Financial decisions. Syllabus strand Number N

Transcription

1 Financial decisions Syllabus strand Number N Margaret works in a clothing factory sewing pre-cut fabrics. The company has just received an order to make uniforms for a large travel company. Margaret and her co-workers are paid according to the number of pieces of clothing they complete. As an incentive to be more productive, the employees are paid at a bonus piece rate for additional articles completed beyond the expected daily output. Because Margaret does not earn the same amount each week, she needs to be able to check that her wages have been calculated correctly. Can you help her? Ex A Wages and salaries: N 6. Ex B Working overtime: N 6. Ex C Piecework: N 6. Ex D Commission and royalties: N 6. Ex E Gross and net pay: N 6. Ex F Budgeting: N 6. Ex G Calculating GST and VAT: N 5. Ex H Compound interest: N 6.

2 re you 8 Maths Quest READY? 8 for Victoria Are you ready? Try the questions below. If you have difficulty with any of them, extra help can be obtained by completing the matching SkillSHEET. Either click on the SkillSHEET icon next to the question on the Maths Quest 3 CD-ROM or ask your teacher for a copy.. Converting units of time a In a year, there are how many: i months ii fortnights iii weeks? b Convert each of the following to the units shown in brackets. i 4 years (months) ii 36 weeks (fortnights) iii fortnights (weeks) iv 5 fortnights (years). Finding a percentage of a quantity (money) Calculate each of the following. a 0% of $34 b 5.5% of $78 c.5% of $9.60 d 75% of $ Converting a percentage to a decimal fraction 3 Convert each of the following to a decimal fraction. a 0% b 7.5% c 37.5% d 85.75%.5 Rounding money to the nearest 5 cents 4 Round each of the following to the nearest 5 cents. a 8c b $7.84 c $43.78 d $4.3.6 Increasing a quantity by a percentage 5 Find the price of each of the following after a 0% increase. a $55 b $7.40 c $36 d 0c

3 Chapter Financial decisions 9 Wages and salaries Self-employed people charge a fee for their service or sell goods for a profit. Employees may be paid for their work in a variety of ways. A wage is based on a fixed rate per hour. Hours worked outside the normal work period are paid at a higher rate. A salary is a fixed annual (yearly) amount, usually paid fortnightly or monthly. There is no extra pay for hours outside the normal work period but time off in lieu may be arranged. WORKED Example Susan has an annual salary of $ How much is she paid: a weekly? b fortnightly? c monthly? a Annual means per year, so divide the salary by 5 because there are 5 weeks in a year, a Weekly salary = $ $43.84 and round to decimal places. Answer the question in a sentence. Susan s weekly wage is $ b There are 6 fortnights in a year so divide the salary by 6, and round to decimal places. b Fortnightly salary = $ $ Answer the question in a sentence. Susan s fortnightly salary is $ c There are months in a year so divide the salary by, and round to decimal places. c Monthly salary = $ $ Answer the question in a sentence. Susan s monthly salary is $ Frisco has casual work at a fast-food store. He is paid $6.50 per hour Monday to Friday and $9.80 per hour over the weekends. Calculate his total pay for a week in which he worked from 5.30 pm to 0 pm on Friday and from 6 pm to 9.5 pm on Saturday. Find the number of hours worked Monday Friday 5.30 pm to 0 pm is 4 -- hours. to Friday and how much he is paid. $ = $9.5 Find the number of hours worked over the Saturday 6 pm to 9.5 pm is 3 -- hours. 4 weekend and how much he is paid. $ = $ Find the total number of dollars earned. Total earned = $9.5 + $3.85 = $6.0 Write the answer in a sentence. Frisco s total pay was $ WORKED Example remember remember. year = 5 weeks = 6 fortnights = months. Hourly rates are usually greater on weekends or outside normal working hours. 3. A wage is a fixed rate per hour. 4. A salary is a fixed annual amount.

4 0 Maths Quest for Queensland Book 3 A Wages and salaries SkillSHEET. WORKED Example Converting units of time WORKED Example Johann has an annual salary of $ How much is he paid: a weekly? b fortnightly? c monthly? Anna earns $4 300 per annum. How much does she earn: a weekly? b fortnightly? c monthly? 3 Find the annual salary of workers with the following weekly incomes: a $368 b $ c $ How much is earned per annum by those paid fortnightly salaries of: a $783? b $836.90? c $08.56? 5 Find the hourly rate for these workers. a Rahni earns $48.75 for 5 hours. b Francisco is paid $54.75 for 4 -- hours. c Nhan earns $ for a 38-hour week. d Jessica works 7 -- hours a day for 5 days to earn $ Which of each pair is on the higher rate of pay: a $390 per month or $700 per annum? b $ per fortnight or $4300 per month? 7 Paul receives $ per annum and is given a 4% wage rise. Hannah earns $40 86 per annum and gets a -- % increase. Who is better off after the rise and by how much? 8 Juan has casual work for which he is paid $7.0 per hour Monday to Friday and $9.95 per hour on the weekends. Calculate his total pay for a week in which he worked from 5 pm to 0 pm on Thursday and from.30 pm to 7.00 pm on Saturday. 9 Mimi worked the following hours in one week. Wednesday 5.30 pm to 9.00 pm Thursday 6.45 pm to 9.00 pm Friday 7.5 pm to 0.30 pm If her pay is $8.30 per hour up to 9.00 pm and $0.08 per hour after that, what is her total pay? 0 Tania has regular casual work as a sales assistant from 5 pm to 9 pm on Fridays and from 8.30 am to.00 pm on Saturdays. How much does she earn per fortnight at the flat rate of $8.75 per hour?

5 Chapter Financial decisions Working overtime Employees who work overtime spend extra hours at work. Employees who earn a wage receive extra pay at a higher rate for the time they work beyond the normal hours. Time-and-a-half means the worker is paid -- times the normal hourly rate. Double time means the worker is paid twice the normal hourly rate. An employee s gross wage is the amount paid before tax is taken out. WORKED Example 3 Lani is paid $48.75 for a regular 38-hour week and time-and-a-half for overtime. For working on Sundays or public holidays, she receives double time. What is her gross wage for a week in which she works 43 hours, 3 of which were on a Sunday? Find the hourly rate for a regular week, Regular hourly rate = $ rounded to the nearest cent. $.8 Write the total earned for the regular Total for 38 regular hours = $ hour week. Find the number of hours worked Hours overtime = overtime. = Find the total amount earned from Overtime wage = $(.8.5) overtime. = $33.84 Find the amount earned on Sunday. Sunday wage = $(3.8 ) = $67.68 Find the gross wage. Gross wage = $ $ $67.68 = $530.7 Answer the question in a sentence. Lani s gross wage is $ remember remember Overtime is time worked beyond normal hours. Employees who earn a wage receive an increased rate of pay to compensate for the extra hours worked. B Working overtime Calculate the following overtime payments: a 3 hours at time-and-a-half when the hourly rate is $8.54 b 4 -- hours at double time when the hourly rate is $.68 c 5 hours at time-and-a-half and -- hours at double time when the hourly rate is $6.50.

6 Maths Quest for Queensland Book 3 Calculate the following total weekly wages: a 38 hours at $.50 per hour, plus hours at time-and-a-half b 40 hours at $4.9 per hour, plus 3 -- hours at time-and-a-half c hours at $8.3 per hour, plus 3 hours at time-and-a-half and hours at double time. 3 Julio is paid $47.80 for a regular 38-hour week and time-and-a-half for overtime. a What is his hourly rate of pay? b How much is he paid for 3 hours of overtime? c What is his gross wage for a week in which he works 4 hours? 4 Juliana is paid $56.30 for a regular 39-hour week and time-and-a-half for overtime. a What is her hourly rate of pay? b How much is she paid for hours of overtime? c What is her gross wage for a 4-hour week? WORKED Example 3 5 Albert is paid $ for a 40-hour week, time-and-a-half for overtime and double time for Sundays and public holidays. What is his gross wage for a week in which he works 48 hours, 5 of which are on Anzac Day? 6 Rema earns $46.84 per 38-hour week as a secretary. She works 4 hours overtime at time-and-a-half in one particular week. What is her pay for that week? SkillSHEET. Finding a percentage of a quantity (money) 7 Normal hourly rates for a 5-year-old are $7.56. Casual workers get an extra 5% loading instead of sick and holiday pay. a What is the casual hourly rate? b How much is a 5-year-old casual paid for a 4 -- hour shift? 8 Karen receives an annual salary of $6 57. a What is her fortnightly pay? b What is she paid for her annual 4-week holiday, for which she receives an extra 7 -- % loading? 9 Brian earns $6.40 for a standard 39-hour week, time-and-a-half for overtime, and a $7.53 per week allowance for working on scaffolding. Calculate his gross pay for a week in which he works on scaffolding, and does 4 hours overtime. 0 Santiago is a baker who works only on weekends. On Saturdays he earns time-and-ahalf for the first 4 hours and double time after that. On Sundays it s all double time. If the baker s award for normal working hours is $6.80 per hour, how much does he earn in a weekend in which he works from 7.30 pm Saturday to 3.00 am Sunday and 8.30 pm to midnight on Sunday? multiple choice A standard working week is 38 hours and a worker puts in 3 hours overtime at timeand-a-half and hours at double time. To how many hours at the standard rate is her total work time equivalent? A 43 B C D 45

