Ch11

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Chapter 11 Consumer Arithmetic This chapter deals with solving consumer arithmetic problems involving earning and spending money, simple interest and loans. After completing this chapter you should be able to: ✓ calculate weekly, fortnightly, monthly and yearly earnings for various types of income ✓ calculate net income after considering common deductions ✓ calculate simple interest using the formula ✓ apply the simple interest formula to problems involving investing money ✓ calculate and compare the cost of purchasing goods by different means ✓ calculate a ‘best buy’.

Syllabus reference NS5.1.2 WM: S5.1.1–S5.1.5

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Diagnostic test 1

Carol earns $397.20 per week. This is equivalent to a yearly salary of: A $19 860 B $20 654.40 C $10 327.20 D $19 065.60

2

A salary of $41 808 p.a. is not equivalent to:

7

A $804 per week B $3216 per fortnight

Alex is a real estate agent. He charges the following commission for selling home units: 3% of the first $150 000 and 1.5% for the remainder of the selling price. His commission for selling a home unit for $210 000 would be: A $6300

B $3150

C $4500

D $5400

8

C $3484 per month

4

5

6

Sam earns $360 per week. This is equivalent to a monthly income of: A $1440

B $1260

C $1560

D $1594.29

B $831.60

C $920.70

D $950.40

9

Bettina earns $680 per week. She is entitled to 4 weeks annual recreation leave and receives an additional holiday loading of 17.5%. Her total holiday pay for 4 weeks is: A $2720

B $2839

C $3196

D $476

Deborah is paid $0.48 for each pair of shorts that she sews. If she can sew an average of 12 pairs of shorts per hour and she works a 38-hour week, then her average weekly earnings are:

Sun.

$14.38

$17.98

$21.57

The table shows the award wages for a kitchen hand employed as a casual. The wages of a casual kitchen hand who works 10 hours Monday to Friday, 4 hours on Saturday plus 5 hours on Sunday is:

Chan works a 36-hour week and is paid $19.80 per hour. His total wages for a week in which he works an additional 4 hours at time-and-a-half and 3 hours at double time is: A $712.80

Sat.

Kitchen hand

D $10 452 per quarter 3

Mon.–Fri.

10

11

A $273.22

B $323.57

C $305.62

D $337.93

Simon earns $465 per week. The deductions from his salary each week are tax $140, superannuation $32, health insurance $36.80. His net pay for the week is: A $256.20

B $673.80

C $320.20

D $536.20

The simple interest on $2490 at 4.5% p.a. for 5 years is: A $112.05

B $2602.05

C $560.25

D $3050.25

Michelle invested $3000 for 4 years and earned $780 in interest. The annual rate of interest was:

A $5.76

B $18.24

A 26%

B 6.5%

C $218.88

D $1094.40

C 1.04%

D 4%

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12

13

A camera store offers a discount of 12% for paying cash. The cash price of a camera marked as $499 is:

The following conditions for the deferred payment scheme apply: i

Pay nothing for 12 months.

A $439.10

B $439.12

ii

C $59 90

D $59.88

Balance plus interest to be repaid by equal monthly instalments over the two years following the interest free period.

iii

Simple interest of 16% p.a. is charged for the 3-year period of the agreement.

The method of purchasing goods by which a deposit is paid and the balance is paid off over a short period of time with no interest charged, but the goods cannot be taken until full payment has been made is called: A time payment

The total amount you would have to pay for the television under this scheme is:

B hire purchase

C deferred payment D lay-by 14

15

16

A refrigerator costing $1895 can be bought on terms for $295 deposit and 24 monthly instalments of $84. The total cost of buying the refrigerator on terms would be:

17

A $1498

B $1737.68

C $1977.36

D $2217.04

Using the table on page 344, the monthly repayment on a loan of $16 500 over 3 1--2- years at 12% p.a. is, to the nearest cent:

A $1895

B $2016

A $468.41

B $548.04

C $2311

D $2190

C $639.34

D $483.05

A television set costing $1289 can be bought on the following terms: deposit $289 and the balance to be repaid over 3 years by equal monthly instalments. Simple interest is charged at 11% p.a. If the TV is bought on these terms, the monthly repayment would be:

18

A $36.94

B $47.62

19

C $39.59

D $30.83

Which of the following is the best value? A 350 mL for $1.40 B 750 mL for $2.85 C 2 L for $6.40 D 5 L for $16.50

A television set is advertised as follows:

The price of a TV including GST is $495. The amount of GST included is: A $49.50

B $45

C $445.50

D $450

98sit $N1o 4 depo No repayments for 12 months (conditions apply)

If you have any difficulty with these questions, refer to the examples and questions in the sections listed in the table. Question Section

1–3

4, 5

6

7

8

9

10, 11

12

13

14, 15

16

17

18

19

B

C

D

E

F

G

I

J

L

M

N

O

P

Q

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A. EARNING AN INCOME There are a number of different ways in which people are paid for providing their labour, knowledge, skills and services. If people work for themselves they charge a fee, some people rely on income from investments, but most people work for an employer. By research and discussion, complete the table below that shows the ways people are paid when they work for an employer.

Exercise 11A Earning an income Method of payment

Description

Salary

A fixed amount per year usually paid weekly or fortnightly.

Wages

Based on an hourly rate for an agreed number of hours per week. Usually paid weekly or fortnightly.

Commission

A percentage of the value of goods or services sold is paid. Sometimes a low wage, called a retainer, is paid in addition to this.

Piecework

A fixed amount for each item produced or completed.

Fee

A fixed amount for a service provided.

Casual

A fixed hourly rate for the number of hours worked.

Examples of occupations

Advantanges/ Disadvantages

B. SALARIES AND WAGES Example 1 Georgina earns a salary of $670.85 per week. How much does she earn per: a fortnight b year? a Fortnightly salary = $670.85 × 2 = $1341.70 b Yearly salary = $670.85 × 52 = $34 884.20

(using 1 fortnight = 2 weeks) (using 1 year = 52 weeks)

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Exercise 11B 1

Convert the following weekly salaries into the equivalent salary per: i fortnight ii year a $457 b $1025.60 c $1378.94

Example 2 Harry earns a salary of $48 600 p.a. How much does he earn per: a week

b fortnight

p.a. is short for per annum, which means per year.

c month?

a Weekly salary = $48 600 ÷ 52 (using 1 year = 52 weeks) = $934.62 to the nearest cent b Fortnightly salary = $48 600 ÷ 26 (using 1 year = 26 fortnights) = $1869.23 to the nearest cent c Monthly salary = $48 600 ÷ 12 (using 1 year = 12 months) = $4050

2

Convert the following yearly salaries into the equivalent salary per: i week ii fortnight iii month a $52 400 b $95 370 c $82 900

3

Convert the annual salaries shown in the advertisements below to the equivalent: i weekly ii fortnightly iii monthly salaries a b Fashion Girl's Surfwear Designer $80K Exciting position for the right person. Ph 9444 222

c Cleaner/Housekeeper $40K Rare opportunity to work in fine home. Ph 9666 000

Foreman $110K Experienced foreman required for city project. Ph 9333 000

$80K is a short way of indicating $80 000.

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Example 3 Brad earns $288 per week. What is his monthly salary? 1 month ≠ 4 weeks, so we must calculate Brad’s yearly salary first. Yearly salary = $288 × 52 = $14 976 Monthly salary = $14 976 ÷ 12 = $1248 4

Convert the following weekly salaries into monthly salaries: a $225 b $196 c $674

Example 4 Bruno earns $3600 per month. What is his equivalent weekly salary? Again, we must calculate the yearly salary first. Yearly salary = $3600 × 12 = $43 200 Weekly salary = $43 200 ÷ 52 = $830.77 to the nearest cent 5

Convert the following monthly salaries to the equivalent weekly salaries. a $4200 b $5635 c $3599

6

Scott earns $68 840 p.a., Lisa earns $1350 per week and Paula earns $5700 per month. Who earns the most?

Example 5 Ella works a 35-hour week and is paid $23.86 per hour. What are her weekly wages? Weekly wages = 35 × $23.86 = $835.10 7

Calculate the weekly wages for a person who works a 35-hour week and is paid: a $18.90/h b $26.48/h c $84.50/h

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Example 6 Yoshi earns $1389.50 for working a 35-hour week. What is his hourly rate of pay? Hourly rate = $1389.50 ÷ 35 = $39.70 8

Calculate the hourly rate of pay for a person who works a 35-hour week and is paid weekly wages of: a $994 b $847 c $626.50

Example 7 Sophie works a 38-hour week and is paid $28.75 per hour. How much does she earn in a: a week

b fortnight

c year?

a Weekly wages = 38 × $28.75 = $1092.50 b Fortnightly wages = $1092.50 × 2 = $2185 c Yearly wages = $1092.50 × 52 = $56 810

9

How much does a person earn in a i week ii fortnight iii year if the person works a 38-hour week and is paid: a $43/h b $52.90/h c $75.30/h

Example 8

Remember that 1 month is not equal to 4 weeks!

Fiona earns $16.80 per hour and works a 36-hour week. What are her average monthly wages? Weekly wages = $16.80 × 36 = $604.80 Yearly wages = $604.80 × 52 = $31 449.60 Monthly wages = $31 449.60 ÷ 12 = $2620.80

10

What are the average monthly wages for a person who works a 36-hour week and earns: a $18.20/h b $32.90/h c $76.50/h

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C. ADDITIONAL PAYMENTS Example 1 Ben normally works a 35-hour week and is paid $18.90 per hour. Calculate his total wages for a week in which he works an additional 5 hours overtime at time-and-a-half. Full-time employees who earn wages are expected to work a minimum number of hours each day, or each week, as negotiated in their workplace agreement. Overtime is paid to people who work hours in addition to those required by their workplace agreement and it is paid at a higher rate. The most common rates of overtime payment are: a ‘time-and-a-half’, i.e. the employee is paid at 1 1--2- times the normal hourly rate of pay, e.g. if the normal rate of pay is $20/hour then the employee would be paid ($20 × 1 1--2- =) $30/hour at time-and-a-half. b ‘double time’, i.e. the employee is paid double the normal rate of pay, e.g. if the normal rate of pay is $20/hour then the employee would be paid ($20 × 2 =) $40/hour at double time. Normal pay = $18.90 × 35 = $661.50 Overtime = ($18.90 × 1.5) × 5 = $141.75 Total wages = $661.50 + $141.75 = $803.25

Exercise 11C 1

Dianne normally works a 35-hour week and is paid $23.40 per hour. Calculate her total wages for a week in which she works an additional 4 hours at time-and-a-half.

