid in full. The same is true for
cash advances, obtained with ‘55 days interest-free period’ cards. An extract from the
Commonwealth Bank brochure explains the procedure.
Source: Commonwealth Bank. Credit Cards — Conditions of Use — Valid as at 04/01.
No interest-free days cards
We charge interest on the outstanding amount of each
purchase, permitted transaction and cash advance from
the date the purchase, permitted transaction or cash
advance is debited to your card account until you repay
the purchase, permitted transaction or cash advance.
We calculate interest for a statement period in three
steps:
• first, we average the outstanding balances over the
statement period;
• then we multiply the average by the daily percentage
rate applying to your card account; and
• finally, we multiply the result we get from the prior step
by the number of days in the statement period.
The result we get from the last step is the amount of
interest we charge to your card account in the statement
period.
When do we debit interest?
We debit your card account on the last day of each
statement period with the interest we calculated during
that statement period up to and including that last day.
For a ‘no interest-free period’ credit card, calculate the interest charged on the average
outstanding daily balance of $220 with the interest percentage rate of 13.95% p.a. if the
statement covers a 30-day period.
THINK WRITE
Calculate the daily percentage rate. Daily % rate =
=
= 0.038 22
Calculate the daily interest charged on
the outstanding balance.
Interest = 220 ×
= 0.084 08
Find the interest charged over the
30-day period and round-off to the
nearest cent.
Total interest for 30 days
= 0.084 08 × 30
= 2.522 47
= $2.52 (to the nearest cent)
1
annual % rate
365
---------------------------------
13.95
365
-------------
2
0.038 22
100
--------------------
3
10WORKEDExample
MQ Maths A Yr 11 - 03 Page 90 Wednesday, July 4, 2001 2:35 PM
29.
C h a p t e r 3 S p e n d i n g m o n e y 91
For ‘up to 55 days interest free’ credit cards, no interest is charged if the amount is paid
in full by the due date which is usually 25 days from the date of the statement. If the closing
balance is not repaid in full by the due date, the cardholder then temporarily loses the
interest-free option. The interest is usually charged on the outstanding balance from the
day of the ﬁrst purchase (that is, it is backdated!) until the outstanding balance is paid in
full. Any purchases made before the balance is fully repaid are also added to the total. So
basically if the balance is not paid in full by the due date, the card is effectively a ‘no
interest-free period’ card, but with the higher interest rate being applied.
For a ‘55 days interest free’ credit card, calculate the amount of interest charged on an
outstanding balance of $450 which was repaid 10 days after the due date, given that the
ﬁrst purchase was made on the ﬁrst day of the 30-day statement period and the annual
percentage interest rate was 15%. (Assume that no other purchases were made after the
end of the statement.)
THINK WRITE
Calculate the length of time for which
the interest is charged, keeping in mind
that it is charged from the date of the
ﬁrst purchase and until the balance was
repaid.
The number of days from the ﬁrst purchase to
the last day of statement = 30 (as the purchase
was made on the ﬁrst day and the period covers
30 days).
The number of days from the date of the state-
ment to the due date = 25.
The number of days from the due date to the
date of actual payment = 10.
Total days = 30 + 25 + 10 = 65
Calculate the daily interest rate. Daily interest rate =
= 0.041 096
Find the interest charged on $450 over
the period of 65 days and round-off to
the nearest cent.
Interest = $450 × × 65
= $12.02
1
2
15%
365
-----------
3
0.041 096
100
-----------------------
11WORKEDExample
remember
1. The two options for Visa, MasterCard or Bankcard are:
(a) no annual fee and no interest-free period
(b) an annual fee and a speciﬁc interest-free period.
2. The bank requires a minimum monthly payment which is usually the greater of
a certain ﬁxed amount or a speciﬁc percentage of the closing balance.
3. For all transactions made with a ‘no interest-free period’ card and for cash
advances obtained with an ‘up to 55 days interest-free period’ credit card,
the interest is calculated from the date of the ﬁrst purchase.
4. For interest-free period credit cards, if the closing balance is paid in full by the
due date indicated on the statement, no interest is incurred. Otherwise, interest
is charged until the balance is repaid.
remember
MQ Maths A Yr 11 - 03 Page 91 Wednesday, July 4, 2001 2:35 PM
30.