7 Chapter Financial decisions 3 MATHS MATHS QUEST H C A L LL E N G G E E Julie earns twice the hourly rate of pay than her sister Susan. On a particular day, Julie worked for six and a half hours and Susan worked for nine hours. If their combined wage for this day was $34.00, find their hourly rate and how much each of them received. At Donald s store, employees are paid time-and-a-half for the first two hours beyond their normal hours and double-time for the hours thereafter. Donald worked a total of 4 hours in a week; four of these were at time-and-a-half and two were at double-time. Calculate Donald s hourly rate if he earned $3.0 for this week. Career profile JO MOONEY Direct care worker Name: Jo Mooney Profession: Direct care worker Qualifications: Certificate IV in Community Services/Disability Employed at a Community Residential Unit I have always been interested in working with people with intellectual disabilities. My work involves directing and aiding clients in their daily lives. We try to teach them independent living skills we teach them how to get to work using public transport, help them with their washing, cooking and cleaning. The staff members are also responsible for the day-to-day running of the house including maintenance, finance, and so on. Maths is very useful in everyday life. I use maths every day in my job. Here are just a few examples.. Our clients are on a pension. We help them to work out a budget for a fortnight. We have to ensure that they cover all their expenses for the fortnight.. Petty cash and grocery ledgers need to be kept for the household s shared expenses. 3. We use maths in our cooking each evening. We may have a recipe for 4 and need to make enough for anywhere between to 0 people. As a direct care worker, I am paid a wage. This wage can vary depending on the hours worked and the time of the day or week. Permanent and casual staff members are also paid at different rates. If I work on a Saturday, my hourly rate is calculated at time-and-a-half. On a Sunday it is double time while on public holidays it is double-time-and-a-half. If I work after 6.00 pm, my pay for that day is also increased by 0%. Questions. List ways in which Jo uses maths in her job.. For a permanent Grade first-year care worker, the hourly rate is $.56. Calculate the hourly rate for working on a: (a) Saturday (b) Sunday (c) public holiday. 3. For a casual Grade 5 third-year care worker, the hourly rate is $9.08. Calculate the hourly rate for working on a: (a) Saturday (b) Sunday (c) public holiday. 4. Find out more about courses offered to become a direct care worker.

8 4 Maths Quest for Queensland Book 3 Piecework Clothing industry and factory workers can be paid for each piece or article completed. This kind of payment is not usually for permanent employees and other benefits are not included. Len has a job washing cars in a car yard. He is paid $4.50 per car washed. Calculate what Len earns in an afternoon where he washes 4 cars. Find the amount earned by multiplying the pay rate by the number of cars washed. Amount earned = $ = $08 Answer the question in a sentence. Len earns $08. WORKED Example 4 A person may also be paid on a sliding scale where the pay rate increases as the number of completed items increases. WORKED Example 5 Angelica is a machinist in a factory. For the first 80 garments she is paid $.96 per garment and then $.50 per garment thereafter. What are her gross wages for a week in which she produces 3 garments? Find how many more than the basic Extra garments = garments she makes. = 43 Find her total payment for the first Payment for basic garments = 80 $ garments. = $35.80 Find her total payment for the garments Payment for bonus garments = 43 $.50 at the bonus rate. = $07.50 Find her gross wage. Gross wage = $ $07.50 = $ Write the answer in a sentence. Angelica earns a gross wage of $ In some cases, piecework is paid for multiple rather than single units. For example, for letterbox deliveries you may be paid per 000 deliveries made.

9 Chapter Financial decisions 5 WORKED Example Holly is delivering brochures to letterboxes in her local area. She is paid $3.00 per 000 brochures delivered. Calculate what Holly will earn for a delivery of 3500 brochures. 6 3 Divide the number of brochures delivered by 000 to calculate the number of thousands of brochures delivered. Multiply the number of thousands deliveries by $3.00 to calculate what Holly is paid = 3.5 So 3.5 thousand brochures are delivered. Holly s pay = 3.5 $3.00 = $80.50 Answer the question in a sentence. Holly earns $ remember remember. Piecework means being paid a certain amount for each piece produced.. In order to increase production, the rate may be paid on a sliding scale. 3. The payment may be made for multiple rather than single units of work. C Piecework WORKED Example 4 WORKED Example 5 WORKED Example 6 Hitani is paid 65 cents for each teacup she decorates. How much is she paid for decorating 50 teacups? A group of 6 friends take a job picking fruit over summer. They are paid $4.50 for each basket of fruit picked. Calculate the earnings of each person in the group if: a Ross picked 3 baskets b Rachel picked baskets c Monica picked 9 baskets d Chandler picked 8 baskets e Joey picked 3 baskets f Phoebe picked 9 baskets. 3 Jack makes leather belts. The piece rate is $.5 each for the first 50 belts and $.50 thereafter. What is his income for a day in which he produces 68 belts? 4 A production-line worker is paid $.50 for each of the first 75 toasters assembled, then $.80 per toaster thereafter. How much does she earn on a day in which she assembles 0 toasters? 5 Rudolf earns $8.50 per 000 leaflets delivered to letterboxes. Calculate what Rudolf will earn for a week in which he delivers 7500 leaflets.

10 6 Maths Quest for Queensland Book 3 6 Dimitri earns $4.50 for each box of fruit picked. a How much does he make for picking 0 boxes? b How many boxes must he pick to earn at least $50? c If he takes 4 hours to pick boxes, what is his hourly rate of pay? 7 Pauline uses her home computer for word processing under contract to an agency. She is paid $7 per page for the first 50 pages, $9 per page from 5 00 pages, and $0 per page thereafter. Calculate her gross pay for a period in which she prepares: a 48 pages b 67 pages c 3 pages. 8 Gustav is paid 30 cents for each toy assembled, up to the first 00. For the next 50 he receives 40 cents per toy. Any more than that attracts a payment of 50 cents per toy. Calculate his gross pay for the day in which he assembles: a 98 toys b 36 toys c 67 toys 9 Rani delivers bills to letterboxes and is paid $8 per thousand. a How much does she earn for delivering 500 items? b How many must she deliver to earn $00? c If she takes 6 hours to deliver each thousand on average, what is her hourly rate of pay? 0 Georgio delivers pizzas. He is paid $3 per delivery from 5 pm to 9 pm and $4 per delivery after 9 pm. a How much does he earn on a night in which he makes deliveries by 9 pm and 4 deliveries between 9 pm and 0.30 pm? b What are his average earnings per hour if he has worked from 5 pm to 0.30 pm? Tina packs canned goods into boxes as they come off a production line. In a shift she is paid 0 cents per box up to 600, then 5 cents per box thereafter. Find her earnings for a shift in which she packs: a 580 boxes b 60 boxes c 650 boxes. d What is her average hourly rate of pay for an 8-hour shift in which she packs 635 boxes? WorkSHEET. multiple choice If a pieceworker earns x cents per article up to 00 articles and y cents per article thereafter, then his total earnings (in dollars) for a time in which he produces 35 articles is: 00x + 35y A 00x + 35y B 00y + 35x C x + 35y D

11 Chapter Financial decisions 7 Commission and royalties Commission is a method of payment used mainly for salespeople. The commission paid is usually calculated as a percentage of the value of goods sold. A royalty is a payment made to a person who owns a copyright. For example a musician who writes a piece of music is paid a royalty on CD sales. An author who writes a book is also paid a royalty based on the number of books sold. Royalties are calculated in the same way as commission; that is, as a percentage of sales. WORKED Example 7 Jack is a songwriter who is paid a royalty of % on all sales. Calculate the royalty that Jack earns if a song he writes sells CDs to the value of $ Find the royalty by calculating % of $ Answer the question in a sentence. Royalty = % of $ = 0. $ = $8 000 Jack earns $8 000 in royalties. In some cases a sales representative is paid a small wage or retainer plus a percentage of the value of the goods or services sold. WORKED Example A car salesperson is paid a retainer of $350 per week plus a commission of 8% of the profits made by the company on cars sold. a How much does the salesperson earn in a week when no sales are made? b How much does the salesperson earn in a week during which a $5000 profit was generated by that person s sales? a If no sales are made, only the retainer is a The salesperson is paid only the retainer, paid. which is $350. b State the retainer. b Retainer = $350 Find the commission paid by finding the percentage of the profits Commission = 8% of $5000 = 0.08 $5000 = $400 Find the total earnings by adding the Total earnings = $350 + $400 commission to the retainer. = $750 Answer the question in a sentence. The salesperson earns $750.