2

Rebecca normally works a 36-hour week and is paid $17.20 per hour. Calculate her total wages for a week in which she works an additional 3 hours at time-and-a-half.

3

Tim is paid $18.60 per hour for a normal 35-hour week and time-and-a-half for any extra hours worked. How much would he earn for a week in which he worked 40 hours?

Example 2 Ringo normally works a 35-hour week and is paid $36.15 per hour. Calculate his total wages for a week in which he works an additional 5 hours at time-and-ahalf and 3 hours at double time. Normal pay = $36.15 × 35 = $1265.25 Overtime = ($36.15 × 1.5) × 5 + ($36.15 × 2) × 3 = $488.03 Total wages = $1265.25 + $488.03 = $1753.28

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4

Jarrod normally works a 35-hour week and is paid $31.20 per hour. Calculate his total wages for a week in which he works an additional 5 hours at time-and-a-half and 3 hours at double time.

5

Martha normally works a 35-hour week and is paid $28.60 per hour. Calculate her total wages for a week in which she works an additional 8 hours at time-and-a-half and 5 hours at double time.

6

Dana normally works a 38-hour week and is paid $36.15 per hour. Calculate her total wages for a week in which she works an additional 4 hours at time-and-a-half and 2 hours at double time.

7

Erin is paid $24.70 per hour. She is paid the normal rate for the first 7 hours worked each day, time-and-a-half for the next 2 hours and double time thereafter. Calculate her total wages for a day on which she worked: a 8 hours b 9 hours c 10 hours

8

Rob is paid $26.30 per hour. He is paid the normal rate for the first 6 hours worked each day, time-and-a-half for the next 2 hours and double time thereafter. Calculate his total wages for a day on which he worked a 8 hours b 9 hours c 10 hours

Example 3 Don works a 35-hour week and is paid time-and-a-half for any extra hours worked. One week he worked 5 hours overtime and was paid $969. What is his hourly rate of pay? Let the hourly rate of pay be $y, then y × 35 + y × 1.5 × 5 = 969 35y + 7.5y = 969 42.5y = 969 969 y = ----------42.5 = 22.8 i.e. Don earns $22.80 per hour.

9

Angela works a 35-hour week and is paid time-and-a-half for any extra hours worked. One week she worked 4 hours overtime and was paid $1102.90. What is her hourly rate of pay?

10

Daniel works a 35-hour week and is paid time-and-a-half for any extra hours worked. One week he worked 7 hours overtime and was paid $982.80. What is his hourly rate of pay?

11

Pete works his normal 35-hour week plus 4 hours overtime at time-and-a-half and 3 hours at double time. He was paid $1576.38. What is his hourly rate of pay?

12

Glenda is paid $17.90 per hour for working a 35-hour week and time-and-a-half for any extra hours worked. One week she was paid $733.90. How much overtime did she do?

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Example 4 Paul works for a builder and earns $66 000 per year. At the end of the year the builder decides to pay Paul a bonus equal to one month’s salary. Calculate Paul’s bonus. A bonus is an extra payment made to employees, often as a reward for meeting deadlines, exceeding profit targets, producing a high quantity of work etc. Bonus = $66 000 ÷ 12 = $5500 13

Jenni works as a secretary and earns $58 600 per year. At the end of the year her employer pays her a bonus of one month’s salary. Calculate Jenni’s bonus.

14

Abdul is paid $23.50 per hour and works a normal 35-hour week. At the end of the year his employer pays him a bonus of 5% of his yearly wages. Calculate Abdul’s bonus.

15

A company made a profit of $194 000 for the year. The owner decided to share 60% of the profit between her 80 employees as a bonus. Calculate the bonus paid to each of the employees.

16

For completing a project ahead of schedule, each member of the project team was given a bonus of 3% of the after-tax profit made. Calculate the bonus paid to each member of the team if the after-tax profit was $120 000.

17

An engineering design company decided to pay its 12 employees an equal share of 20% of the profit on a special project, as a bonus. If each of the 12 employees received a bonus of $1300, how much profit did the company make on this project?

18

Mark’s total income for the year was $57 337.28. This included a bonus of one month’s salary. What is Mark’s normal annual income (i.e. his income without any bonus)?

Example 5 Tanya earns $810 per week. She is entitled to 4 weeks annual recreation leave and receives an additional holiday loading of 17.5%. Calculate Tanya’s: a holiday loading b total pay for this holiday period. Holiday loading (leave loading) is an extra payment given to employees when they take their annual recreation leave. It is usually calculated as 17.5% of 4 weeks normal salary or wages. a Normal pay for 4 weeks = $810 × 4 = $3240 Holiday loading = 17.5% of $3240 = 0.175 × $3240 = $567

b Holiday pay = $3240 + $567 = $3807 or Holiday pay = 117.5% of 4 weeks pay or Holiday pay = 1.175 × 4 × $810 or Holiday pay = $3807

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19

Kylie earns $760 per week. She is entitled to 4 weeks annual leave and receives an additional holiday loading of 17.5%. Calculate Kylie’s: a holiday loading b total pay for this holiday period

20

Vinh works a normal 35-hour week and is paid $17.90 per hour. He is entitled to 4 weeks annual leave and receives an additional holiday loading of 17.5%. Calculate Vinh’s: a holiday loading b total pay for this holiday period

21

Sunny earns $1230 per fortnight. She is entitled to 4 weeks annual leave and receives an additional holiday loading of 17.5%. Calculate Sunny’s total pay for this holiday period.

22

Wesley earns $43 940 per year. He is entitled to 4 weeks annual leave and receives an additional holiday loading of 17.5%. Calculate Wesley’s total pay for this holiday period.

Example 6 Zoe works as a receptionist. She is entitled to 4 weeks annual leave and receives a holiday loading of 17.5%. One year her total holiday pay was $3092.60. What is Zoe’s weekly salary? Let the weekly salary be $z, then 117.5% of 4 × z = 3092.60 i.e. 1.175 × 4 × z = 3092.60 4.7 × z = 3092.6 3092.6 z = -----------------4.7 = 658 i.e. Zoe earns $658 per week.

23

Tiffany is entitled to 4 weeks annual leave and receives a holiday loading of 17.5%. One year her total holiday pay was $4512. What is Tiffany’s weekly salary?

24

Bin is entitled to 4 weeks annual leave and receives a holiday loading of 17.5%. One year his total holiday pay was $4812.80. Calculate his holiday loading.

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Investigation 1 WM: Reasoning, Applying Strategies

Calculating total pay Here is a spreadsheet to calculate the total pay for the employees of a factory. 1 2 3 4 5 6 7 8

A Employee

B Rate ($/h)

C Normal time (h)

24.72 18.94 23.65 26.36 16.78 15.43

36 36 36 35 35 40

Bill Sue Alan Gillian Natasha Eric

D Overtime (h) time-and-a-half 8 6 4 5

E Overtime (h) double time 4 1 2 3

1

1

F Total pay

1

Copy the spreadsheet.

2

In Cell F3 type the formula ‘= (C3 + D3*1.5 + E3*2) × B3’.

3

To find the total pay for the other employees: • Highlight cells F3 to F8. • Go to Edit. • Select Fill Down.

4

Add some more employees, put in their rate and the number of hours worked. Calculate their total pay.

D. PIECEWORK Piecework is a method of earning money in which the employee is paid for the number of items (pieces) produced or completed.

Example 1 Peta works at home sewing children’s tops. She is paid $3.20 for each top she produces. How much does she earn for a week in which she produces 120 tops? Income = 120 × $3.20 = $384

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Exercise 11D 1

Kerry is paid $0.83 per item for ironing shirts in a factory. How much does she earn for a week in which she irons 240 shirts?

2

Patricia earns $1.03 for each dress she finishes in a clothing factory. If, on average, she can finish 7 dresses per hour and she works a 35-hour week, what are her average weekly earnings?

3

Joe works for a men’s hairdresser and is paid $9 for each haircut he does. If he averages 16 haircuts per day for 6 days, how much does he earn?

4

Terry has a job assembling door locks. One week he assembles 450 locks and is paid $216. How much is he paid for assembling each lock?

5

Wayne works for Sparkler Lighting Co. assembling lamps. He is paid the following daily piecework rates: up to 50 lamps $1.45 /lamp No. assembled for each lamp over 50 and up to 70 $1.60 /lamp 55 for each lamp over 70 $1.90 /lamp Mon. Tues. 48 Here is Wayne’s work card for the week. Wed. 62 Calculate Wayne’s earnings for the week. Thurs. 76 Fri. 52

E. COMMISSION Commission is a method of earning income by which the employee is paid a percentage of the value of their sales.

Example 1 Georgia works as a salesperson and is paid a commission of 6% of the value of her sales. If Georgia sells $12 000 worth of goods one week, what is her commission? Commission = 6% of $12 000 = 0.06 × $12 000 = $720

Exercise 11E 1

A real estate agent charges a commission of 1.5% of the value of any house he sells. Calculate how much he will earn if he sells a house for: a $660 000 b $320 000 c $980 000

2

Joanne has a part-time job selling cosmetics. She is paid a commission of 18% of all sales. Calculate how much she earns in one month if her sales are: a $9000 b $5400 c $2300

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3

Daina is a stockbroker. She receives a commission of 2.5% of the selling price of any shares that she sells. How much commission would she earn for selling shares worth: a $15 000 b $27 000 c $243 000?

The commission earned for buying or selling shares is called brokerage.

Example 2

‘In excess of’ means ‘more than’.

Steve has a job selling clothing. He earns a commission of 19.5% of all weekly sales in excess of $5000. How much commission does he earn on sales of: a $4800

b $8650?

a As Steve’s sales are not more than $5000 he earns no commission. b Excess = $8650 − $5000 = $3650 Commission = 0.195 × $3650 = $711.75

4

Fiona has a job selling cleaning equipment. She earns a commission of 17.5% of all weekly sales in excess of $10 000. How much commission does she earn on weekly sales of: a $8000 b $12 000 c $24 000?