92 M a t h s Q u e s t M a t h s A Ye a r 1 1 f o r Q u e e n s l a n d
Credit cards
1 The XYZ Bank requires the minimum payment off credit card balances to be:
(a) the closing balance if it is under $25, or
(b) the greatest of:
ii(i) the excess of the closing balance over the credit limit, or
i(ii) 2.5% of the closing balance (rounded down to the nearest dollar), or
(iii) $25.
Calculate the minimum payments on each of the following balances.
a $17.50 b $26.49
c $147.42 d $785.00
e $1326.12 f $2312.58
g $3489.60 h $1954.00 with a limit of $1900
i $2320.48 with a limit of $2300 j $3080.00 with a limit of $3000
2 For a ‘no interest-free period’ credit card, calculate the interest charged on an average
outstanding daily balance of $430 with a percentage interest rate of 14.01% p.a. if the
statement covers a 30-day period.
3 An ‘up to 55 days interest free’ credit card holder used his card on 15 March to obtain
a cash advance of $365, which he repaid on 20 March. What was the amount of interest
charged on the cash advance at the rate of 15.01% p.a.?
4 Here is some information extracted from a monthly credit card statement:
Statement begins: 1 April; Statement ends: 30 April; Payment due date: 25 May
Date Transaction Details Amount
03 Apr HBA 180.00
08 Apr Myer Indooroopilly 89.00
16 Apr Optus 252.25
22 Apr Coles Fairﬁeld 112.90
30 Apr Sportsgirl City 69.95
a Calculate the interest-free period for each of the above transactions.
b Complete the following sentence: ‘To make full use of the “up to 55 days interest
free” option, the purchases should be made at the of the statement
period’.
5 For a ‘55 days interest free’ credit card, calculate the amount of interest charged on an
outstanding balance of $625 which was repaid a fortnight after the due date, given that
the ﬁrst purchase was made on the ﬁrst day of the 30-day period and the annual
percentage rate was 14.98%. (Assume that no other purchases were made after the end
of the statement in question.)
6 Study the statement for the ‘55 days interest-free period’ credit card which follows and
answer these questions.
a What is the length of the period of time covered by this statement?
b What was the closing balance of the previous statement?
3E
WORKED
Example
9
WORKED
Example
10
WORKED
Example
11
MQ Maths A Yr 11 - 03 Page 92 Wednesday, July 4, 2001 2:35 PM
31.
C h a p t e r 3 S p e n d i n g m o n e y 93
c Did the payment of the previous statement balance incur any interest charges?
Explain your answer.
d Explain how the minimum amount due was calculated.
e Explain how the amount of available credit was calculated.
7 The closing balance for the statement in question 6 was repaid in full on 20 June. Find
the amount of interest charged, if:
a no further purchases were made until that date
b a further $300 was spent on 31 May.
Date
29 Apr
30 Apr
3 May
8 Apr
4 May
4 May
5 May
Reference Number
74900052MENTAJ
89101123XYZ
FIZ3456ROGERDUTY
72345670J4U00ABCD
12345678GOODILUV
789108ABCD1234
7654321XYZWRST
MS ILA NORMAN
32 BROWN STREET
BUNDABERG Q 4670
MS ILA NORMAN
Transaction Details
Payment received - thank you
Interest charges
Goverment duties - last month
Travel Wide Melbau
Books & Musical World Carlton AU
SCUD Shoes Noble Park AU
Groovy Music Nth Mlbourne AU
Amount (A) $
22.10-
2.50
0.32
296.18
47.00
128.00
176.00
2345 6789 1234 9299
1 OF 1
2345 6789 1234 9299
$0.00 $22.10 + $650.00 - $22.10 + $650.00
Overdue/Over limit Opening Balance
Available credit $350
Credit limit $1000
Daily percentage rate .04136
Annual percentage rate 15.100
New charges Payments/refunds Closing Balance
8 APRIL 2001
5 MAY 2001
30 MAY 2001
30 MAY 2001
SPECIMEN STATEMENT ONLY – USED FOR PURPOSE OF ILLUSTRATION.
