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1

Earning and managingmoney The main mathematical ideas in this chapterare: ▶ using different methods for calculatingincome ▶ calculating allowances, bonuses, royalty payments, commission and holiday loading ▶ calculating piecework payments ▶ calculating government allowances, pensions and health payments ▶ evaluating superannuation ▶ calculating net pay and grosspay ▶ calculating allowable deductions ▶ calculating taxableincome ▶ calculating the Medicarelevy ▶ calculating tax refunds or payments.

FINA NCIA L MATHEMATICS MS -F1 Money Ma ttersF1.2

1A

1

What is the result of calculating 28.67 + 139.48?

A 168.15 C 110.81 1A

2

3

4

5

6

7

D 4

How many weeks in 2 years? A 8 B 24

C 52

D 104

How many hours have elapsed from 6:00 am to 8:00 pm? A 2 B 10

D 14

10 How many hours have elapsed from 9:30 am to 4:30 pm? A 5 B 7 C 7.5 D 13

1B

11 What is 65% of $240? A $156 B $1560 C $27 D $2708

1C

12 What is 42 as a percentage of 70? A 60% B 42% C 167% D 29.4%

1C

13 What is $27 as a percentage of $60? A 22% B 27% C 45% D 60%

1C

14 Georgia scored 65 marks out of 80 in a mathematics test. What is her percentage mark? A 81.25% B 80% C 65.25% D 8.125%

How many days in 168 hours? B 6

A 7 C 5 1A

D 180

9

D 52

1A

How many minutes in 3 hours? A 24 B 60

C 120 1A

D 744.9

How many months in 3 years? B 24

C 12

D 50.56

What is the result of calculating 2.9796 ÷ 0.04? A 0.7449 B 7.449

C 74.49 1A

1A

What is the result of calculating 47.86 × 2.7? B 17.726

A 45.16 C 129.222 1A

D 58.56

8

A 12 C 36

What is the result of calculating 243.81 – 185.25? A 142.64 B 69.66

C 429.06 1A

B 42.618 D 157.05

1A

ARE YOU READY?

ARE YOUREADY?

If you had difficulty with any of these questions or would like further practice, complete one or more of the matching Support sheets available on your obook assess. Q1–2 Support sheet 1A.1 Adding and subtracting decimal numbers Q3–4 Support sheet 1A.2 Multiplying and dividing decimal numbers Q5–8 Support sheet 1A.3 Converting units of time Q9–10 Support sheet 1A.4 Calculating elapsed time Q11 Support sheet 1B.1 Calculating the percentage of a quantity Q12–14 Support sheet 1C.1 Calculating an amount as a percentage of another Chapter 1 Earning and managing money

3

1A Earning anincome These resources are available on your obook assess: • Spreadsheet 1A: Convert between annual, monthly, weekly and hourly income • assess quiz 1A:Test your skills with an auto-correcting multiple-choicequiz wage a fixed regular payment earned for work or services, usually based on an hourly rate and typically paid daily, weekly, or fortnightly salary a fixed regular payment, typically paid monthly but often expressed as an annual sum, made by an employer to an employee

Money earned by working is the basis of most people’s income.Without an income people are unable to satisfy their basic needs. There are many ways people receive money for work done. Most people work for an employer who pays them for their work. An amount earned based on hours worked is called a wage. A fixed amount earned regardless of the number of hours spent working is called a salary. This section deals with salary and wage payments. A salary is an income that is usually described as an amount per annum (p.a.) or per year, although the salary may be paid weekly, fortnightly or monthly. People who are paid salaries include nurses, government employees, teachers and other professionals. Awage is based on an hourly rate for a certain number of hours worked. Wages are usually paid on a weekly or fortnightly basis. People who are paid wages include factory workers, shop assistants, building workers and mechanics. When converting from yearly salaries to monthly, fortnightly and weekly amounts, the following areused. 1year = 365days = 12months = 52weeks = 26 fortnights

per annum (p.a.) for each year (used in financial contexts)

Employees may be permanent or casual, and may work full-time or part-time. Permanent employees receive benefits such as sick leave and holidaypay.

EXAMPLE1A–1 Calculating salary payments Jenny works as a pastry chef. Her salary is $51 064 per annum. Express this salary as an amount: a per month b per week c per fortnight. Solve

Think

a

Monthly = $51 064÷12 =$4255.33

There are 12months in a year. Divide the annual income by 12.

b

Weekly=$51 064÷52 = $982

There are 52 weeks in a year. Divide the annual income by 52.

c

Fortnightly = $51 064÷26 =$1964

There are 26 fortnights in a year. Divide the annual income by 26.