Example 3 Carol sells internet plans. She is paid the following rates of commission: • 1.5% of the first $20 000 worth of sales, • 2.5% of any sales above $20 000. Calculate how much she earns in a week in which her sales are: a $16 000

b $24 000

a Commission = 1.5% of $16 000 = 0.015 × $16 000 = $240 b Commission = 1.5% of $20 000 + 2.5% of ($24 000 − $20 000) = 0.015 × $20 000 + 0.025 × $4000 = $400

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5

Harry sells internet plans. He is paid the following rates of commission: • 2% of the first $20 000 worth of sales, • 3.5% of any sales above $20 000. Calculate how much he earns in a week in which his sales are: a $13 000 b $19 990 c $20 000 d $25 000

6

Zane has a job selling advertising. He is paid a commission on his weekly sales as follows: • 1% for the first $50 000 worth of sales, • 2% of the next $30 000 worth of sales and • 6% of the value of any remaining sales.

e $38 000

‘Rate’ means the percentage rate of commission.

How much would Zane earn in a week in which his sales are: a $46 000 b $50 000 c $65 000 d $80 000 e $92 000 7

Marie is a real estate agent. She charges the following commission for selling home units: • 3% for the first $160 000 of the selling price of the unit, • 2% for the next $50 000 and • 1.5% for the remainder of the selling price. Calculate how much Marie would earn for selling a unit for: a $150 000 b $180 000 c $210 000 d $280 000

e $360 000

Example 4 Chad sells washing machines. He is paid a fixed wage of $200 per week plus a commission of 3% of sales. How much does he earn in a week in which his sales are $5480? Commission = 0.03 × $5480 = $164.40 Weekly earnings = Retainer + Commission = $200 + $164.40 = $364.40

The fixed part of Chad’s wages ($200) is called a retainer.

8

Therese sells printers for computers. She is paid a retainer of $250 per week plus a commission of 4% of her sales. How much does she earn in a week in which she sells $14 970 worth of printers?

9

Michael works for a bookseller. He is paid a retainer of $280 per week plus a commission of 2% of sales. How much does he earn in a week in which his sales are: a $7650 b $3000 c $12 000 d $4700 e $8260?

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10

Complete the following table to show the weekly earnings of the sales team for a pharmaceutical company. Employee R. Roberts H. Low J. Thum K. Trau G. Flood

Retainer

Rate

Sales

Commission

$200 $150 $100 nil nil

2% 5% 6% 8% 9%

$4 200 $8 600 $10 450 $12 900 $15 360

$84

Weekly earnings

11

Jacqueline works as a sales representative for a hardware company. She is paid a retainer of $250 per week plus a commission of 3% of any sales in excess of $6000. How much would she earn in a week in which her sales were: a $4500 b $6400 c $7200 d $8430 e $10 960?

12

Hassan gets a job as a salesperson with a mobile phone company. He is offered two methods of weekly payment: A Retainer of $200 plus commission of 3%, or B No retainer, commission of 8%. a How much would Hassan earn, using each method, if his weekly sales were: i $0 ii $3000 iii $4000 iv $5000 v $10 000? b Which method of payment would you advise Hassan to choose? Give reasons.

13

Phillipa works as a salesperson and is paid a commission of 5% of sales. If Phillipa earns a commission of $821 in one week, what was the value of the goods that she sold?

14

One week Alex sells two cars costing $32 000 each. If he was paid a commission of $1280, what is the rate of commission that he is paid?

15

Joe is paid a retainer plus a commission of 4% of sales. If he receives $980 for selling $18 000 worth of goods, what is the retainer that he is paid?

16

Sally is paid a retainer of $220 per week plus a commission of 3% of sales. One week she earned $478. What was the value of the goods that she sold?

17

Sasha is paid a retainer of $180 per week plus a commission of 6% of sales in excess of $5000. One week he earned $858, what was the value of the goods that he sold?

18

Jacques is paid the following commission for selling computers: 1.5% of the first $25 000 worth of sales 2.5% of any sales in excess of $25 000. One week he earns a commission of $750. What was the value of the computers he sold in this week?

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F. CASUAL AND PART-TIME JOBS Casual and part-time workers are paid for the number of hours worked. The hourly rate is higher than for full-time workers because they may not be entitled to benefits such as holiday leave and sick leave. They may also be paid special rates for weekends and public holidays. The difference between casual and part-time workers is dependent on the number of hours worked.

Example 1 The table below shows part of an award agreement for tradespersons. Tradespersons Bricklayer Carpenter Painter Sign writer Roof tiler

Full-time $ per hour

Casual $ per hour

15.90 16.08 15.63 15.89 15.79

19.08 19.30 18.76 19.07 18.95

a Tom is a full-time bricklayer who works a 35-hour week. Calculate his normal weekly wages. b Bob is a qualified bricklayer who is employed as a casual for 35 hours one week. How much more than Tom does Bob earn? a Tom’s wages = $15.90 × 35 = $556.50 b Bob’s wages = $19.08 × 35 = $667.80 $667.80 − $556.50 = $111.30 i.e. Bob earns $111.30 more than Tom for this week.

Exercise 11F Use the table in example 1 above to do questions 1–4. 1

Emma is a sign-writer who does casual work. She works the following hours one week: Monday 3 hours, Tuesday 4 hours, Wednesday 3 hours, Friday 5 hours. How much does she earn?

2

a Matt is a full-time painter who works a 35-hour week. Calculate his normal weekly wages. b During a busy period he employs a casual to work with him for the 35 hours. How much extra does the casual earn for the week’s work?

3

Jack is a full-time roof tiler. Due to extra demand he employs two casuals to help him for 7 hours on each of 3 days. What is the wages bill for the two casuals?

4

Grant is a carpenter who is employed as a casual. One week he earns $463.20. How many hours did he work?

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Example 2 The table below shows part of the Restaurant Employees Award. Casual $ per hour

Kitchen hand Waiter Grill cook Grade 6 chef

Mon.–Fri.

Sat.

Sun.

14.38 14.92 15.73 18.69

17.98 18.65 19.66 23.36

21.57 22.38 23.59 28.03

Calcuate the wages of a casual waiter who works 8 hours from Monday to Friday, 6 hours on Saturday and 4 hours on Sunday. Wages = 8 × $14.92 + 6 × $18.65 + 4 × $22.38 = $320.78

Use the table in example 2 to do questions 5–8. 5

Emily is employed as a casual kitchen hand for 3 hours per day for each day Monday to Friday. Calculate her wages.

6

Trent is a grade 6 chef who works as a casual on Saturday for 6 hours and Sunday for 6 hours. Calculate his wages.

7

Calculate the wages of a casual grill cook who works the following hours: M

T

W

3 8

T

F

S

S

3

4

6

3

Con is employed as a casual kitchen hand. One week he worked 3 hours on Saturday, 4 hours on Sunday and the remaining hours were all worked in the period Monday to Friday. If he received $226.50 for the week’s work, how many hours did he work from Monday to Friday?

The table below shows the Restaurant Award rates for Grade 1 juniors. Juniors: Casual $ per hour Age (years)

Mon.–Fri.

Sat.

Sun.

17 18 19 20

8.92 10.07 11.51 12.95

11.15 12.58 14.38 16.18

13.38 15.10 17.26 19.42

Use the table above to answer questions 9–12.

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9

How much would a 17-year-old casual employee earn for working: a 8 hours from Monday to Friday b 4 hours on Saturday c 6 hours on Sunday d 6 hours Monday to Friday and 5 hours on Saturday e 10 hours Monday to Friday, 4 hours on Saturday and 3 hours on Sunday?

10

a Ben is 18 years old and does casual work in a coffee shop. How much does he earn for working 4 hours on Saturday and 6 hours on Sunday? b Lara is 20 years old; how much would she earn for working the same hours as Ben?

11

Sarah and Ella work in a café. Sarah is 17 years old and Ella is 18 years old. One week they both work the same shifts, as shown below. M

T

W

T

F

S

S

3

3

–

4

4

5

3

How much more than Sarah does Ella earn for this week? 12

Jenny is 19 years old and does casual work as a waitress on Friday, Saturday and Sunday nights. One week she worked 5 hours on Friday night, 6 hours on Saturday night and was paid $204.24 for the week. How many hours did she work on Sunday night?

G. NET EARNINGS The total amount earned by an employee is called gross income. However this is not the amount of money that the employee actually takes home because deductions are made. The most common deductions are federal income tax, health insurance and superannuation. The amount actually received, after deductions, is called net earnings or take-home pay. Net Earnings = Gross Income − Deductions

Example 1 Julie earns $890 per week. The deductions from her salary each week are: tax $265.83, health insurance $43.59 and superannuation $42.70. Calculate her net earnings each week. Total deductions = $265.83 + $43.59 + $42.70 = $352.12 Net Earnings = $890 − $352.12 = $537.88

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Exercise 11G 1

Patricia earns $940 per week. The deductions from her salary each week are: tax $280.78, health insurance $37.62 and superannuation $56.40. Calculate her net earnings each week.

2

David earns $760 per week. The deductions from his salary each week are: tax $212.80, health insurance $32.40 and superannuation $30.40. Calculate his net earnings each week.

3

Sue earns $43.80 per hour and works a 36-hour week. The deductions from her wages each week are: tax $536.11, superannuation $94.61 and health insurance $51.25. She pays union fees of $7.60 and also has $50 per week paid directly into an investment account. Calculate her take-home pay each week.

4

Yuchen earns $63.70 per hour and works a 38-hour week. The weekly deductions from her wages include: tax $871.42, superannuation $217.85 and health insurance $44.90. She also pays $5 per week to her favourite charity and has $70 per week paid into a special savings account. Calculate her take-home pay.

5

James’s gross salary is $1230 per week. His employer deducts 31% of his gross earnings for tax and he contributes 9% of his gross income into a superannuation fund. His health fund contributions are $39.99 and professional association fees are $13.20 per week. Calculate his net weekly earnings.