Valid as at 05/01.
MQ Maths A Yr 11 - 03 Page 93 Wednesday, July 4, 2001 2:35 PM
32.
94 M a t h s Q u e s t M a t h s A Ye a r 1 1 f o r Q u e e n s l a n d
TAXI
The exchange rate
When Karla visits New Zealand she will not be able to use Australian currency (for
example to hire a taxi or buy food). She ﬁrst has to convert Australian dollars (A$) to
New Zealand dollars (NZ$). How many NZ$ can she buy with one A$? This varies
from day to day according to what is called the exchange rate. A table showing
exchange rates for all major currencies is shown below.
Karla takes her Australian currency to a bank (preferably after prior arrangement)
and they will sell her New Zealand dollars. Using the table above, we see that they will
sell her NZ$1.2659 for every A$1 she hands over.
YOUR DOLLAR
Buying Selling
$1A eq: $ US .............................. 0.5885............. 0.5829
$1A eq: £ Sterling ....................... 0.3897............. 0.3827
$1A eq: Austrian schil..................... 8.74................. 8.52
$1A eq: $ Canada....................... 0.8691............. 0.8500
$1A eq: Danish Krone................. 4.7340............. 4.8174
$1A eq: EUR............................... 0.6346............. 0.6196
$1A eq: $ Fiji............................... 1.2483............. 1.1935
$1A eq: Finland Markka.............. 3.7729............. 3.6852
$1A eq: French franc .................. 4.1624............. 4.0657
$1A eq: Ger. d-mark ................... 1.2412............. 1.2122
$1A eq: Greek drachma.............. 213.92............. 208.59
$1A eq: $ Hong Kong ................. 4.6236............. 4.5094
$1A eq: India r’pee.................... On App............On App.
$1A eq: Indonesia r/piah............. 5364.0............. 4885.0
$1A eq: £ Ireland ........................ 0.4998............. 0.4881
$1A eq: Italian lira....................... 1229.0............. 1199.0
$1A eq: Japan yen........................ 64.37............... 63.13
$1A eq: Malay ringgit................ On App............On App.
$1A eq: New Taiwan $.................. 18.30.........................
$1A eq: Dutch gilder ................... 1.3985............. 1.3658
$1A eq: $ New Zealand .............. 1.2877............. 1.2659
$1A eq: Norway kroner............... 5.2129............. 5.0657
$1A eq: Papua NG kina............ On App.............. 1.3155
$1A eq: Philippine peso............ On App.............. 25.729
$1A eq: $ Singapore................... 1.0293............. 0.9940
$1A eq: $ Solomons ................... 2.9599............. 2.6311
$1A eq: Sth. Africa rand.............. 4.1083............. 4.0056
$1A eq: Sth. Korea wan.............. 867.10.........................
$1A eq: Spain pesetas................ 105.59............. 103.12
$1A eq: Sri Lanka r’pee ............ On App................ 39.36
$1A eq: Sweden krona ............... 5.3905............. 5.2594
$1A eq: Swiss franc.................... 0.9836............. 0.9611
$1A eq: Thailand baht................... 24.19............... 21.90
$1A eq: Vanuatu valu ................... 80.22............... 77.27
If Karla exchanges A$400 for NZ$, how much will she get?
THINK WRITE
Use the selling price in the table. The bank will sell NZ$1.2659 for A$1
Multiply by 400. A$400 is worth NZ$1.2659 × 400
Write the answer. Karla will receive NZ$506.36
1
2
3
12WORKEDExample
MQ Maths A Yr 11 - 03 Page 94 Wednesday, July 4, 2001 2:35 PM
33.
C h a p t e r 3 S p e n d i n g m o n e y 95
The exchange rate
Use the table of exchange rates on page 94.
1 Convert A$100 to each of the following currencies.
a US dollars b UK pounds
c Italian lira d French francs
2 Convert each of these amounts to Australian dollars.
a 220 US dollars b 320 UK pounds
c 400 EUR (Euros) d 400 000 Indonesian rupiah
3 Angie plans to visit Tokyo on business. She changes A$800 into Japanese yen.
a How much does she receive in yen?
b If the trip is suddenly cancelled and she changes the yen she has back to A$, how
much will she have?
c How much money has she lost because of this ‘double’ exchange?