12 8 Maths Quest for Queensland Book 3 In other examples, the commission may be paid on a sliding scale. This means that a different percentage is calculated on different parts of the sale price. A real estate agency receives 4% commission on the first $ of a sale and % on the remainder. How much commission is received on the sale of a $ property? WORKED Example 9 Find the commission on the first $ Commission at 4% = 4% of $ = 0.04 $ = $300 Find the difference between the value Difference = $ $ of the property and $ = $0 000 Find the commission on this difference. Commission at % = % of $0 000 = 0.0 $0 000 = $400 Find the total commission. Total commission = $300 + $400 = $5600 Answer the question in a sentence. The commission received on this sale is $5600. EXCEL EXCEL SkillSHEET SkillSHEET Spreadsheet.3 Converting a percentage to a decimal fraction.4 Finding a percentage of a quantity (money) WORKED Example 7 Converting percentages to fractions or decimals WORKED Example 8 Spreadsheet Finding the percentage of an amount remember remember. Commission is a percentage of the value of the goods sold and is paid to the salesperson.. The retainer is the fixed amount paid to a sales representative. 3. A royalty is a payment made to a person who owns copyright. 4. Royalties, like commission, are calculated as a percentage of sales. D Commission and royalties Danyang is a writer who is paid a royalty of 0% on all sales. Calculate the royalty she earns in a year if a book she writes sells copies to the value of $ A home-improvements company pays commission at the rate of 6% on all sales. What would be the earnings of a person who had sales to the value of: a $8000? b $697.50? 3 Linda is a car salesperson who is paid a.5% commission. Calculate the amount of money Linda earns in a week where her sales total $ Gordon is paid a retainer of $00 per week plus a commission of 6% of the profits made by the company on the goods that he sells. a How much does Gordon earn in a week when no sales are made? b How much does Gordon earn in a week during which a $7000 profit was generated by his sales?

13 iinvestigation Chapter Financial decisions 9 WORKED Example 9 nvestigation 5 Alfonso gets a retainer of $35 per week plus a commission of 5 -- % on sales. What are his total earnings in a week in which his sales are: a $000? b $4500? c $7384? Commission and 6 Bryce is an author. His publisher pays him a fixed allowance of $500 per month, plus royalties 4 -- % royalty on sales. What would be his income for a month in which his book sales totalled: a $0? b $000? c $5 000? d $3 750? 7 A real estate agency receives 4% commission on the first $ of a sale and % on the rest. How much commission is received on the sale of a $ property? 8 At a second real estate agency, the commission rate is 5% on the first $8 000 of sale price and -- % on the remainder. Find the commission on the sale of the $ property. 9 Ingrid s real estate agency pays her 4% commission on the first $ of sale price, then % thereafter. How much commission would she receive on the sale of a property worth: a $48 000? b $5 000? c $35 000? 0 Yanu works for a boat broker who pays him 8% of the first $5 000 of the sale price, 3 then 3 -- % on the rest. Calculate the commission he receives on the following sales: 4 a $0 000 b $ c $ Veronica earns $50 per week plus 3 -- % on sales, while Francis earns 6% commission only. a How much does each earn on sales of $3600? b What level of sales would yield each the same income? Wolfgang, a car salesman, is paid a weekly retainer of $375, plus 0% of the dealer s profit on each vehicle. Find his total income for weeks in which the dealer s profits on vehicles he sold were: a $3500 b $5980 c $ multiple choice A salesperson is paid x% commission on $000 of sales. The simplest expression for the commission value is: A $0x B $000x C $ x D 0x% multiple choice Alfonso is paid a retainer of $r per week plus 4% commission on all sales. What are his total earnings for a fortnight in which his sales reach $s? A r + 4s B (r s) C r s D r s Earning money Search the classified section in the newspaper for a job in these 4 categories. Find a job that pays a salary and find out what that salary is. Find a job that pays a wage and find out what the hourly rate for that job is. Is there a possibility of overtime in this job? 3 Find a job that pays a commission. What is the rate of commission? Is a retainer involved? 4 Find a job where payment is made by piece. What is the amount that is paid per unit of work? Financial decisions 00 Mathcad GAMEtime

14 30 Maths Quest for Queensland Book 3 This chemical carries ries the genetic message e for plant and animal development. elopment. Calculate the commission to be paid for the transactions given. The amount and the letter beside each gives the puzzle s answer code. Sally's Stock Brokers Charges 0.8% commission on share transactions. $340 Grand Real Estate Commission charges are 3% on first $ then 3.5% on remainder. House sold for $ Factory sold for $ Unit goes for $0 000 Flat sells for $ Office sells for $ Cheryl's Sports Cheryl pays her managers a commission of 0.4% on the monthly income of her stores. BOB (Kew store) has sales of $ SANDRA (Newcastle store) brings in $ BRUCE (North Perth) manages $ in sales. LINDA (Glenelg) has sales of $ A B C D E C I O X $ worth of mining shares $ shares in Myer $4 500 in BHP shares $9800 in Bank shares $850 in IBM shares Colin's Cute Cars Colin pays his salesmen a 4.5% commission on their sales. Bill sells a VW for $800 and a Ford for $5300. Kerryn sells a HOLDEN for $7 00. Frank sells a VOLVO for $ 750. Yvonne sells a HONDA for $3 000 and a BMW for $6500. Barbara's Transport L N O R U C D E Barbara pays her state managers a commission of.8% on their yearly profits. GEORGE (NSW) has a profit of $ RACHEL (Vic) has a profit of $ I I Y $58.75 $00 $3.0 $7488 $78.40 $960 $0 45 $340 $000 $6.80 $3350 $560 $9300 $4950 $ $4575 $8 $ $4

15 iinvestigation Chapter Financial decisions 3 Fixed incomes Many people who are in unfortunate circumstances rely on government allowances for an income. These allowances include the youth allowance, pensions and other welfare benefits. nvestigation Investigating government payments Youth allowance What is the youth allowance? How much is paid per week for the youth allowance? 3 What conditions are placed on receipt of the youth allowance? 4 What will be the total received by a person after one year of receiving the youth allowance? 5 Find out the average weekly income for an 8-year-old person. Compare this with a person who receives the youth allowance. Unemployment benefits 6 What is the difference between unemployment benefits and the youth allowance? 7 How much is paid per week for the unemployment benefit for a: a single person? b married person with no children? c married person with children? 8 Do you have to work to receive the unemployment benefit? 9 What conditions are placed on a person receiving unemployment benefits? (For example, they may need to show that they are looking for work.) 0 Compare the amount received by a person on unemployment benefits with the average weekly income for an adult in Australia. Pensions Name three different types of pension that are paid by the government. What are the conditions for receiving each of these pensions? 3 How much is received per week for each of these pensions? 4 Does the amount received vary according to marital status and the number of dependants?