H. BUDGETS A budget is a financial plan for the future. It is a means by which you can save for future purchases and avoid over-spending. To prepare a budget you need to determine your expected income and estimate your expected expenses. Your income needs to be larger than your expenses if you are to live within your means. To prepare a budget, for a given time period (e.g. week, month, year): • calculate your total income • estimate your total expenses • calculate income minus expenses • adjust income or expenses if necessary.

Example 1 Karen has just started work and still lives at home with her parents. Her weekly take-home salary is $480. Each week she pays $110 for board, $49 for fares and $35 for lunches. She spends $120 per week on entertainment, $95 per fortnight on personal items and $330 per month on clothes. a Prepare an annual budget for Karen. b Karen wants to go on an overseas holiday in 3 years time. The cost of the holiday is $7899. Determine whether or not Karen will be able to take her holiday. c If Karen will not have sufficient money to take her holiday, how could she adjust her budget so that she would be able to afford the holiday?

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Salary ($480 × 52) = $24 960 Board ($110 × 52) = $5720 Fares ($49 × 52) = $2548 Lunches ($35 × 52) = $1820 Entertainment ($120 × 52) = $6240 Personal items ($95 × 26) = $2470 Clothes ($330 × 12) = $3960 Total = $22 758 Income − Expenses = $2202 Karen has an excess of income over expenses so she will be able to live satisfactorily on this budget and save some money. b If Karen saves all her money, then in 3 years she will have $2202 × 3 = $6606. She is $7899 − $6606 = $1293 short of her target. c Karen must either increase her income or decrease her expenses by at least ($1293 ÷ 3 =) $431 per year. She could increase her income by finding employment with a higher salary or getting a second job. She could decrease her expenses by, for example, reducing her spending on clothes to $290 per month. She would then save ($40 × 12 =) $480 per year on expenses. Or, if she reduced her spending on entertainment to $110 per week, she would save ($10 × 52 =) $520 per year. She would then be able to afford to take the holiday. a Income Expenses

Exercise 11H 1

Naomi lives at home with her parents. Her weekly take-home salary is $590. Each week she pays $100 for board, $53 for fares and $42 for lunches. She spends $150 per week on entertainment, $84 per fortnight on personal items, $380 per month on clothes. a Prepare an annual budget for Naomi. b Naomi wants to go on an overseas holiday in 3 years time. The cost of the holiday is $12 550. Determine whether or not Naomi will be able to take her holiday.

2

Matthew’s net earnings are $540 per week. He shares a house for which he pays $120 per week rent. Each week he spends $110 on food, $145 on entertainment and $25 on personal items. The loan repayments on his car are $380 per month. He spends $45 per week on petrol and the six-monthly service is $380. Annual registration and insurance amount to $1148. His mobile phone costs him $24 per month. a Prepare an annual budget for Matthew. b How could Matthew adjust his budget so that he can live within his means?

3

George is a full-time TAFE student. He receives an allowance of $320 per fortnight from the government and averages earnings of $120 per week from his part-time job. His expenses are: rent $320 per month, food $90 per week, phone $110 per quarter, entertainment $70 per week, books $350 per year. a Prepare an annual budget for George. b George has already saved the money to buy a car. He estimates that it would cost him $30 per week for petrol, $80 per month for maintenance and $840 per year for registration and insurance. Can George afford to own and run a car?

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4

Kate and Robert want to prepare a budget for next year and have gathered the following information. Income: Kate’s take-home pay is $490 per week and Robert clears $380 per week. Interest of $230 from investments is expected in February and August of next year. Expenses: Home loan repayments, $980 per month Food, $160 per week Electricity, $480 each quarter Telephone, $110 per month Council rates, $340 each quarter Water rates, $186 per quarter Car registration and insurance, $780 per year Comprehensive car insurance, $810 per year Car loan repayments, $108 per week Car running expenses, average $190 per month Clothing, average $350 per month Personal items, $45 per week a Prepare an annual budget for Kate and Robert. b In order to reduce the cost of their loans, Kate and Robert wish to increase their loan repayments. Can they afford to do this? What advice would you give Kate and Robert?

I. SIMPLE INTEREST When investing money in a financial institution, such as a bank, the bank pays for the use of your money. This payment by the bank is called interest and is calculated as a percentage of the amount invested. Similarly, when you borrow money a charge is made for the use of the bank’s money. This charge is also called interest and is calculated as a percentage of the amount borrowed. There are two methods of calculating the interest: simple interest and compound interest. If the interest is calculated as a fixed percentage of the original amount invested (or borrowed), then it is called simple interest.

Example 1 Calculate the simple interest if $8000 is invested for 3 years at 4.5% p.a. Interest for 1 year = 4.5% of $8000 = 0.045 × $8000 = $360 Interest for 3 years = $360 × 3 = $1080 If $P is invested for T years at r % p.a. then the simple interest, I, can be found using the formula: I = PRT

r where P is called the principal, R is called the interest rate p.a.  R = -------- and T is the time in years.  100

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Example 2 Use the simple interest formula to calculate the simple interest earned on an investment of $10 800 at 3.9% p.a. for 5 years. I = PRT = $10 800 × 0.039 × 5 = $2106

Exercise 11I 1

Calculate the simple interest if $7000 is invested for 2 years at 5% p.a.

2

Calculate the simple interest if $12 000 is invested for 4 years at 3% p.a.

3

Complete the following table. Principal

Annual interest rate

Time invested (years)

$5 800 $15 000 $24 000 $6 500 $18 000 $9 300 $6 000

7% 3.5% 4.5% 5% 2.8% 3.4% 3%

4 3 5 6 2 4 3

Simple interest

Example 3 Calculate the amount to which $7000 will grow in 3 years if invested at 6.5% p.a. simple interest. Interest = $7000 × 0.065 × 3 = $1365 Amount after 3 years = $7000 + $1365 = $8365

4

Calculate the amount to which $9000 will grow in 3 years if invested at 6.5% p.a. simple interest.

5

Calculate the amount to which $20 000 will grow in 5 years if invested at 4% p.a. simple interest.

6

If I invest $13 500 at 7.4% p.a. simple interest, how much will I have in 4 years time?

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Example 4 Calculate the simple interest earned on $6000 at 8% p.a. for 16 months. 16 The number of years the money is invested = ------ , hence 12 16 Interest = $6000 × 0.08 × -----12 = $640 7

Calculate the simple interest earned on the following investments: a $5000 at 9% p.a. for 18 months b $7000 at 8% p.a. for 15 months c $12 500 at 10% p.a. for 9 months d $3800 at 12% p.a. for 27 months e $24 000 at 7.8% p.a. for 45 months

Example 5 Rene invested $4700 at 6% p.a. simple interest and earned $1128 in interest. For how long did he invest his money? Interest for 1 year = 0.06 × $4700 = $282 No. of years invested = $1128 ÷ $282 =4 i.e. Rene invested his money for 4 years. 8

Harry invested $13 000 at 6% p.a. simple interest and earned $4680 in interest. For how long did he invest his money?

9

Joy invested $2800 at 3.5% p.a. simple interest and earned $490 in interest. For how long did she invest her money?

Example 6 Colin invested $4000 for 5 years and earned $700 in interest. What was the annual rate of simple interest? Interest for 1 year = $700 ÷ 5 = $140

140 Annual interest rate = ------------- × 100% 4000 = 3.5%

10

Kim invested $6000 for 5 years and earned $2100 in interest. What was the annual rate of simple interest?

11

Lauren invested $17 000 for 4 years and earned $3128 in interest. What was the annual rate of simple interest?

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J. PURCHASING GOODS BY CASH When paying cash to purchase goods, the cost is rounded to the nearest 5 cents.

Example 1 How much would you actually pay in cash to purchase goods that cost: a 87 cents

b $2.43

c $2.99?

Rounding off to the nearest 5 cents, you would pay a 85 cents b $2.45

c $3.00

Exercise 11J 1

2

How much would you actually pay in cash to purchase goods that cost: a 76c b $5.28 c $2.79 d $7.31 e $3.97 g $16.23 h $21.99 i $54.85 j $39.14 k $17.36 Calculate the change given when: a $10 is offered to pay for goods worth $5.83 c $10 is offered to pay for goods worth $8.22 e $20 is offered to pay for goods worth $18.36 g $50 is offered to pay for goods worth $28.57

b d f h

f l

$8.52 $69.98

$10 is offered to pay for goods worth $4.99 $20 is offered to pay for goods worth $12.84 $20 is offered to pay for goods worth $6.01 $50 is offered to pay for goods worth $48.19

Example 2 An electrical store offers a discount of 12% for cash purchases. Find the cash price of a television set marked as $799. Discount = 12% of $799 or Price = 88% of $799 = 0.12 × $799 = 0.88 × $799 = $95.88 Price = $799 − $95.88 = $703.12 = $703.12 Rounding the discounted price to the nearest 5 cents, the cash price is $703.10.

3

An electrical store offers a discount of 12% for cash purchases. Find the cash price of a sound system marked at $479.

4

A builders’ hardware store offers a discount of 6% for cash purchases. Find the cash price for goods worth: a $147 b $463 c $224 d $180.56 e $68.99

5

List some advantages and disadvantages of using cash to purchase goods.

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K. USING CREDIT CARDS A credit card is a convenient method for purchasing and paying for goods. You can pay for the goods later, you don’t need to carry large amounts of cash, you can take advantage of sales, and a monthly statement of purchases is provided. The financial institution issuing the card charges an annual fee and if the balance owing at the end of each month is paid within the interest-free period (which varies from 0 to 55 days) then no further costs are involved. However, if any balance is owing after the interest-free period has finished then there is an initial charge equal to one month’s interest on the balance outstanding and, in addition, an interest charge compounded daily from the end of the interest free period. There is a minimum payment that must be made each month. It is also possible to obtain cash advances up to a certain limit. In this case interest is charged daily from the time the cash is withdrawn.

Exercise 11K

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Use the statement on the previous page to answer the following questions. 1

What is the: a date the statement period starts and ends c daily interest rate for purchases e available credit g minimum payment that must be made

b annual interest rate for purchases d credit limit f date by which payment must be made

2

Calculate the: a total purchases made b total credits (CR) c Opening Balance + Purchases + Financial Institution Tax − Credits. Is this the closing balance?