4 Holly travels to Germany. She changes A$660 into German marks (deutschmarks,
or DM).
a How many German marks does she have?
b When in Germany she spends DM 480. How many marks does she have left?
c If she changes these back to Australian dollars, how much will she have?
5 During an economic crisis in 1998, Indonesia experienced severe inﬂation. In one
week, on Monday, A$1 would have bought 9500 rupiah whereas on Thursday A$1
would have bought 10 900 rupiah. On holidays in Indonesia at this time, Joel
exchanged A$120 and paid for a camera on Monday. How much would he have saved
if he had waited to make the transaction on Thursday (assuming the marked price did
not change).
If Karla exchanges NZ$350 for A$ when she returns, how much will she get?
THINK WRITE
Use the buying price in the table. The bank will buy NZ$1.2877 for A$1
Divide 350 by 1.2877. NZ$350 is worth A$350 ÷ 1.2877
Write the answer. Karla will receive A$271.80
1
2
3
13WORKEDExample
remember
1. When you exchange A$ for other currencies the bank sells you the other
currency. Therefore:
multiply by the selling price
2. When you exchange other currencies for A$ the bank buys the other currency
from you. Therefore:
divide by the buying price
remember
3F
WORKED
Example
12
WORKED
Example
13
Work
SHEET 3.2
MQ Maths A Yr 11 - 03 Page 95 Wednesday, July 4, 2001 2:35 PM
34.
96 M a t h s Q u e s t M a t h s A Ye a r 1 1 f o r Q u e e n s l a n d
1 What are the two types of expenses in a budget?
2 Car insurance costs $440 per year. Write this expense as a weekly amount.
3 John’s after-tax pay is $1800 per fortnight. Express this as a yearly amount.
4 Consider the following readings of an electricity meter:
June 44 500 kWh
September 47 610 kWh
Calculate the electricity consumption for this quarter.
5 If credit card interest is calculated using an annual rate of 18%, what is the daily rate
of interest that is charged?
6 What date is 55 days after March 10?
7 On a credit card statement, what does a ﬁgure of $540.65 in the ‘Closing Balance’
mean?
8 When converting Australian dollars to other currency, which value should be used —
buying or selling?
Questions 9 and 10 refer to the following:
Buy Sell
Pounds sterling 0.3327 0.3127
9 Convert 25 Australian dollars to UK pounds.
10 Convert 50 UK pounds to Australian dollars.
2
MQ Maths A Yr 11 - 03 Page 96 Wednesday, July 4, 2001 4:30 PM
35.
C h a p t e r 3 S p e n d i n g m o n e y 97
Discount
• Discount = Original price − Sale price
• Percentage discount =
• Sale price = Original price − percentage of the original price
= (100 − percentage discount)% of the original price
Proﬁt and loss
• Proﬁt = Sale price − Cost price
• Percentage proﬁt =
• Loss = Cost price − Selling price
• Percentage loss =
Budgeting
• A budget is a table containing an estimate of income and expenditure.
• Expenses can be ﬁxed and unavoidable, or variable.
• Savings can be made by reducing variable expenses.
• All entries in the budget table should be calculated for the same time period as the
budget itself (that is, weekly, monthly, quarterly or yearly).
Credit cards
• For ‘Up to 55 days interest-free period’ cards, the closing balance should be paid in
full by the due date (usually 25 days from the date of the statement). Otherwise,
interest is charged until the balance is repaid.
• For ‘No interest-free period’ cards, interest is calculated from the date of purchase
and until the balance is repaid.
• The bank requires a minimum monthly payment. The amount is shown on the
monthly statement.
Exchange rate
• The rate at which international currencies may be exchanged varies on a daily
basis.
• To change Australian dollars into another currency, multiply by the selling price.