16 3 Maths Quest for Queensland Book 3 Gross and net pay Although we may calculate a person s pay, this is not the amount that is actually received. The amount that we calculate, based on their wage or salary, is called gross pay or gross wage. From your gross pay, several deductions may be made for items such as tax, union fees, private health insurance, superannuation and so on. The amount left after these deductions have been taken out is called the net pay and it is this amount that you actually receive. To calculate an employee s net pay we subtract any deductions from the gross pay. WORKED Example 0 Jill s gross pay is $ per week. Jill has deductions for tax of $4.55, superannuation of $.50 and union fees of $0.80. Calculate Jill s net pay. From $ (gross pay) subtract $4.55 (tax), $.50 (superannuation) and $0.80 (union fees). Net pay = $ $4.55 $.50 $0.80 Net pay = $530 In some cases you will be required to calculate the size of a deduction based on either an annual amount or a percentage. WORKED Example Bill is a mechanic and he has his union fees deducted from his pay each week. If the annual union fee is $58.70, calculate the size of Bill s weekly union deduction. Divide $58.70 (the annual union fee) by 5. Round the answer off to the nearest cent. Weekly deduction = $ Weekly deduction = $. WORKED Example Sam is a salary earner and her gross fortnightly salary is $86. Sam pays 4% of her gross pay each fortnight in superannuation. Calculate how much is deducted from Sam s pay each fortnight for superannuation. Calculate 4% of $86 (gross pay). Superannuation = 4% of $86 Superannuation = 0.04 $86 Superannuation = $74.48

17 remember remember Chapter Financial decisions 33. Gross pay refers to pay before any deductions are made.. Net pay refers to the pay received after deductions have been taken out. Net pay = gross pay deductions 3. Some deductions are calculated on an annual basis and then taken out in equal weekly or fortnightly amounts. 4. Some deductions are calculated as a percentage of gross earnings. E Gross and net pay WORKED Example 0 Brian is a bricklayer and his gross pay is $ per week. His weekly deductions are $4.50 for tax, $5.70 for superannuation and $8.50 for health fund contributions. Calculate Brian s net pay each week. Copy and complete the table below. Gross pay Deductions Net pay $ $99.45 $ $95.40 $ $33.85 $ $89.56 $ $ WORKED Example 3 Jack works in a holiday resort and is paid a wage of $.50 per hour for a 36-hour working week. His deductions are $50.5 for tax, $3.50 for health insurance, $.50 for superannuation and $0 for the resort s social club. Calculate Jack s net pay. 4 Wendy is on an annual salary of $ She is paid fortnightly. a Calculate Wendy s fortnightly gross pay. b If Wendy has fortnightly deductions of $ for tax, $87.95 for superannuation and $3.50 as a contribution to a professional organisation, calculate her net pay. 5 Tim works as a chef and is a member of the union. If Tim s union fees are $ per year and he has his fees deducted from his pay weekly, calculate the size of Tim s weekly deduction. 6 Bronwyn is a salary earner who is paid fortnightly. She has her fees for private health insurance deducted from her pay fortnightly. If the annual premium for Bronwyn s health cover is $875, calculate the amount that needs to be deducted from her pay each fortnight.

18 eenrichment 34 Maths Quest for Queensland Book 3 WorkSHEET. WORKED Example 7 June is paid a wage of $8.95 per hour for a 38-hour working week. a Calculate June s gross weekly pay. b June pays union fees of $365 per annum. Calculate the amount that should be deducted from her pay each week for union fees. c June has $45.50 deducted from her pay each week for tax. Calculate her net pay. 8 Nick is on an annual salary of $ and is paid fortnightly. a Calculate Nick s gross fortnightly pay. b Nick pays fortnightly into a private health fund for which the annual premium is $ Calculate the fortnightly payment. c Nick has his health fund payment and tax of $57.0 deducted from his fortnightly pay. Calculate Nick s net fortnightly pay. 9 Jasmin earns a weekly wage of $ She puts 3% of this wage into a superannuation fund. Calculate the amount that Jasmin pays in superannuation. 0 Tony earns a gross fortnightly salary of $ He pays 7% of his gross salary in superannuation. Calculate the amount that Tony has deducted from his salary each fortnight for superannuation. Daniel is paid $8.0 per hour for a 38-hour working week. a Calculate Daniel s gross weekly wage. b Daniel pays 5.5% of his gross weekly wage in superannuation. Calculate his weekly superannuation contribution. c Daniel pays tax of $35.60 as well as his superannuation contribution. Calculate Daniel s weekly net wage. Cathy is on an annual salary of $ and is paid fortnightly. a Calculate Cathy s gross fortnightly salary. b Cathy pays 4.75% of her gross salary in superannuation. Calculate the amount that is to be deducted from Cathy s fortnightly salary for superannuation. c Cathy has union fees of $530 per annum and private health insurance of $650 per annum deducted from her pay fortnightly. Calculate the total deduction made for both union fees and health insurance. d If Cathy pays $ in fortnightly tax as well as the above deductions, calculate her net weekly pay. nrichment Percentages in tests Xanthe, Yana and Zac each sat for three tests (English, Maths and Science) and received marks as shown in the table below. The tests were of the multiple choice/short answer type where no part marks were possible. English (out of 45) Maths (out of 60) Science (out of 80) Xanthe Yana Zac

19 iinvestigation Chapter Financial decisions 35 Comment on the following claims, backing your statements with mathematical evidence. Xanthe says that she performed best in Science. Yana claims that she performed better in Science than Xanthe did in English. Zac thinks his performance in Science is no better than his performance in English or Maths. Xanthe, Yana and Zac have a friend, Wendy. Wendy s English mark was the same as the average of Xanthe s, Yana s and Zac s English marks. Wendy s Maths result was 0% more than Yana s Maths result. Wendy s Science result was 5% more than Zac s Science result. What marks did Wendy receive for English, Maths and Science? 3 When Veronica s marks on the three tests were considered along with the other four students marks, the average performance on each of the three tests was calculated as 80%. Is this possible? Explain. 4 Create tables to display the marks and percentages of each of the five students on the three tests. 5 List the order of performance of the students on each subject test (most proficient to least proficient). nvestigation Working piece rate At the beginning of the chapter we were introduced to Margaret who works in a clothing factory sewing pre-cut fabrics. She and her co-workers are paid for each piece or article of clothing completed. A large travel company has placed an order for slacks, skirts, shirts and coats for their workers. Because these articles require a different time to complete, they all attract a different piece rate. A bonus rate applies to articles produced beyond the expected daily rate. The daily rates and expected daily output for each type of garment are as follows: slacks $0 each for the first 0 pairs, then $.50 for each pair thereafter skirts $7.50 each for the first 3 skirts, then $9.40 for each skirt thereafter shirts $8.50 each for the first shirts, then $0.60 for each additional shirt coats $6.50 each for the first 6 coats, then $0.60 for each additional coat What daily wage could a worker expect for producing the expected daily output of each of the items? Compare the bonus piece rate with the normal piece rate. 3 On Monday, Margaret completed 5 shirts. How much did she earn that day? 4 What is the minimum number of coats that she would need to sew on Tuesday to earn more than she earned on Monday?

20 36 Maths Quest for Queensland Book 3 5 At the end of the week Margaret looked at her pay slip and saw that her daily output throughout the week was 5 shirts on Monday, 7 coats on Tuesday, 3 slacks on Wednesday, 5 skirts on Thursday and shirts on Friday. a Which was her most productive day in terms of money earned? b What was her weekly wage? 6 From previous pay slips, Margaret calculated her income for the last financial year as $8 64 after all allowable deductions. The income tax payable on this amount is $65 plus 30c for each $ over $ 600. The compulsory Medicare levy payable is.5% of her annual income after allowable deductions. a How much income tax is Margaret expected to pay over the year? b How much Medicare levy is she due to pay? 7 Perhaps you or your friends have a part-time job. See if you can obtain some pay slips to investigate and check the different methods of payment. Wendy works hours per week at a rate of $.74 per hour. Calculate Wendy s weekly wage. David is paid an annual salary of $ Calculate David s fortnightly pay. 3 Rebecca is paid a commission of 7.% of the value of all sales she makes. Calculate Rebecca s pay in a week where her sales total $ Veronica works assembling radios. She is paid $5.3 for every radio assembled. Calculate Veronica s pay in a week where she assembles 45 radios. 5 Christy is paid $34.50 per 000 letterbox deliveries. Calculate what Christy is paid for 00 deliveries. 6 Matthew is paid $.68 per hour at ordinary rates. Calculate what Matthew earns per hour in overtime when he is paid at time and a half. 7 Calculate Norman s earnings for a 6-hour shift at double time when his ordinary rate of pay is $8.45 per hour. 8 Darren is a bank teller who is paid $9.80 per hour. Calculate what Darren will earn in a week where he works 37 hours at ordinary rates as well as 5 hours at time and a half. 9 Zelko s gross wage is $ per week. He has deductions of $80.93 for tax, $3.80 for superannuation and $.5 for union fees. Calculate Zelko s net wage. 0 Noel works as a salesman and is given the option of a commission of 5% of sales or a weekly retainer of $350 plus a commission of 4% of sales. If he anticipates his sales to be approximately $5 000 per week, which is the better deal?