3

What percentage is the minimum repayment due of the closing balance?

4

List some advantages and disadvantages of using credit cards to purchase goods.

L. LAY-BY Some retail stores allow customers to purchase goods by a method called lay-by. Under a lay-by agreement a deposit is paid and the goods are put aside. The remainder of the cost price must be paid off within a given period of time. The customer cannot collect the goods until the balance is completely repaid, but no interest is charged.

Example 1 Nick decides to lay-by a tool set costing $849 and pays a deposit of $100. Over the next 3 months he makes repayments of $150, $85, $90, $160, $120 and $70. How much more does he have to repay to be able to collect the tool set? Total amount repaid = $100 + $150 + $85 + $90 + $160 + $120 + $70 = $775 Balance = $849 − $775 = $74 Nick still has $74 to pay before he can collect the tool set.

Exercise 11L 1

Ben decides to lay-by an electric saw costing $569 and pays a deposit of $120.Over the next 3 months he makes repayments of $60, $45, $90, $70, $70 and $80. How much more does he have to repay to be able to collect the saw?

2

Zoe lay-bys a bike costing $225 for her son’s birthday and pays a deposit of $60. Each week for the next 5 weeks she makes payments of $25. How much more does she have to repay to be able to collect the bike?

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Example 2 Isabella lay-bys a dress costing $324 and pays a deposit of $50. She wants to collect the dress in approximately 3 months time to wear to a wedding. If she pays off the balance by making 3 equal monthly instalments, calculate: a the balance to be repaid

b the amount of each monthly instalment

a Balance = $324 − $50 = $174

b Monthly instalment = $174 ÷ 3 = $58

3

Martine lay-bys a dress costing $485. She pays a deposit of $80 and pays off the balance by making 4 equal monthly instalments. Calculate: a the balance to be repaid b the amount of each monthly instalment

4

Yvonne lay-bys a new electric oven costing $778. She is required to pay a 10% deposit and repay the balance by 12 equal weekly instalments. Calculate the: a deposit b balance to be repaid c amount of each weekly instalment

5

Josh lay-bys a new DVD player costing $456. He is required to pay a 15% deposit and repay the balance by 6 equal fortnightly instalments. Calculate the: a deposit b balance to be repaid c amount of each fortnightly instalment

6

List some advantages and disadvantages of using the lay-by method to purchase goods.

M. BUYING ON TERMS

Buying on terms is sometimes called hire purchase.

When an item is bought on terms a deposit is paid and the item is received immediately. The balance of the price is borrowed and this balance plus simple interest is repaid by equal instalments over a fixed term.

Example 1 A refrigerator costing $2998 can be bought on terms for $299 deposit and 24 monthly instalments of $139.45. a Calculate the total cost of buying the refrigerator on terms. b How much would you save by paying cash? a Total cost = $299 + 24 × $139.45 = $3645.80 b Amount saved by paying cash = $3645.80 − $2998 = $647.80

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Exercise 11M 1

A refrigerator costing $2599 can be bought on terms for $399 deposit and 24 monthly instalments of $115.50. a Calculate the total cost of buying the refrigerator on terms. b How much would you save by paying cash?

2

A laptop computer costing $2298 can be bought on terms for $229 deposit and 18 monthly repayments of $135.60. a Calculate the total cost of buying the computer on terms. b How much would you save by paying cash?

3

A home theatre system costing $1598 can be bought on the following terms: 10% deposit and 48 weekly instalments of $37.15. a Calculate the total cost of buying the system on terms. b How much would you save by paying cash?

4

A hi-fi sound system costing $879 can be bought on the following terms: deposit 15% and 26 fortnightly repayments of $39.98. a Calculate the total cost of buying the system on terms. b How much would you save by paying cash?

Example 2 A computer costing $3498 can be bought on terms for $300 deposit and 36 monthly repayments of $124.17. a b c d e

Calculate the total cost of buying the computer on terms. Find the total amount of interest charged. Calculate the amount of interest paid annually. What was the amount of money borrowed? Calculate the annual rate of interest charged.

a Total cost = $300 + 36 × $124.17 b Interest = $4770.12 − $3498 = $4770.12 = $1272.12 c Annual interest = $1272.12 ÷ 3 = $424.04 d Amount borrowed = Balance owing after paying the deposit = $3498 − $300 = $3198 e Annual interest rate = =

annual interest × 100% amount borrowed $424.04 × 100% $3198

= 13.3%

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5

A camera costing $1499 can be bought on terms for $200 deposit and 24 monthly repayments of $74.69. a Calculate the total cost of buying the camera on terms. b Find the total amount of interest charged. c Calculate the amount of interest paid annually. d What was the amount of money borrowed? e Calculate the annual rate of interest charged.

6

A television costing $5890 can be bought on terms for $300 deposit and 36 monthly repayments of $199.53. a Calculate the total cost of buying the computer on terms. b Find the total amount of interest charged. c Calculate the amount of interest paid annually. d What was the amount of money borrowed? e Calculate the annual rate of interest charged.

7

A dining room suite was advertised for $5990 or $500 deposit and 48 monthly repayments of $187.58. a Calculate the total cost of buying the dining room suite on terms. b Find the total amount of interest charged. c Calculate the amount of interest paid annually. d What was the amount of money borrowed? e Calculate the annual rate of interest charged.

Example 3 A wide-screen plasma TV set can be bought for $7998 cash or on the following terms: deposit $799, the balance to be repaid over 2 years by 24 equal monthly repayments. Simple interest is charged on the balance at 12% p.a. If the TV is bought on terms calculate: a the balance owing after the deposit is paid b the interest charged on the balance owing c the monthly repayment a Balance owing = $7998 − $799 b Interest = $7199 × 0.12 × 2 = $7199 = $1727.76 c Balance owing + Interest = $7199 + $1727.76 = $8926.76 Monthly repayment = $8926.76 ÷ 24 = $371.95 (to the nearest cent) 8

Peter buys a second-hand car advertised for $9600 on the following terms: deposit $2000, the balance to be repaid over 2 years by equal monthly repayments. Simple interest is charged at 12% p.a. Calculate: a the balance owing b the interest charged on the balance owing c the monthly repayment

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9

Angela buys a car advertised for $12 900 on the following terms: deposit $3000, the balance to be repaid over 3 years by equal monthly repayments. Simple interest is charged at 9% p.a. Calculate: a the balance owing b the interest charged on the balance owing c the monthly repayment

10

Adrienne buys a washing machine advertised for $4990 on the following terms: deposit 10% and the balance repaid over 2 years by equal monthly repayments. Simple interest is charged at 15% p.a. Calculate: a the deposit b the balance owing c the interest charged on the balance owing d the monthly repayment

11

Robin buys a new car advertised for $19 900 on the following terms: deposit 15%, the balance to be repaid over 4 years by equal monthly repayments. Simple interest is charged at 11.9% p.a. Calculate: a the deposit b the balance owing c the interest charged on the balance owing d the monthly repayment

12

List some advantages and disadvantages of purchasing goods on terms.

Investigation 2 WM: Applying Strategies, Reasoning

Monthly repayments The spreadsheet below calculates the monthly repayment when an item is bought on terms. A 1 Item

B

C

D

E

F

G

H

Cash Deposit Interest Repayment Balance Interest on Monthly price ($) rate (% p.a.) period (years) owing balance Repayment

2 Computer

2998

298

12

2

3 TV

1899

189

15

2

4 Furniture

4672

250

11.6

3

5 Air conditioner

7659

1000

14.2

4

6 Refrigerator

3628

628

9.9

3

1

Copy the spreadsheet.

2

In Cell F2 type the formula ‘= B2 − C2’. This is the balance owing after the deposit is paid.

3

In Cell G2 type the formula ‘= F2*D2/100*E2’. This is the amount of interest charged on the balance.

☞

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4

In Cell H2 type the formula ‘= (F2 + G2)/(E2*12)’. This is the monthly repayment.

5

If the computer was paid off over 3 years instead of 2: a What would be the monthly repayment? b How much more interest would be paid? (Hint: Change repayment period to 3 and use the arrow key to move right.)

6

Try changing the repayment period and/or the interest rate for the other items to investigate the effect on the monthly repayment and the amount of interest paid.

7

Use some advertisements from newspapers or magazines to check the advertised monthly repayment for several items. If there is a difference, investigate for hidden charges.

N. DEFERRED PAYMENT Many advertisements make statements such as ‘No repayments for 12 months’ or ‘Pay nothing until next June’. Under these arrangements the goods may be taken immediately the finance contract is approved and no payment needs to be made for the agreed period of time. This type of financial arrangement is known as a deferred payment scheme.

Example 1 Michael sees a television set advertised as shown opposite. When Michael approaches the retailer to buy the television, he is given the conditions opposite for the deferred payment scheme. a Calculate the total amount Michael would have to pay for the television under this scheme. b Calculate the monthly instalments.

$2498

NO DEPOSIT NO DEPOSIT NO REPAYMENTS NO REPAYMENTS FOR 1212 MONTHS FOR MONTHS (Conditions apply.)

Conditions: (i) Pay nothing for 12 months. (ii) Balance plus interest to be repaid by equal monthly instalments over the two years following the interest-free period. (iii) Simple interest of 16% p.a. is charged for the 3-year period of the agreement. (iv) Establishment fee of $110. (v) Account service fee of $2.95 per month for the 3-year period of the agreement.

a Michael must pay interest on $2498 for 3 years. Interest = $2498 × 0.16 × 3 = $1199.04 Total cost = Price + Interest + Establishment fee + Account service fee = $2498 + $1199.04 + $110 + $2.95 × 36 = $3913.24 b Michael has to repay this amount by 24 equal instalments. Monthly instalment = $3913.24 ÷ 24 = $163.05

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Exercise 11N 1

$2999

A computer is advertised as shown opposite. a Calculate the total amount you would have to pay for the computer under this scheme. b Calculate the monthly instalments.

NO DEPOSIT NO REPAYMENTS FOR 12 MONTHS (Conditions apply.)