• To change a foreign currency into Australian dollars, divide by the buying price.
summary
Discount
Original price
--------------------------------- 100%×
Profit
Cost price
------------------------ 100%×
Loss
Cost price
------------------------ 100%×
MQ Maths A Yr 11 - 03 Page 97 Wednesday, July 4, 2001 2:35 PM
36.
98 M a t h s Q u e s t M a t h s A Ye a r 1 1 f o r Q u e e n s l a n d
1 If the original price of a ‘Patches’ doll is $40, determine its selling price after a discount of
12.5% is applied.
2 A pair of Italian-made shoes was discounted from $180 to $150. Calculate the percentage
discount.
3 The price on a 5-piece cookware set is reduced by 15% to $212.50. What was the price of
the set before the discount?
4 Copy and complete the following table.
5 If the cost price of
a microwave is $210
and the percentage
proﬁt is 22%, what
is its selling price?
6 Selling a damaged
rug at $125 will
incur 37.5% loss.
What was the cost
price of the rug?
Item
Cost price
($)
Percentage
discount
Discount
($)
Selling price
($)
a 200 12%
b 150 142.50
c 98 9.80
d 16.25 113.75
e 20% 332.80
f 33 % 76
CHAPTER
review
3A
3A
3A
3A
1
3
---
3B
3B
MQ Maths A Yr 11 - 03 Page 98 Wednesday, July 4, 2001 2:35 PM
37.
C h a p t e r 3 S p e n d i n g m o n e y 99
7 Calculate the percentage proﬁt or loss for each of the following:
a a 3-piece lounge room suite: CP $1500, SP $2700
b a 50-mL bottle of French perfume: CP $58, SP $130
c last season’s dress: CP $40, SP $25
d a damaged toy set: CP $18, SP $10.
8 Rose has listed her major expenses as follows:
a Prepare a weekly expenditure budget for Rose. (Put all amounts to the nearest dollar.)
b Calculate the approximate amount that she can save per year if her average weekly take
home pay is $470.
9 Gas is charged at 0.6935c per megajoule (MJ) for the ﬁrst 4000 MJ used and 0.8839c per
MJ thereafter. Find the cost of using 6000 MJ (to the nearest cent).
Item Cost Period
Rent $434 Monthly
Electricity $130 Quarterly
Gas $60 Every 2 months
Phone $300 Quarterly
Car registration $420 Yearly
Car insurance $450 Yearly
Contents insurance $155 Yearly
Health insurance $40 Monthly
Food $100 Weekly
Sport $30 Weekly
Entertainment $20 Weekly
Clothes $120 Monthly
Holidays $1200 Yearly
3B
3C
3D
MQ Maths A Yr 11 - 03 Page 99 Wednesday, July 4, 2001 2:35 PM
38.
100 M a t h s Q u e s t M a t h s A Ye a r 1 1 f o r Q u e e n s l a n d
10 An electricity bill consists of a charge for consumed electricity and the service-to-property
charge. The rates for consumption are $0.1186 for the ﬁrst 1020 kWh and $0.125 per kWh
thereafter. The service charge is constant at $35. Calculate the total charge if the current
reading of the meter shows 56 230 while the previous reading was 53 250.
11 The minimum balance owing on a credit card account is taken to be the larger of $25 or
2.5% of the balance owing, or the excess of the closing balance over a credit limit. If the
closing balance was $1440 with a credit limit of $1400, determine the minimum balance
due.
12 An ‘up to 55 days interest-free period’ credit card was used for purchases which after the
30-day interval totalled $1400.
a Find the minimum amount due if the current credit limit on this card is $2000 and the
bank requires the largest of $25, 2.5% of the outstanding balance or the excess above the
credit limit.
b If the balance was paid 10 days after the due date (which was 25 days from the
statement date), what was the interest at 16% p.a. from the start of the 30-day interval?
13 Ben is in a difﬁcult situation. He needs to convert US$100 to UK pounds and the only way
this can be done is to convert the US$ to A$ and then change the A$ to UK pounds. What
amount will he have in UK pounds? Use the table on page 94.
3D
3E
3E
testtest
CHAPTER
yyourselfourself
testyyourselfourself
3
3F
MQ Maths A Yr 11 - 03 Page 100 Monday, September 24, 2001 7:12 AM
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