21 Chapter Financial decisions 37 Budgeting Once we have earned money we need to allocate the money to cover our expenses; otherwise, we may spend more than we earn! Allocating money to cover expenses is called making a budget. A budget is divided into two parts: income and expenditure. A budget is balanced when income and expenditure are equal. Consider the budget below, drawn up for Tanya, who earns a net wage of $700. Income Expenditure Wages $700 Rent Groceries Bills Car loan Car running costs Entertainment Credit card Savings $50 $00 $00 $75 $50 $60 $50 $5 Total $700 Total $700 When designing a budget, it is important to look for all your expenses and set money aside for them. For example, electricity bills arrive every 3 months and money should be set aside each week so that when the bill does arrive you have the money to pay for it. The amount set aside should be based on the normal amount of the bill over a year, with that amount divided into weekly or fortnightly amounts. For bills such as electricity and telephone, an extra amount should be allowed, as you do not know the exact amount of the bill until it arrives. Such an allowance covers the possibilities of a price rise or increased usage. This is not necessary for bills such as council rates or insurance, as these are known in advance. Ben receives four electricity bills each year. For the previous year they were for $36, $87, $69 and $05. How much should Ben budget for electricity bills out of each week s pay? We should allow an extra 0% to cover the possibility of price increases or extra usage. 3 4 WORKED Example 3 Calculate the total of the previous years Annual total = $36 + $87 + $69 + $05 bills. Annual total = $597 To calculate the weekly amount, divide Weekly amount = $597 5 $597 by 5. Weekly amount = $.48 Increase $.48 by 0%. 0% of $.48 = $.6 Make a practical approximation of the Ben should budget $.50 per week to cover answer. the electricity. Some bills are calculated over different lengths of time, so the simplest way to develop a budget is to calculate all bills over a year.

22 38 Maths Quest for Queensland Book 3 WORKED Example 4 Marlene has the following bills. Electricity $0 every months Telephone $95 per quarter Car insurance $54 every 6 months Rates $50 per year Calculate the total amount that Marlene should budget for all of these bills each fortnight, allowing for an extra 0% to cover possible increases. Calculate the total annual amount for electricity. Electricity = $0 6 Electricity = $660 Calculate the total annual amount for telephone. Telephone = $95 4 Telephone = $380 3 Calculate the total annual amount for car insurance. Car insurance = $54 Car insurance = $508 4 Calculate the total annual amount for Rates = $50 rates. 5 Find the annual total for all of these bills. Total = $660 + $380 + $508 + $50 Total = $798 6 Increase $798 by 0%. 0% of $798 = 0 00 $798 0% of $798 = $ Divide $ by 6. Fortnightly allowance = $ Fortnightly allowance = $ Round off and give a written answer. Marlene should allow about $8 per fortnight to cover her bills. To bring a budget into balance, any money that is not spent can be saved. The amount saved can be calculated by subtracting the expenses to which we are committed from the total earnings. WORKED Example 5 Peter earns $950 per fortnight. He allows $0 per fortnight for his bills, $50 per fortnight for groceries, $70 per fortnight for car running costs and $80 per fortnight for entertainment. Peter also has a mortgage for which the payment is $600 per month. a Calculate the amount Peter should allocate each fortnight for his mortgage. b Calculate the amount of money Peter can save each fortnight. c Draw up a budget for Peter, showing his income and expenditure. a Calculate the annual mortgage amount. a Annual mortgage = $600 Annual mortgage = $700 Calculate the fortnightly amount by dividing by 6. Fortnightly amount = $700 6 Fortnightly amount = $76.9 b Calculate total expenses. b Total expenses = $ $0 + $50 + $70 + $80 Total expenses = $786.9 Calculate savings by subtracting all expenses from $950. Savings = $950 $76.9 Savings = $63.08

23 Chapter Financial decisions 39 c Draw up a budget by listing income and expenses in two columns. c Income Expenditure Wages $950 Mortgage Bills Groceries Car Savings $76.9 $0.00 $50.00 $70.00 $63.08 Total $950 Total $ To do work on budgeting you will need to be able to interpret the information on various household bills. WORKED Example 6 Look at the extract from a sample telephone bill below. Telstra Corporation Limited ABN Tax Invoice Issued Feb 03 Bill enquiries 3 00 Turn over for further enquiries Your Bill Account number Bill number T MR BILL SAMPLE THRIVING BUSINESS PTY LTD 5 WEST ROAD THE GURDIES QLD 4984 Total $3,46.60 Pay by 6 Mar 03 Account Activity Your Reference: Thriving Business Account Previous balance $,7.45 We received $,75.00 Balance $.55cr New charges pay by 6 Mar 03 $3,464.5 includes rounding of $0.0cr Usage charges to 0 Mar 03 $, Services and equipment rental to 0 Apr 03 $, Directory charges for this bill $6.46 Group plan balance $537.7cr Other charges and credits for this bill $30.50 Total $3,46.60 GST included in new charges $34.69 To avoid a late fee of $5.50 please pay by the due date Continued over page

24 40 Maths Quest for Queensland Book 3 a What is the total amount payable on the account? b By what date should this account be paid? c Why is a credit balance of $.55 indicated? d GST is charged at the rate of 0%. Confirm an amount of $34.69 GST on this account. a Look for a Total label. a The total amount payable is $ b Look for a Pay by label. b This account must be paid by 6 March 003. c Look at Previous balance and We received. d The amount due includes GST so it represents 0%. Calculate the GST (which represents 0%). c An amount of $75 was paid on the previous account when only $7.45 was due. This leaves a credit of $.55. d Total due (including GST) = $ So $ represents 0%. $ % $ % GST = $34.69 So $34.69 is the GST payable on this account. remember remember. A budget is a statement of income and expenditure.. A budget is in balance when income and expenditure are equal. 3. When preparing a budget, you should calculate weekly or fortnightly amounts based on annual expenditure. 4. Any unspent money should be set aside as savings to bring a budget into balance. 5. To manage a budget you will need to be able to read a variety of household bills. F Budgeting WORKED Example 3 Vesna gets her telephone bill quarterly. Last year her four bills were $89.50, $03.40, $0.30 and $ Calculate the amount that Vesna should budget for her telephone bill each week, allowing approximately 0% to cover price increases or extra usage. Christopher pays $360 each year in council rates. Calculate how much he should budget each fortnight for council rates. 3 Isabelle pays $34.65 per month in car insurance. Calculate the amount that she should budget each week for car insurance. 4 Tristan s mortgage repayments are $750 per month. Calculate the amount that Tristan should budget for each fortnight to cover his mortgage bill.

25 Chapter Financial decisions 4 WORKED Example 4 5 Mr and Mrs Banks have the following bills. Electricity $30 every quarter Telephone $08 per quarter Car insurance $35 per month House insurance $9.50 per month Council rates $00 per year Calculate the amount that Mr and Mrs Banks should budget for each week, to pay all these bills, allowing an extra 0% for extra usage or price increases. 6 Mr and Mrs Duric have the following bills. Electricity $05 every months Car insurance $87 every 6 months Telephone $5 per quarter Home contents insurance $365 per year Rent $80 per week Private health insurance $00 per year Calculate the total amount that Mr and Mrs Duric must budget for each fortnight, to cover all these bills. WORKED Example 5 7 Neville earns $685 per week. His weekly expenses are $00 for rent, $90 for groceries, $75 for bills, $70 for car running costs, $60 for entertainment and $50 for miscellaneous expenses. a Calculate the amount that Neville can save each week. b Present the above information in the form of a budget for Neville. 8 Petria has the following bills. Electricity $0 every quarter Telephone $80 every quarter Council rates $800 per annum Water rates $700 per annum Insurance $70 per month a Calculate the amount that Petria must budget each fortnight for the above bills. b Petria has a mortgage with a monthly repayment of $900. Calculate the amount that Petria must budget each fortnight for her mortgage. c Petria has a net fortnightly pay of $345. If Petria budgets $50 per fortnight for groceries, $80 for entertainment, $30 for medical expenses and $70 for car running costs, calculate the amount that Petria can save each fortnight. d Prepare the above information in a budget for Petria. WORKED Example 6 9 Look at the extract from a sample telephone bill on pages 4 and 43 and answer the following questions. a What is the amount due on this account? b By what date must this amount be paid? c This account is for more than one phone. Detail the services provided in the account. d How much GST was paid on STD calls from the landline? e How many local calls were made from the landline? f What is the monthly rental paid for a handset? g Why is an overdue payment of $60 registered in the Account Activity? h Verify the amount of $3.70 as the GST paid on this account.