Conditions: (i) Pay nothing for 12 months. (ii) Balance plus interest to be repaid by equal monthly instalments over the two years following the interest-free period. (iii) Simple interest of 16% p.a. is charged for the 3-year period of the agreement. (iv) Establishment fee of $110. (v) Account service fee of $2.95 per month for the 3-year period of the agreement.

2

A second-hand car is advertised as follows.

$8599 No Deposit No Repayments for 12 Months

a Calculate the total amount you would have to pay for the car under this scheme. b Calculate the monthly instalments.

(Conditions apply.) Conditions: (i) Pay nothing for 12 months. (ii) Balance plus interest to be repaid by equal monthly instalments over the three years following the interest-free period. (iii) Simple interest of 15% p.a. is charged for the 4-year period of the agreement. (iv) Establishment fee of $125. (v) Account service fee of $2.55 per month for the 4-year period of the agreement.

3

A sofa bed is advertised for $1598 with no deposit and no repayments for 6 months. The conditions of the agreement are: (i) Pay nothing for 6 months. (ii) Balance plus interest to be repaid by equal monthly instalments over the 12 months following the interest free period. (iii) Simple interest of 1.5% per month is charged for the 18 months of the agreement. (iv) Establishment fee of $135. (v) Account service fee of $2.85 per month, for the 18 month period of the agreement a Calculate the total amount you would have to pay for the bed under this scheme. b Calculate the monthly instalments.

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O. LOANS To purchase expensive items some people prefer to organise a personal loan through a bank, credit union or other financial institution. Personal loans often cost less than other forms of payment, such as buying on terms or deferred payment schemes, because of lower interest rates and lower fees. Banks have tables from which the monthly repayments can be determined. For example, the table below shows the monthly repayments of principal plus interest on each $1000 borrowed for various interest rates. Monthly repayments on each $1000 borrowed Annual interest rate Loan term (months)

10.0%

10.5%

11.0%

11.5%

12.0%

12.5%

13.0%

13.5%

14.0%

12

87.9159 88.1486 88.3817 88.6151 88.8488 89.0829 89.3173 89.5520 89.7871

18

60.0571 60.2876 60.5185 60.7500 60.9820 61.2146 61.4476 61.6811 61.9152

24

46.1449 46.3760 46.6078 46.8403 47.0735 47.3073 47.5418 47.7770 48.0129

30

37.8114 38.0443 38.2781 38.5127 38.7481 38.9844 39.2215 39.4595 39.6984

36

32.2672 32.5204 32.7387 32.9760 33.2143 33.4536 33.6940 33.9353 34.1776

42

28.3168 28.5547 28.7939 29.0342 29.2756 29.5183 29.7621 30.0071 30.2532

48

25.3626 25.6034 25.8455 26.0890 26.3338 26.5800 26.8275 27.0763 27.3265

54

23.0724 23.3162 23.5615 23.8083 24.0566 24.3064 24.5577 24.8104 25.0647

60

21.2470 21.4939 21.7424 21.9926 22.2444 22.4979 22.7531 23.0098 23.2683

Example 1 Use the table above to calculate the monthly repayments on a loan of $8300 for 4 years at 13%. From the table, the monthly repayment for each $1000 borowed = $26.8275 Monthly repayments for $8300 = $26.8275 × 8.3 = $222.67 to nearest cent

Exercise 11O 1

Use the table above to calculate the monthly repayments on a loan of $9000 for 3 years at 12%.

2

Use the table above to calculate the monthly repayments on loans of: a $85 000 for 2 1--2- years at 10.5% b $67 000 for 5 years at 11% c $14 600 for 3 1--2- years at 13.5% e $12 450 for 42 months at 11.5%

d $16 000 for 54 months at 14%

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Example 2 a Use the table to calculate the monthly repayments on a loan of $6900 for 3 years at 12.5%. b Calculate the total cost of the loan if there is a loan application fee of $180. a Monthly repayment = $33.4536 × 6.9 = $230.83 b Total cost of loan = $230.83 × 36 + $180 = $8489.87

3

a Use the table to calculate the monthly repayments on a loan of $7000 for 3 years at 11%. b Calculate the total cost of the loan if there is a loan application fee of $180.

4

a Use the table to calculate the monthly repayments on a loan of $15 500 for 4 years at 13.5%. b Calculate the total cost of the loan if there is a loan application fee of $250.

5

Calculate the cost of the following loans. (Calculate the monthly repayment first.) a $5000 for 3 1--2- years at 12%, loan application fee $300 b $12 000 for 4 1--2- years at 14%, loan application fee $200 c $8500 for 2 years at 10.5%, loan application fee $260 d $9400 for 60 months at 11.5%, loan application fee $210 e $18 000 for 42 months at 10%, loan application fee $190

Use the table given for questions 6–8. 6

Terry borrowed $20 000 at 11.0% p.a. His monthly repayments were $654.77. Over what period of time did he borrow the money?

7

Natasha borrowed $18 000 over 4 1--2- years. The monthly repayments were $446.59. What was the interest rate charged?

8

Bill took out a loan over 3 years at 12.5% p.a. His monthly repayments were $802.89. How much money did Bill borrow?

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P. COMPARING PRICES Example 1 Which is the better buy, 3 kg of apples for $13.38 or 5 kg for $21.60? Method 1

Method 2

Find the cost per kilogram: 3 kg for $13.38 = ($13.38 ÷ 3) per kg = $4.46 per kg 5 kg for $21.60 = ($21.60 ÷ 5 ) per kg = $4.32 per kg 5 kg for $21.60 is the better buy because the cost per kilogram is cheaper. Find the amount of apples per dollar: 3 kg for $13.38 = (3 ÷ 13.38) kg for $1 = 0.224 kg for $1 5 kg for $21.60 = (5 ÷ 21.6) kg for $1 = 0.231kg for $1 5 kg for $21.60 is the better buy because you get more apples per dollar.

Exercise 11P 1

Which is the better buy: a 3 kg of oranges for $4.00 or 5 kg for $6.60? b 2 kg of meat for $15.96 or 3 kg for $23.97? c 1.5 litres of soft drink for $2.70 or 2 litres for $3.50? d a 350 g packet of cereal for $2.20 or a 575 g packet for $3.69? e a 150 mL bottle of sauce for $2.29 or a 750 mL bottle for $10.99?

2

Which of the following is the best value? a Tuna: 95 g tin for $1.33, 185 g tin for $2.17, 425 g tin for $3.50 b Cordial: 750 mL for $1.12, 2 L for $3.10, 4 L for $6.06 c Sandwich spread: 115 g jar for $1.43, 175 g jar for $1.96, 235 g jar for $2.49 d Chocolate: 55 g block for $0.98, 250 g block for $2.58, 375 g block for $3.94 e Milk Flavouring: 375 g tin for $2.69, 750 g tin for $5.29, 1.25 kg tin for $8.28

3

Harry’s Car Hire charges $28 per day with no limit on the number of kilometres travelled to hire a new Toyota Corolla. Ray’s Car Rental charges $20 per day plus 8 cents per kilometre travelled to rent the same car. Which company is cheaper if you are likely to travel, each day: a 80 km b 100 km c 150 km?

4

To hire a new Holden Commodore each day, Bob’s Rentals charges $45 plus 7 cents per kilometre travelled. Sophie’s Rentals charges $48 per day plus 5 cents per kilometre travelled. Which company is cheaper if you are likely to travel, each day: a 100 km b 300 km c 150 km?

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5

On savings accounts, Bob’s Bank charges a management fee of $5.50 per month. The first five transactions are free and then a fee of 28 cents per transaction is charged. Bill’s Bank charges a monthly management fee of $6.00 plus 9 cents per transaction. Which bank is cheaper to use if your average number of monthly transactions is: a 5 b 10 c 15?

6

The Mobile Phone Company offers two plans. Plan A has a connection fee of $12 per month and calls cost 21 cents/30 seconds. Plan B has a connection fee of $15 plus call charges of 16 cents/30 seconds. Which plan would be cheaper, and by how much, if your expected calls per month were: a 20 minutes b 30 minutes c 50 minutes?

7

Terry’s Telecommunications has two mobile phone plans. The Starnet Plan has a monthly fee of $25, 50 free calls then 45 cents/call. The Supernet Plan has a monthly fee of $35, 100 free calls and then 35 cents/call. Which plan is cheaper, and by how much, if the expected number of calls per month total: a 50 b 100 c 200?

Q. GOODS AND SERVICES TAX (GST) A federal tax, known as the GST, is applied to most goods and services in Australia. It is calculated at the rate of 10% of the purchase price of the goods or services. The price excluding the GST (i.e. the price before the GST is added) is written ‘price excluding GST’ and the price including the GST (i.e. the price after the GST is added) is written ‘price including GST’.

Example 1 Calculate the GST and the price including GST on a camera with a listed price of $710, price excluding GST. GST = 10% of $710 = 0.1 × $710 = $71 Price including GST = $710 + $71 = $781

Exercise 11Q 1

Calculate the GST and the price including GST on the following items: a microwave oven $440, price excluding GST b computer $3690, price excluding GST c TV repairs $258, price excluding GST d DVD player $397, price excluding GST e plumber’s bill for services $1800, price excluding GST

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Example 2 Calculate the price including GST on a mobile phone listed as $299, price excluding GST. Price including GST = list price + 10% of the list price = 110% of the list price = 1.10 × $299 = $328.90

2

Calculate the price including GST on the following items whose price, excluding GST, is given. a car battery $95, price excluding GST b ticket to Rugby Final $225, price excluding GST c bottle of wine $17, price excluding GST d printer repairs $336, price excluding GST e electrician’s bill $457, price excluding GST

Example 3 Calculate the GST included on a television set advertised for $899, price including GST. Price excluding GST + GST = $899 i.e. price excl. GST + 10% of price excl. GST = $899 i.e. 110% of price excl. GST = $899 1.1 × price excl. GST = $899 price excl. GST = $899 ÷ 1.1 = $817.27 GST = $899 − $817.27 = $81.73

3

Calculate the GST included in the price of the following items: a TV $1189, price including GST b lounge suite $4970, price including GST c BBQ chicken $10.89, price including GST d perfume $148, price including GST e dress $124, price including GST

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Example 4 Calculate the GST included on a television set advertised for $899, price including GST. Note that example 3 above could have been calculated as follows. 110% of price excl. GST = $899 11 i.e. ------ × price excl. GST = $899 10 11
price excl. GST = $899 ÷ -----10 10 = ------ × $899 11 1 Hence GST = ------ × $899 11 = $81.73 This leads to the ‘GST Rule of Thumb’ which 1 states that GST = ------ of price including GST. 11

4

Use the GST Rule of Thumb to check your answers to question 3.