Apply When converting from an annual income, divide by the required number: 12 for monthly 52 forweekly 26 for fortnightly

EXERCISE1A Earning anincome

2 Caterina earns $86 924 per annum. Calculate her weeklypay. 3 Express each of the following annual salaries as an amount: i per month ii per week

a $38 903 d $109 870

b $27 106 e $75 076

iii per fortnight. c f

$30 098 $50 990

EXAMPLE1A–2 Calculating annual and monthly salary payments Michiko works part-time and earns $283 perweek. a How much does Michiko earn peryear? b How much does Michiko earn permonth? Solve

Think There are 52 weeks in a year. Multiply the weekly wage by 52.

a

Yearly=$283×52 =$14 716

b

Monthly=$14 716÷12 There are 12months in a year. Divide the annual amount by 12. =$1226.33 One month is not 4 weeks, because 12 × 4=48, not 52 weeks.

Apply When converting weekly amounts to annual amounts, multiply by52. Always use the annual income divided by 12 to find the monthly income. If the annual income is not provided, convert to it first.

4 Jason earns $421 per week for weekend work. Complete the following tofind: a Jason’s annualincome b Jason’s monthlyincome Annual income=$421×____ Monthly income=$21 892÷____  =____ =____ 5 Ashley earns $379 per week for part-time work. How much does Ashleyearn: a per year? b permonth? FINA NCIA L MATHEMATICS

UNDERSTANDING , FLUENCY AND CO MMUNICAT ING

1 Amy earns $19 884.80 per annum for part-time work. Complete the following to find how much sheearns: a Monthly=____ ÷ 12 =____ b Weekly=$19 884.80÷____ =____ c Fortnightly=____÷____ =____

6 Calculate the annual salary amount for each of these workers. Name

Weekly wage

C. Cooke

$847.94

D. Moussa

Annual salary 

$1021.06



B. Boje

$630.54



T. Lambert

$570.38



Chapter 1 Earning and managing money

5

UNDERSTANDING , FLUENCY AND CO MMUNICAT ING

7 a b c

d e f

David works part-time and receives an annual salary of $41 398.45. How much does he earn eachweek? Debra works part-time and receives a monthly salary of $2933. How much does she earn eachweek? Ali works part-time and receives an annual salary of $46 837.25. How much does he earn each fortnight? Kristy works full-time and receives an annual salary of $78 500. How much does she earn each fortnight? Iain works part-time and receives a monthly salary of $3599.60. How much does he earn each fortnight? Ngoc works full-time and receives an annual salary of $74 292. How much does she earn eachmonth?

8 Convert each of the following to an annual salary, if necessary, and calculate the difference between the annual salaries. a Kylie:$1136.60 a week and Stacey:$54 642ayear and Paul:$55 271ayear b Roland:$1803 a fortnight c Binh:$2610 a month and Aaron:$693.20aweek

EXAMPLE1A–3 Calculating wage payments Monica is paid $21.65 per hour for casual work. How much does she earn if sheworks: a 6 hours in oneday? b 6 hours per day for fivedays? Solve

Think

a

Pay=$21.65×6 =$129.90

b

Pay=$21.65 ×6×5 Multiply the daily rate ($21.65×6) =$649.50 by the number ofdays (5).

The find the amount earned, multiply the hourly rate, ($21.65) by the number of hours (6).

9 Clare works in a jewellery store earning $28.45 per hour. Complete the following to find the amount Clare earns: a in an 8-hourday Pay=____ × 8=____ b for a 38-hourweek Pay=____ × ____=____ 10 Aaron works as an assistant in a clothing store and is paid $21.75 an hour for a 35-hour week. Calculate his weeklywage. 11 Madonna works as a receptionist. If she is paid $20.90 an hour, how much does she earn in a 38-hourweek?

6

Oxford Insight Mathematics Standard 11

Apply Incomes stated as hourly rates need to be multiplied by the number of hours to find the total income.

13 Kristie is a junior and earns $14.43 an hour. Calculate her weekly wage if sheworks: a 18 h b 35 h c 40 h d

48h.