26 4 Maths Quest for Queensland Book 3 Telstra Corporation Limited ABN Tax Invoice Issued 04 Sep 03 Bill enquiries 3 00 Turn over for other enquiries Your Bill Account number Bill number T MR BILL SAMPLE MAIN ROAD VEGEFIELD QLD 4444 Pay immediately $60.00 Overdue from previous bill Pay by 9 Sep 03 $99.65 New charges Total $ Account Activity Your Reference: Billy Bob s Bill Previous balance $6.38 We received $0.38cr Overdue pay immediately $60.00 New charges pay by 9 Sep 03 $99.65 includes rounding of $0.0cr Total $ GST included in new charges $3.70 To avoid a late fee of $5.50 please pay by the due date Summary of Charges incl GST Telephone $9. $.75 Mobile 0477 xxx xxx $3.0 $.45 Mobile 0488 xxx xxx $3.0 No change Internet and data service $5.00 $0.0 FOXTEL $9.39 New service Total $99.65 $30.5

27 Chapter Financial decisions 43 Account Issued 04 Sep 03 page 3 of 5 Item Service summary and call details continued Excl GST $ Incl GST $ Telephone line Summary charges Call charges Local nbrhood to 03 Sep 95 calls Local to 03 Sep 06 calls.0.3 Calls to 3 numbers to 03 Sep 6 calls STD to 03 Sep 7 calls Calls direct to mobiles to 03 Sep 5 calls.94.4 Services and equipment rental HomeLine Plus Line 9.49 per month Rental 05 Sep to 04 Oct Telephone Handset per month Rental 05 Sep to 04 Oct.47.7 Once off charges and credits Telephone line connection Fee for overdue account payable Total for $08.38 $9. Call charges detail STD calls Date Time Place Number Rate Min:Sec 08 Aug 0:37pm Nuriootpa 08856xxxx Day 3: Aug :07 pm Nuriootpa 08856xxxx Day : Aug 04:08 pm Nuriootpa 08856xxxx Day 4: Aug 0:38 pm Adelaide 0883xxxx Day : * Aug :00 am Adelaide 08856xxxx Day 3: * Aug :04 am Adelaide 08834xxxx Day : * Aug 05:48 pm Port Lincoln 0883xxxx Day 0: Total for STD $3. $3.4 Calls direct to mobiles Date Time Place Number Rate Min:Sec 08 Aug 0:37 pm Mobile 04xxxxxx Peak 0: Aug :07 pm Mobile 0435xxxxxx Off peak 0: Aug 04:08 am Mobile 04xxxxxx Peak 0: Aug 0:38 am Mobile 040xxxxxx Peak : Aug 9:34 am Mobile 043xxxxxx Peak 3: Total for calls direct to mobiles $.94 $.4

28 44 Maths Quest for Queensland Book 3 0 Look at the extracts from a sample electricity account below. a What is the amount payable on this account? b What is the GST contribution to the account? c On which date is payment due? d What period of time does this account cover? e What is the daily Ambulance Cover levy? f What is the average daily cost of electricity for the period of this account? g How many times a year are accounts issued?

29 Look at the extracts from a sample Energex gas account. Chapter Financial decisions 45

30 46 Maths Quest for Queensland Book 3 a What is the amount due for this account? b What is the due date for payment? c How many days does this account cover? d How much GST is paid on the account? e What is the minimum charge on this account? f Provide details of the calculation involved in determining that the daily average for this invoice is Look at the extract from the sample rate account from the Brisbane City Council. ABN BRISBANE CITY COUNCIL Rate Account Mailing Code *OVERSEAS Property Location 0 SAMPLE ST MITCHELTON Issue Date 4 Feb 003 Bill Number Enquiries (07) hours 7 days MS SAMPLE 0 SAMPLE ST MITCHELTON QLD 4053 Account Period 0 Jan Mar 003 Australia Post * The rates and charges set out in this notice are levied by the service of this notice and are due and payable within 30 days of the issue date. Full payment by the Due Date includes $5.00 Discount (rounded). Compounding interest of % per annum will accrue daily on any amount owing immediately after this date. Nett Amount Payable Due Date $ Mar 003 Summary of Charges Opening Balance 8.69 Brisbane City Council Rates & Charges State Government Charges Gross Amount Discount (rounded) allowed if received by Due Date Nett Amount Payable CR Page of 4 If mailing your payment please tear off this slip and return with payment. Please do not pin or staple this slip. See reverse for payment methods. Phone Pay Transaction no. Date Biller Code: Ref: MS SAMPLE 0 SAMPLE ST MITCHELTON 50 * Gross Nett Due Date $ $ Mar 003

31 Chapter Financial decisions 47 a What is the net amount payable on this account? b By what date must this amount be paid? c How much discount is allowed if payment is made by this date? d What interest rate is charged on any amount owing after the due date? e What was the water consumption for the period of the rate notice? f How much is the Fire Service Levy on the account? g What is the yearly charge for rubbish removal? Calculating GST and VAT The Australian government has introduced a Goods and Services Tax (GST) on most items purchased. At the moment, the tax amounts to 0% of the purchase price of the item, but this percentage is subject to change at any time the government decides to do so. Some items (fresh food, some educational costs and some medical costs) are exempt from the tax. In calculating the GST payable on an item, we simply calculate 0% of the purchase price.

32 48 Maths Quest for Queensland Book 3 WORKED Example 7 A CD player has a pre-gst price of $89. Calculate the GST payable on the purchase of the player. Calculate 0% of $89. GST payable = 0% of $89 = 0. $89 = $8.90 When calculating the amount required to purchase an item, you will need to add the GST to the pre-tax price. The quickest way to do this will be to calculate 0% of the pre-tax price. By using this method we add the 0% GST to 00%, which represents the cost of the item. In this way there is only one calculation to make. WORKED Example 8 The Campbell family goes to the Pizza Hut for lunch. The cost of the meal is $3.80 not including the GST. How much will the Campbells have to pay for the meal, including the GST? Calculate 0% of $3.80. Total cost = 0% of $3.80 =. $3.80 = $36.08 Give a written answer, rounding your answer to the nearest 5c. The cost of the meal will be $36.0. When you are given the total cost of an item, including GST, to calculate the pre-tax price of the item we need to reverse the above process. This means that we need to divide the total cost by 0%, written as a decimal fraction. WORKED Example 9 Calculate the pre-tax price of a car that costs $ 945, including GST. Total cost is 0% of the price. The pre-tax price is total cost divided by.. Price = $ 945. = $9 950 Taxes similar to the GST apply in many countries. These taxes are levied at different percentages in different countries and in many cases are called value added tax (VAT). The methods used to calculate the amount of VAT are the same as for Australia s GST; however, the rate must be checked for each question.

33 Chapter Financial decisions 49 WORKED Example 0 New Zealand has a VAT levied at a rate of.5%. Rebecca goes on holidays to New Zealand and rents a car for five days at a rate of $NZ4.75 per day. Calculate the total cost of renting the car including the VAT. Calculate the cost of the car by multiplying the daily rate by the number of days. Add the VAT by calculating.5% of the cost. Cost = $NZ = $NZ3.75 Total cost =.5% of $NZ3.75 = $NZ40.47 Note that in other countries there may be c and c pieces and so we do not take the answer to the nearest 5c. Also, if paying by credit card, the exact amount is charged, rather than an amount rounded to the nearest 5c. remember remember. The GST is a tax of 0% of the purchase price of all items other than a few exemptions.. To calculate the amount of GST payable, calculate 0% of the purchase price. 3. To calculate the total cost of an item, including the GST, calculate 0% of the pre-tax price. 4. To calculate the price of an item when you are given the total cost, including the GST, divide the total cost by 0%. 5. A value added tax (VAT) is similar to the GST that is applied in many countries. The VAT rate varies between countries; however, the same methods of calculation are used as for our GST. G Calculating GST and VAT WORKED Example 7 Calculate the GST payable on a CD that has a pre-tax price of $.90. Round your answer to the nearest 5c. Calculate the GST payable on each of the following items (prices are pre-tax): a a bottle of cordial at $.80 b a bike at $45.50 c a pair of shoes at $39.95 d a plane fare at $495 e a restaurant meal for which the bill totals $ Rounding money to the nearest 5 cents SkillSHEET