5

Find the missing amounts in the following. a

Tax Invoice Services rendered = $850 GST = Total including GST =

c Tax Invoice Services rendered = GST = $48.80 Total including GST = $536.80

b

Tax Invoice Taxable items Shirt $69.95 Tie $29.95 Total including GST = $99.90 GST included in total =

d Tax Invoice Taxable items 5 CDs @ $32.90 including GST = GST included in total =

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non-calculator activities 1

David earns $300 per week. How much does he earn per: a fortnight b year c month?

2

Convert a salary of $43 800 p.a. to the equivalent salary per month.

3

Alice works a 35-hour week and is paid $20 per hour. How much does she earn for a week in which she works an additional 4 hours at time-and-a-half and 1 hour at double time?

4

Katya earns $1.20 for each lamp she makes. If on average she can finish 10 lamps per hour and she works a 36-hour week, calculate her average weekly earnings.

5

Maria sells household cleaners. She is paid a commission of 5% of sales. How much does she earn in a week in which her sales are $8000?

6

Jack’s gross weekly income is $847. The deductions from his salary each week are: tax $206, superannuation $51.60 and health insurance $26.53. Calculate his net earnings each week.

7

A sports goods store offers a discount of 10% for cash purchases. Find the cash price of a basketball marked as $89.

8

Alex lay-bys a tool set costing $638 by paying a deposit of $125. Over the next 3 months he makes repayments of $100, $120 and $185. How much more does he have to repay in order to collect the tool set?

9

A sound system can be bought for $589 cash or on the following terms: deposit $189 and 24 equal monthly repayments of $23. a What is the total cost of the sound system if it is bought on terms? b How much interest would be paid?

10

Calculate the GST included in the price of a DVD player costing $187, price including GST.

Language in Mathematics

1

List four different ways in which people are paid for providing their labour or services.

2

Explain the meaning of: a overtime

b bonus

c holiday loading

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3

Use the following words or phrases in a sentence: gross income, deductions, net earnings

4

What is the difference in meaning between the words principal and principle?

5

The following words have a mathematical meaning as well as other meanings in ordinary English. Use a dictionary to complete the table. Word

Mathematical meaning

351

Other meaning

credit deposit balance 6

7

✓

Complete the following words from this chapter by replacing the vowels. a f — rtn — ghtly b r—t——n—r c b — dg — t

d d — sc — — nt

Three of the words in the following list have been spelt incorrectly. Rewrite them with the correct spelling: peacework, purchase, cash, survice, loan, invesment.

Glossary balance cash deductions excluding gross income including labour overtime repayment simple interest

bonus commission deferred payment expenses GST income lay-by piecework retainer take-home pay

budget compare deposit flat interest holiday loading instalment loan principal salary time-and-a-half

CHECK YOUR SKILLS

buying on terms credit discount fortnight hire purchase investment net earnings purchase service wages

1

Samantha earns $326.80 per week. This is equivalent to a yearly salary of: A $15 686.40 B $16 340 C $16 993.60 D $17 320.40

2

A salary of $33 228 p.a. is not equivalent to: A $639 per week B $2556 per fortnight C $2769 per month D $8307 per quarter

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3

Garry earns $342 per week. This is equivalent to a monthly income of: A $1368 B $1470.60 C $1482

D $1539

4

Sally works a 36-hour week and is paid $14.80 per hour. Her total wages for a week in which she works an additional 5 hours at time-and-a-half and 3 hours at double time is: A $732.60 B $651.20 C $710.40 D $769.60

5

Bianca earns $560 per week. She is entitled to 4 weeks annual recreation leave and receives an additional holiday loading of 17.5%. Her total holiday pay for 4 weeks is: A $2240 B $392 C $2338 D $2632

6

David is paid $0.37 for each tree that he plants. If he can plant an average of 18 trees per hour and he works a 36-hour week, then his average weekly earnings are: A $6.66 B $13.32 C $239.76 D $479.52

7

Tony is a real estate agent. He charges the following commission for selling home units: 3% of the first $150 000 and 1.5% for the remainder of the selling price. His commission for selling a home unit for $220 000 would be: A $6600 B $5550 C $3300 D $9900 Casual $ per hour

8 Waiter

Mon.–Fri.

Sat.

Sun.

14.92

18.65

22.38

✓

The table shows the award wages for a waiter employed as a casual. The wages of a casual waiter who works 10 hours Monday to Friday, 4 hours on Saturday plus 5 hours on Sunday is: A $335.70 B $283.48 C $317.05 D $350.62 9

10

Stephen earns $487 per week. The deductions from his salary each week are tax $139, superannuation $42, and health insurance $31.80. His net pay for the week is: A $699.80 B $421.80 C $358.20 D $274.20 The simple interest on $3480 at 5.5% p.a. for 4 years is: A $7656 B $191.40 C $765.60

D $4245.60

11

Michelle invested $5000 for 3 years and earned $825 in interest. The annual rate of interest was: A 5.5% B 16.5% C 33.3% D 3.33%

12

A camera store offers a discount of 12% for paying cash. The cash price of a camera marked as $459 is: A $55.08 B $55.10 C $403.92 D $403.90

13

The method of purchasing goods by which a deposit is paid, the balance is paid off over a short period of time, no interest is charged but the goods cannot be taken until full payment has been made is called: A time payment B hire purchase C deferred payment D lay-by

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14

A refrigerator costing $1395 can be bought on terms for $295 deposit and 24 monthly instalments of $61. The total cost of buying the refrigerator on terms would be: A $2859 B $1759 C $1464 D $2564

15

A television set costing $1089 can be bought on the following terms: deposit $289 and the balance to be repaid over 2 years by equal monthly instalments. Simple interest is charged at 13% p.a. If the TV is bought on these terms, the monthly repayment would be: A $42 B $57.17 C $37.67 D $51.27

16

A television set is advertised as shown opposite. The total amount you would have to pay for the television under this scheme is: A $1598 B $1853.68 C $2365.04 D $2109.36

$1598

✓

NO DEPOSIT NO REPAYMENTS FOR 12 MONTHS (Conditions apply.)

Conditions: (i) Pay nothing for 12 months. (ii) Balance plus interest to be repaid by equal monthly instalments over the two years following the interest free period. (iii) Simple interest of 16% p.a. is charged for the 3-year period of the agreement.

17

Using the table on page 344, the monthly repayment on a loan of $24 000 over 2 1--2- years at 11.5% is, to the nearest cent: A $38.51 B $924.30 C $696.82 D $1124.17

18

Which of the following is the best value? A 350 mL for $2.80 B 750 mL for $5.25

19

C 2 L for $15.00

D 5 L for $39

The price of a TV, including GST, is $583. The amount of GST included is: A $58.30 B $53 C $524.70

D $530

If you have any difficulty with these questions, refer to the examples and questions in the sections listed in the table. Question Section

1–3 4, 5 B

C

6

7

8

9

D

E

F

G

353

10, 11 12 I

J

13 14, 15 16

17

18

19

L

O

P

Q

M

N

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REVIEW SET 11A 1

David earns $463.90 per week. How much does he earn per: a fortnight b year c month?

2

Convert a salary of $56 000 p.a. to the equivalent salary per: a week b fortnight c month

3

Alice works a 35-hour week and is paid $18.70 per hour. How much does she earn for a week in which she works an additional 4 hours at time-and-a-half and 3 hours at double time?

4

Michelle works a 35-hour week and is paid time-and-a-half for any extra hours worked. One week she worked 4 hours overtime and was paid $746.32. What is her hourly rate of pay?

5

Travis earns $560 per week. He is entitled to 4 weeks annual leave and receives an additional holiday loading of 17.5%. Calculate his total pay for this holiday period.

6

Sharon is entitled to 4 weeks annual leave and receives a holiday loading of 17.5%. One year her total holiday pay was $2641.40. What is Sharon’s weekly salary?

7

Nerida earns $0.98 for each dress she finishes in a clothing factory. If on average she can finish 12 dresses per hour and she works 8 hours per day for 4 days, calculate her average weekly earnings.

8

Cass sells computers. She is paid a retainer of $220 per week plus a commission of 2% of sales. How much does she earn in a week in which her sales are $12 800?

9

Jim is paid a retainer plus a commission of 4% of sales. If he receives $800 for selling $13 000 worth of goods, what is the retainer that he is paid?

10

Sam works as a casual in a fruit shop. He gets paid $11.60 for any hours worked from Monday to Friday, $12.90 per hour for Saturdays and $13.60 for Sundays. Calculate how much he earns for a week in which he works 6 hours between Monday and Friday, 5 hours on Saturday and 4 hours on Sunday.

11

Jack’s gross weekly income is $768 per week. The deductions from his salary each week are: tax $224, superannuation $38.40 and health insurance $33.76. Calculate his net earnings each week.

12

Calculate the simple interest on $3600 if invested at 9% p.a. for: a 4 years b 20 months

13

A sports goods store offers a discount of 16% for cash purchases. Find the cash price of a pair of running shoes marked as $179.

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14

List two advantages and two disadvantages of using a credit card to purchase goods.

15

Melanie lay-bys a swing set costing $524 by paying a deposit of $150. Over the next 3 months she makes repayments of $100, $120 and $85. How much more does she have to repay in order to collect the swing set?

16

A car costing $10 999 can be bought on the following terms: deposit $3000, the balance to be repaid over 4 years by 48 equal monthly repayments. Simple interest is charged on the balance at 12% p.a. Calculate: a the balance owing b the interest charged on the balance owing c the monthly repayment

17

Use the table on page 344 to calculate the monthly repayments on a loan of $7800 for 3 1--2- years at 12.5% p.a.

18

Terry borrowed $20000 at 11.5% p.a. His monthly repayments were $770.25. Over what period of time did he borrow the money? (Use the table on page 344.)