EXAMPLE1A–4 Calculating annualincome Angus works a 35-hour week and is paid $22.80 per hour. How much does he earn in ayear? Solve Pay per week = $22.80×35 =$798 Annual income=798×52 =$41 496 Angus earns $ 41 496 per year.

Think Find the pay per week by multiplying $22.80 by 35, then multiply by 52 to find the annual income.

Apply Hourly income is the basic building block that, by multiplication, will allow us to calculate income over any time period.

14 Taylor earns $21.60 per hour for a 38-hour week. Complete to find her weekly pay and her annual income. a Pay per week=$21.60 × ____ b Annual income=$820.80 × ____ =____ =____ 15 An electrician works a 38-hour week. Find her yearly pay if she earns $58.40 perhour. 16 Ikbar works a 38-hour week. His hourly rate is $22.27. Find his pay for 1year.

EXAMPLE1A–5 Converting annual salaries toshorter time periods Convert an annual salary of $47 424 for a worker who works 35 hours each weekto: a a weekly salary b an hourly salary. Solve

a

Weekly=$47 424÷52 = $912

b

Hourly = $912÷35 = $26.06

Think Divide the annual salary of $47 424 by 52 to convert to weekly salary. Next, divide the weekly salary ($912) by 35 to convert to the hourly rate.

Apply Converting annual salaries to shorter time periods requires division. Divide by 52 for weekly or by 12 for monthly incomes.

17 Jake works 35 hours per week for an annual income of $54 527.20. Complete to find his weekly pay and his hourlyrate. a Weekly pay=____ ÷ 52 b Hourly pay=____ ÷ ____ =____ =____

FINA NCIA L MATHEMATICS

UNDERSTANDING , FLUENCY AND CO MMUNICAT ING

12 David works at Pizza Barn delivering pizzas. Calculate his weekly wage if he earns $22.20 an hour and worked the following number of hours in a givenweek. a 16 h b 24 h c 35 h d 41h

18 Indoo receives an annual salary of $63 300. Convert this to a weekly salary and find Indoo’s average hourly rate if she works 52 hours perweek. 19 Guido works 7 hours a day, fivedays per week. Find his hourly rate if his annual income is $38 900.

Chapter 1 Earning and managing money

7

P R O B L E M S O LV I N G , R E A S O N I N G A N D J U S T I F I C A T I O N

20 Rodney and Anastasia both work at a shoe factory for an hourly rate of pay of $26.80, including the time taken for their meal breaks. i Calculate the total number of hours worked in one week by each employee.

ii Calculate each employee’s weeklywage. a Name: Rodney Day

In

Out

Hours

Monday

7:00 am

4:00 pm



Tuesday

8:00 am

4:00 pm



Wednesday Thursday

7:00 am

5:00 pm



11:00 am

4:00 pm



9:30 am

2:30 pm



Friday 

Total 



b Name: Anastasia Day

In

Out

Hours

Monday

7:40 am

5:40 pm



Tuesday

10:20 am

4:20 pm



Wednesday

9:00 am

3:00 pm



Thursday

8:30 am

3:30 pm



Friday

8:35 am

3:35 pm





Total 



21 Complete the following wagetable. Day Mon

Tues

Wed

Thurs

Friday

Hours worked

Hourly rate

Weekly rate

S. Smith

7

5

–

1 4__ 2

9



$29.40



D. De Souza

11

4

1 3__ 2

1 6__ 2

7



$26.30



A. Bentley

1 6__ 2

–

–

3





$611.80

C. Johnson

4

2__21

7

2

1 9__ 2 1 1__ 2



$30.34



K. Kernell

3

7__21

5

1 4__ 2

–





$374.80

P. Patrick

1 5__ 2

9

1 2__ 2

–

1 6__ 2



$19.83



Name

22 Jim is a junior and works 26days per month. He averages 7 hours per day. Find his annual income if his hourly rate is $18.17. 23 Nato is paid $35.20 per hour. He works 4 hours per day seven days a week. Find his pay for 1year. 24 Isla is paid $1710 per fortnight. a Find: i her weekly pay

ii her monthly pay b If Isla works 6 hours per five days a week, what is her hourly rate?