34 50 Maths Quest for Queensland Book 3 SkillSHEET.6 WORKED Example 8 Increasing a quantity by a percentage 3 Calculate the GST payable on each of the following items (correct to the nearest cent): a a pizza with a pre-tax price of $4.99 b a tin of baked beans with a pre-tax price of $. c a tin of peaches with a pre-tax price of $.35 d a pack of licorice with a pre-tax price of $.95 e a pack of frozen ice-creams with a pre-tax price of $ A pair of track shoes that cost $45.95 has the 0% GST added to its cost. Calculate the total cost of the sports shoes. 5 Calculate the total cost of each of the following items after the 0% GST has been added (prices given are pre-tax): a a rugby jersey priced at $95 b a CD priced at $4.95 c a rose plant priced at $.30 d a pack of cards priced at $9.95 e a jar of honey priced at $ Liam travels to New Zealand where the VAT is set at.5%. Calculate the amount of tax payable on each of the following items: a a video camera priced at $400 b a chocolate bar for $3.50 c a hiking tour costing $3760 d a helicopter ride costing $85 e a pair of shoes priced at $4.50. WORKED Example 9 7 A restaurant bill totals $84.70, including the 0% GST. Calculate the actual price of the meal before the GST was added. 8 A taxi fare was $8.60 including the 0% GST. Calculate: a the taxi fare without the GST b how much GST was paid. WORKED Example 0 9 George travels to the USA. In the state of Utah the VAT is levied at %. Calculate what George will pay for four nights accommodation in a hotel that charges $5 per night.

35 eenrichment Chapter Financial decisions 5 0 Sally travels to the USA. In California, the VAT is 7.5% of the price of the item. Calculate what Sally will pay for each of the following items: a a card which has a ticketed price of $.80 b Disneyland entry which is $05 c two nights accommodation at a hotel for $0.50 per night d a restaurant meal for which the bill totals $67.45 e a bus fare which costs $8.45. Kim decides to purchase a new car. The pre-tax cost for the basic model of the car is $ It is an extra $000 for an automatic car, an extra $500 for airconditioning, $000 for power steering, $800 for a CD player and $550 for alloy wheels. Calculate the cost of each of the following cars, after the 0% GST has been added: a the basic model car b an automatic car with airconditioning c a car with a CD player and alloy wheels d a car with all of the above added extras. nrichment Understanding percentages Discuss the following statements, giving reasons why you believe they are correct or incorrect. Provide a written response, supported by mathematical calculations, for each. At a 5% off storewide sale, I saved quite a bit on the items I bought. If the discount had been 0%, I would have saved another $5. If a store marks an item up by 0%, then offers a discount of 0%, it ends up at the same price. 3 If a store offers 0% discount at a sale, then another 5% discount for paying cash, I would save more money if the 0% discount was taken off before the 5% discount. 4 If a store marks up its items by 50%, this represents a profit of one-third of the sale price. 5 The Goods and Services Tax (GST) in Australia is 0%. If you take the final price of an item after GST has been added and divide that amount by, it will give you the value of the GST.

36 iinvestigation 5 Maths Quest for Queensland Book 3 nvestigation Examining bank fees and taxes Once we have earned money we use a bank or similar financial institution to look after it until we need it. When we deposit money in the bank the bank pays interest on that account. However, for many accounts where we need instant access to our money the interest paid is very low and there may be fees associated with using the account. Find three bank accounts into which your pay could be deposited electronically. Answer the following questions about them. a What is the interest rate payable on the account? b Is there a minimum balance that must be maintained in the account? c What are the features of this account? (For example, do you get a cheque book?) d Is there a monthly management fee on the account? e How many free transactions are you allowed each month? What are the charges for exceeding this number of transactions? f Are the transaction fees applied differently to deposits and withdrawals? Are they levied differently for over-the-counter and automatic teller and EFTPOS transactions? Bank accounts also attract a number of government taxes. For each of the following taxes find out i if they are imposed by the State or Federal Government and ii at what rate they are imposed: a Electronic Transactions Duty b Stamp Duty c Government Debits Tax.

37 Chapter Financial decisions 53 Yelena is on a salary of $ per year. Calculate this as a fortnightly amount. Dimitri is paid a salary of $ per week. How much is he paid a year? 3 Sung-Li earns $9.70 per hour. Calculate her wage for a 38-hour week. 4 Calculate Veronica s hourly rate of pay, if she earns $638 for a 40-hour working week. 5 Trevor receives a salary of $ per year. Calculate his monthly payment. 6 Rob is paid $57.06 for a week s work. If Rob s hourly rate is $3.87, calculate the number of hours worked. 7 A real estate agency earns 3% commission on the first $0 000 of a sale and.5% thereafter. Calculate the commission received on the sale of a $ property. 8 Daniela is an author and receives a royalty of 8.5% of the total sales of her book. Calculate Daniela s royalty in a year if her book sells copies to the value of $ The pre-gst price of a computer is $495. Calculate the cost of the computer, including the GST. 0 The cost of a set of golf clubs was marked at $995, including the GST. Calculate the pre-tax price of the golf clubs.

38 54 Maths Quest for Queensland Book 3 Last year we looked at investing money at a simple interest rate. We will now consider compound interest as an alternative to simple interest investments. Compound interest In practice, most investments are not calculated using simple interest. If you have a bank account, you would know that when interest is paid the balance of your account grows and it is on this new balance that your next interest payment is calculated. When interest is added to the principal and this new balance is used to calculate the next interest payment, this is called compound interest. We can calculate compound interest by calculating simple interest one period at a time. The amount to which the initial investment grows is called the compounded value or future value. Calculate the future value of an investment of $0 000 at 0% p.a. for 3 years with interest paid at the end of each year, by calculating the simple interest for each year separately. Write the initial principal. Initial principal = $0 000 Calculate the interest for the st year. st year s interest = 0% of $0 000 = $000 3 Calculate the nd year s principal by adding the st year s interest to the nd year s principal = $ $000 = $ 000 initial principal. Calculate the nd year s interest. nd year s interest = 0% of $ WORKED Example Calculate the 3rd year s principal by adding the nd year s interest to the nd year s principal. = $00 3rd year s principal = $ $00 = $ 00 Calculate the 3rd year s interest. 3rd year s interest = 0% of $ 00 = $0 Calculate the future value of the Future value = $ 00 + $0 investment by adding the 3rd year s = $3 30 interest to the 3rd year s principal. To calculate the actual amount of interest received, we subtract the initial principal from the future value. In the example above, the compound interest, CI = $3 30 $0 000 = $330 To compare this with simple interest earnings at the same rate: PrT I = $ = = $3000

39 Chapter Financial decisions 55 The table below shows a comparison between the value of an investment of $0 000 earning 0% p.a. at both simple interest and compound interest. Year I $ $ $ $ $ $ $ $ CI $ $00.00 $ $ $605.0 $775.6 $ $ We can develop a formula for the future value of an investment rather than do each example by repeated use of simple interest. Consider worked example. Let the compounded value after each year be A n. After year A = (increasing $0 000 by 0%) After years A = A (.) = (substituting the value of A ) = After 3 years A 3 = A. = = The pattern then continues such that the value of the investment after n years equals: $ n We can generalise this example to any investment. A = P( + r) n Where A = amount (or future value) of the investment P = principal (or present value) r = interest rate per compounding period expressed as a decimal fraction n = number of compounding periods. Calculate the future value of an investment of $ 000 at 7% p.a. for 5 years, where interest is compounded annually. Write down the formula for the future A = P( + r) n value. Write down the value of P, r (as a P = $ 000, r = 0.07, n = 5 decimal fraction) and n. 3 Substitute into the formula. A = $ Calculate. = $ WORKED Example In the above example interest is paid annually; however, this is not always the case. In many cases interest is paid more often. It may be paid six-monthly, quarterly, monthly or even daily. This is called the compounding period. If interest is paid more often than annually, the value of n is the number of compounding periods during the investment. The interest rate then needs to be converted from a rate per annum to a rate per compounding period.