19

Which is the better buy: 3 kg of tomatoes for $8.97 or 5 kg for $14.80?

20

Calculate the GST included in the price of a bottle of wine costing $18, price including GST.

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REVIEW SET 11B 1

Dan earns $368.54 per week. How much does he earn per: a fortnight b year c month?

2

Convert a salary of $45 600 p.a. to the equivalent salary per: a week b fortnight c month

3

Olivia works a 36-hour week and is paid $21.36 per hour. How much does she earn for a week in which she works an additional 6 hours at time-and-a-half and 2 hours at double time?

4

Stephanie is paid $21.30 per hour for working a 35-hour week and time-and-a-half for any extra hours worked. One week she was paid $873.30. How much overtime did she do?

5

Terry earns $680 per week. He is entitled to 4 weeks annual leave and receives an additional holiday loading of 17.5%. Calculate his total pay for this holiday period.

6

Nick is entitled to 4 weeks annual leave and receives a holiday loading of 17.5%. One year his total holiday pay was $3741.20. Calculate his holiday loading.

7

Joanne sews buttons on shirts in a clothing factory. She is paid $0.38 per shirt. Calculate her income for a week in which she completed the following number of shirts: Mon 165, Tues 189, Wed 212, Thurs 194, Fri 176.

8

Benita sells printers. She is paid a retainer of $260 per week plus a commission of 1.5% of sales. How much does she earn in a week in which her sales are $22 400?

9

Sally is paid a retainer of $220 per week plus a commission of 3% of sales. One week she earned $598. What was the value of the goods that she sold?

10

Dennis works as a casual in a coffee shop. He gets paid $10.90 for any hours worked from Monday to Friday, $13.64 per hour for Saturdays and $14.28 for Sundays. Calculate how much he earns for a week in which he works 10 hours between Monday and Friday, 4 hours on Saturday and 6 hours on Sunday.

11

John’s gross weekly income is $683 per week. The deductions from his salary each week are: tax $216, superannuation $36.78, health insurance $41.20 and savings $50. Calculate his take-home pay each week.

12

Calculate the simple interest on $18 000 if it is invested at 6% p.a. for: a 3 years b 15 months

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13

An electrical goods store offers a discount of 14% for cash purchases. Find the cash price of a toaster marked as $89.

14

List the advantages and disadvantages of using a lay-by to purchase goods.

15

An outdoor furniture setting costing $1889 can be bought on terms for $300 deposit and 24 monthly instalments of $90.04. a Calculate the cost of buying the furniture on terms. b How much interest is paid?

16

A washing machine costing $1655 can be bought on the following terms: deposit $200, the balance to be repaid over 2 years by 24 equal monthly repayments. Simple interest is charged on the balance at 15% p.a. Calculate: a the balance owing b the interest charged on the balance owing c the monthly repayment.

17

Use the table on page 344 to calculate the monthly repayments on a loan of $12 000 for 5 years at 10.5% p.a.

18

Sam borrowed $24000 over 4 years. The monthly repayments were $614.48. What was the interest rate charged? (Use the table on page 344.)

19

A-One Car Hire Co. charges $34 per day with unlimited kilometres to rent a new Corolla. B-One Car Rentals charges $26 per day plus 6 cents per kilometre travelled. Which company is cheaper if you are likely to travel each day: a 60 km b 100 km c 150 km?

20

Calculate the GST included in the price of a pair of shoes costing $128, price including GST.

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Consumer Arithmetic (Chapter 11) Syllabus reference NS5.1.2

REVIEW SET 11C 1

Convert a salary of $36 000 p.a. to the equivalent salary per: a week b fortnight c month

2

Convert a salary of $365 per week to the equivalent monthly salary.

3

Alice works a 38-hour week and is paid $19.20 per hour. How much does she earn for a week in which she works an additional 3 hours at time-and-a-half and 1 hour at double time?

4

Kim works a 35-hour week and is paid time-and-a-half for any extra hours worked. One week she worked 5 hours overtime and was paid $1140.70. What is her hourly rate of pay?

5

Kelly earns $632 per week. She is entitled to 4 weeks annual leave and receives an additional holiday loading of 17.5%. Calculate her total pay for this holiday period.

6

Karen is entitled to 4 weeks annual leave and receives a holiday loading of 17.5%. One year her total holiday pay was $5931.40. What is Karen’s weekly salary?

7

Peta earns $538 per week. At the end of the year her employer pays her a bonus of 5% of her annual salary. Calculate Peta’s bonus.

8

Cameron sells real estate. He charges the following commission for selling home units: 3% of the first $150 00 2% of the next $50000 1% of the remainder of the selling price. Calculate how much Cameron would earn for selling a home unit for: a $145 000 b $185 000 c $220 000

9

Mick is paid a retainer plus a commission of 7% of sales. If he receives $992 for selling $9600 worth of goods, what is the retainer that he is paid?

10

James works as a casual in a bar. He gets paid $15.20 for any hours worked from Monday to Friday, $17.68 per hour for Saturdays and $19.32 for Sundays. Calculate how much he earns for a week in which he works 12 hours between Monday and Friday, 6 hours on Saturday and 6 hours on Sunday.

11

Josh’s gross weekly income is $940 per week. The deductions from his salary each week are: tax $312, superannuation $56.30 and health insurance $41.22. Calculate his net earnings each week.

12

Calculate the simple interest on $13 000 if invested at 6% p.a. for: a 5 years b 21 months

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Consumer Arithmetic (Chapter 11) Syllabus reference NS5.1.2

13

A sports goods store offers a discount of 18% for cash purchases. Find the cash price of a tennis racquet marked as $279.

14

List the advantages and disadvantages of using cash to purchase goods.

15

Sylvie lay-bys a dress costing $465 by paying a deposit of 10%. Over the next 4 weeks she makes repayments totalling $320. How much more does she have to repay in order to collect the dress?

16

A car costing $12 000 can be bought on the following terms: deposit $2000, the balance to be repaid over 3 years by 36 equal monthly repayments. Simple interest is charged on the balance at 8% p.a. Calculate: a the balance owing b the interest charged on the balance owing c the monthly repayment

17

Use the table on page 344 to calculate the monthly repayments on a loan of $24 000 for 4 years at 13% p.a.

18

Lenny borrowed $35 000 at 10.5% p.a. His monthly repayments were $999.41. Over what period of time did he borrow the money? (Use the table on page 344.)

19

Which is the best value? Chocolate: 55 g block for $1.10, 250 g block for $4.88, 375 g block for $7.35.

20

Calculate the GST and the price including GST on a pair of boots costing $498, price excluding GST.

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Consumer Arithmetic (Chapter 11) Syllabus reference NS5.1.2

REVIEW SET 11D 1

Convert a salary of $56 000 p.a. to the equivalent salary per: a week b fortnight c month

2

Holly earns $528 per week. How much is this per month?

3

Alice works a 35-hour week and is paid $24.10 per hour. How much does she earn for a week in which she works an additional 5 hours at time-and-a-half and 4 hours at double time?

4

Gayatri is paid $36.90 per hour for working a 35-hour week and time-and-a-half for any extra hours worked. One week she was paid $1734.30. How much overtime did she work?

5

Ken earns $720 per week. He is entitled to 4 weeks annual leave and receives an additional holiday loading of 17.5%. Calculate his total pay for this holiday period.

6

Ray is entitled to 4 weeks annual leave and receives a holiday loading of 17.5%. One year his total holiday pay was $4091.82. Calculate his holiday loading.

7

Isabella earns $0.71 for each part she builds in a factory that produces electrical appliances. If on average she can finish 15 parts per hour and she works 6 hours per day for 5 days, calculate her average weekly earnings.

8

Kate sells mobile phone plans. She is paid a retainer of $180 per week plus a commission of 6% of sales. How much does she earn in a week in which her sales are $9200?

9

Olivia is paid a retainer of $250 per week plus a commission of 6% of sales. One week she earned $768.40. What was the value of the goods that she sold?

10

Ann works as a casual in a cafe. She gets paid $12.34 for any hours worked from Monday to Friday, $13.85 per hour for Saturdays and $15.98 for Sundays. Calculate how much she earns for a week in which she works 8 hours between Monday and Friday, 6 hours on Saturday and 3 hours on Sunday.

11

Phil’s’s gross weekly income is $895 per week. The deductions from his salary each week are: tax $291, superannuation $42.81 and health insurance $38.26. He also deposits $100 a week into a special savings account and has $10 per week donated directly to a charity. Calculate his take-home pay each week.

12

Calculate the simple interest on $11 400 if invested at 8% p.a. for: a 3 years b 15 months

13

A store offers a discount of 12% for cash purchases. Find the cash price of a pair of sun glasses marked as $189.

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Consumer Arithmetic (Chapter 11) Syllabus reference NS5.1.2

14

List the advantages and disadvantages of using a deferred payment option to purchase goods.

15

A car costing $10 999 can be bought on the following terms: deposit $3000, the balance to be repaid over 4 years by 48 equal monthly repayments. Simple interest is charged on the balance at 12% p.a. Calculate: a the balance owing b the interest charged on the balance owing c the monthly repayment No Deposit

$3999

16

A computer is advertised as shown opposite. a Calculate the total amount you would have to pay for the computer under this scheme. b Calculate the monthly instalments.

No Repayments for 12 months (Conditions apply.)

Conditions: (i) Pay nothing for 12 months. (ii) Balance plus interest to be repaid by equal montly instalments over the two years following the interest free period. (iii) Simple interest of 15% p.a. is charged for the 3-year period of the agreement. (iv) Establishment fee of $110.

17

Use the table on page 344 to calculate the monthly repayments on a loan of $15 500 for 4 1--2- years at 14% p.a.

18

Will borrowed $28000 over 5 years. The monthly repayments were $651.51. What was the interest rate charged? (Use the table on page 344.)

19

On savings accounts, Bob’s Bank charges a management fee of $5.50 per month. The first 5 transactions are free and then a fee of 26 cents per transaction is charged. Bill’s Bank charges a monthly management fee of $7.00 plus 9 cents per transaction. Which bank is cheaper to use if your average number of monthly transactions is: a 10 b 15 c 20?

20

Calculate the GST in the price of a cooked chicken costing $9.90, price including GST.

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