8

Oxford Insight Mathematics Standard 11

P R O B L E M S O LV I N G , R E A S O N I N G A N D J U S T I F I C A T I O N

25 James is a junior and works as a casual employee at the local supermarket. He is paid $16.05 an hour from Monday to Friday and $20.35 an hour on weekends. During a week of his school holidays he worked from 3:00 pm until 6:00 pm Monday to Friday and 8:30 am until 1:30 pm on Saturday and Sunday. a How many hours did he work on weekdays? b How many hours did he work on weekends? c Calculate his income for theweek. 26 Steve is paid a salary of $78 904 perannum. a Calculate Steve’s weekly payrate. b What is his hourly rate if he works 45 hours perweek? 27 Which pay option offers the higher weekly wage? By howmuch? a Option A:$903.20 a week or Option B:$45 103.20ayear b Option A:$953.29 a fortnight or Option B:$2405 amonth or Option B:$47 024ayear c Option A:$3276 a month 28 A spreadsheet is provided on your obook assess to enable you to easily convert between annual, monthly, fortnightly, weekly and hourly income. Use it to check some of your answers for questions in this exercise.

FINA NCIA L MATHEMATICS

CHALLENG E

29 Armin and Richard were comparing their pays. Richard said that he earns more per week than Armin. Richard earns $33 800 per annum, which he said is $704.17 per week. Armin earns $680 perweek. The yearly pay for Richard is correct, but he has made an error in calculating his weeklypay. a Find Armin’s annual income. b Find Richard’s correct weeklypay. c Who really earnsmore? d Richard said that he divided the annual income by 12 to find his monthly pay and then by 4 to find his weekly pay. Find the mistake that Richard made. Explain your answer.

Chapter 1 Earning and managing money

9

1B Allowances, bonuses and loadings overtime extra time worked by employees in excess of their normal workinghours time-and-a-half overtime rate where employees 1

are paid 1 __ times 2 their normal hourly rate double-time overtime rate where employees are paid 2 times their normal hourly rate bonus extra payment paid as an incentive to employees who workhard annual leave loading extra payment added to the holiday pay of employees taking their annual holidays

These resources are available on your obook assess: • Video tutorial 1B: Watch and listen to an explanation of Example 1B-5 • Worksheet1B: Practise your skills with extra problems on earning money • Spreadsheet 1B: Calculate wages including overtime • assess quiz 1B:Test your skills with an auto-correcting multiple-choicequiz

Most employees work under an award that states the maximum number of normal work hours they should work per day or per week, and also their normal working days. Hours worked in excess of these (including weekend, late night and public holiday work) are overtime and are paid at a higher hourly rate than normal time. The two main overtime rates are time-and-ahalf and double-time. Employees who are required to work under difficult, unpleasant or dangerous conditions are often paid an allowance that is above the normal rate of pay. Some examples include an allowance for cleaning toilets, working in confined spaces, working in hot or very cold conditions, or dealing with toxic substances. Allowances may also be paid for uniforms, dry-cleaning of uniforms, travelling, meals, tools andsoon. Employees sometimes are paid extra payments in addition to their normalwages as described below. A bonus is an extra one-off payment paid as an incentive for employees who work hard over a period of time. Employers use bonuses to encourage the employees to work even harder! Employees receive four weeks of annual leave per year. Annual leave loading is an increase in an employee’s pay while on holidays. The holiday loading is a fixed 1 %. __ percentage of the employee’s normal pay. It is usually paid at a rateof 17 2

EXAMPLE1B–1 Calculating overtimerates Convert an hourly rate of $26.20 to an overtime rateof: a time-and-a-half b double-time. Solve

10

a

Time-and-a-halfrate = $26.20×1.5 = $39.30

b

Double-time = $26.20×2 = $52.40

Oxford Insight Mathematics Standard 11

Think

Apply

Multiply the hourly rate of $26.20 To calculate the overtime rate by the overtime loading of 1.5. This multiply the normal hourly rate by is the overtime hourly rate. the overtime factor. Multiply the hourly rate of $26.20 For time-and-a-half the factor by the overtime loading of 2.This is 1.5, and for double-time the factoris 2. is the overtime hourly rate.

EXERCISE1B Allowances, bonuses and loadings UNDERSTANDING , FLUENCY AND CO MMUNICAT ING

1 Jasmine earns $22.24 per hour. Copy and complete the following to find her overtime rateat: a time-and-a-half b double-time. Overtime rate=____ ×1.____ Overtime rate=____×____ =____ =____ 2 Convert these normal hourly pay rates to overtime ratesat: i time-and-a-half ii

a $11.83

b $14....