40 56 Maths Quest for Queensland Book 3 For example, consider an investment of $6000 at 8% p.a. for years with interest compounded quarterly. Interest is paid four times per year and therefore eight times in years. Therefore n = 8. The interest rate must be calculated per quarter. This is done by dividing the annual rate by four. Therefore, in this example the rate is % per quarter, hence r = 0.0. Calculate the future value of an investment of $6000 at 8% p.a. for years with interest compounded quarterly. Write down the formula for A = P( + r) n the future value. Write down the value of P, r P = $6000, r = 0.0, n = 8 (as a decimal fraction) and n. 3 Substitute into the formula. A = $ Calculate. = $ WORKED Example 3 remember remember. The future value of an investment under compound interest can be calculated by calculating the simple interest for each year separately.. The formula used to calculate the future value of an investment is A = P( + r) n. 3. In the formula, n is the number of compounding periods over the term of the investment and r is the interest rate per compounding period. To find r, divide the interest rate per annum by the number of compounding periods per year. H Compound interest WORKED Example WORKED Example Ray has $5000 to invest. He invests it for 3 years at 0% p.a., with interest paid annually. Calculate the future value of the investment by calculating the simple interest on each year separately. Suzanne is to invest $5 000 for years at 7% p.a., with interest paid annually. Calculate the future value of the investment by calculating the simple interest for each year separately. 3 Kiri has $000 to invest. She invests the money at 8% p.a. for 5 years, with interest compounded annually. Use the formula A = P( + r) n to calculate the future value of Kiri s investment.

41 Chapter Financial decisions 57 WORKED Example 3 4 Use the formula to calculate the future value of each of the following investments with interest compounded annually. a $4000 at 5% p.a. for 3 years b $8000 at 3% p.a. for 5 years c $8 000 at 8% p.a. for 4 years d $ 500 at 5.5% p.a. for 3 years e $8750 at 6.5% p.a. for 6 years 5 Carla is to invest $ at 9.% p.a. for 5 years with interest compounded sixmonthly. Calculate the future value of the investment. 6 A passbook savings account pays interest of 0.% p.a. Luke has $500 in such an account. Calculate the future value of the account after years, if interest is compounded quarterly. 7 Noel is to invest $ 000 at 8% p.a. for years with interest compounded quarterly. Calculate the future value of the investment. 8 Vicky invests $ in a one-year fixed deposit at an interest rate of 6% p.a., with interest compounding monthly. a Convert the interest rate of 6% p.a. to a rate per month. b Calculate the future value of the investment upon maturity. 9 Calculate the compounded value of each of the following investments. a $960 for year at 4.50% p.a. with interest compounded six-monthly. b $7500 for 3 -- years at 5.6% p.a. with interest compounded quarterly. c $5 000 for -- years at 7.% p.a. with interest compounded six-monthly. d $4 000 for 4 years at 9% p.a. with interest compounded monthly. e $0 000 for 0 years at.95% p.a. with interest compounded quarterly. 0 3 multiple choice A sum of $5000 is invested for years at the rate of 4.75% p.a., compounded quarterly. The interest paid on this investment, to the nearest dollar, is: A 475 B $495 C $5475 D $5495 multiple choice After selling their house Mr and Mrs Dengate have $ They plan to invest it at 6% p.a., with interest compounded annually. The value of their investment will first exceed $ after: A 8 years B 9 years C 0 years D years multiple choice Warren wishes to invest $0 000 for a period of 5 years. The following investment alternatives are suggested to him. The best investment would be: A simple interest at 9% p.a. B compound interest at 8% p.a. with interest compounded annually C compound interest at 7.8% p.a. with interest compounded six-monthly D compound interest at 7.% p.a. with interest compounded quarterly multiple choice Which of the following investments, to be invested for 6 years and compounded semiannually at 8% p.a., will have a future value closest to $5 000? A $900 B $8500 C $9400 D $ 000

42 iinvestigation 58 Maths Quest for Queensland Book 3 4 Brittany has $3 500 to invest. An investment over a -year term will pay interest of 8% p.a. Calculate the compounded value of Brittany s investment if the compounding period is: a one year b six months c three months d monthly. GAMEtime Financial decisions 00 WorkSHEET.3 5 Kerry invests $ at 8% p.a. for a one-year term. For such large investments interest is compounded daily. a Calculate the daily percentage interest rate, correct to 4 decimal places. b Calculate the compounded value of Kerry s investment on maturity. c Calculate the amount of interest paid on this investment. d Calculate the extra amount of interest earned, compared with the interest calculated at the end of the year. 6 Simon invests $4000 for 3 years at 6% p.a. simple interest. Monica also invests $4000 for 3 years but her interest rate is 5.6% p.a., with interest compounded quarterly. a Calculate the value of Simon s investment on maturity b Show that the compounded value of Monica s investment is greater than Simon s investment. c Explain why Monica s investment is worth more than Simon s, despite receiving a lower rate of interest. EXCEL Spreadsheet Interest nvestigation Compound interest spreadsheets Let us examine a spreadsheet to show the growth of an investment with compounding interest. This spreadsheet models a $0 000 investment at 5% p.a. interest with interest compounded annually (one compounding period per year). Use the graphing function to draw a graph showing the growth of this investment over 0 years. Change the number of compounding periods per year to see the change in the value of the investment. Your graph should change as you change the information. 3 Change other information, such as the principal and interest rate, to see the change in your graph. 4 Write a paragraph outlining the effect these changes have on the future value of an investment.

43 Chapter Financial decisions 59 summary Copy the sentences below. Fill in the gaps by choosing the correct word or expression from the word list that follows. A is a fixed annual amount paid for regular work, which is divided into weekly, fortnightly or monthly payments. Wages are based on a fixed rate per hour, with paid at a higher rate. Special allowances, sick pay, parental leave, and so on are also paid. 3 A may be paid to a salesperson and is calculated as a percentage of the value of goods sold. are special commissions paid to authors, composers, and so on. 4 A person doing is paid according to the quantity of goods produced. 5 is the pay the employee receives before any deductions are taken out. 6 are made from gross pay for tax, superannuation, and so on. 7 The amount left from gross pay after deductions are taken out is called. 8 A is a list of income and expenses. 9 Budgets are used to allocate money to various purposes and to ensure that does not exceed. 0 If income and expenses are equal the budget is said to be. The is a 0% tax paid on the cost of all goods and services with the exception of some basic foods. Some other countries have a value added tax ( ), which is similar to the GST but levied at different rates. 3 interest is the interest added to the principal before the next interest calculation is made. 4 The future value of an investment can be calculated by using the formula A = P( + r) n, where A is the of the investment, P is the, r is the per interest period expressed as a decimal fraction and n is the number of for which the money is invested. 5 The amount of compound interest paid is found by the principal from the future value of the investment. W ORD LIST commission salary piecework overtime royalties gross pay GST balanced compound VAT expenditure union fees deductions budget net pay interest rate principal future value compounding periods subtracting income

44 60 Maths Quest for Queensland Book 3 CHAPTER review A A A B B C C Jane earns an annual salary of $ Calculate her fortnightly pay. Express $ per week as an annual salary. 3 Frank works as a casual shop assistant and is paid $8.0 an hour from 3.30 pm to 5.30 pm, Monday to Friday, and $9.50 an hour from 7 am to noon on Saturday. What is his total pay for the week? 4 Daniel earns $0 an hour for a regular 38-hour week. If he works overtime, he is paid double time. How much would he earn if he worked 4 hours in one week? 5 Bjorn earns $ per week award wage for a 38-hour week. a What is his standard hourly rate? b If he is paid time-and-a-half for normal overtime, what is his pay for a week in which he works 4 hours? 6 Xana makes gift cards as a hobby and is paid 55 cents for each one. a How much would she earn if she made 50 cards? b How many cards would she need to make to earn $44? 7 Kim sells cakes to the local shop. If the shop pays for the ingredients, she is paid $3.0 for each cake that she makes and 50 cents for each slice. If Kim makes 5 cakes and 5 slices one week, how much does she earn? D D 8 A salesperson earns a $50 per week retainer, plus % commission on the first $0 000 sale and -- % on the remainder. What is the total income for a week in which sales to the value of $8 000 were made? 9 Jennifer is to start a new job selling mobile phones. She is paid commission only at the rate of 7 -- % of sales. What value of sales must she make in order to receive commission of $600 in one week?

45 Chapter Financial decisions 6 0 Dale works as a cleaner. Her annual union fees are $ Dale has her union fees deducted from her pay weekly. Calculate the size of Dale s weekly deduction. David earns a salary of $5 495 per annum and is paid fortnightly. a Calculate David s gross fortnightly pay. b David pays 6.5% of his gross fortnightly pay into a superannuation fund. Calculate the size of David s fortnightly superannuation contribution. Jim is paid $.95 per hour and works 38 hours at normal time and hours overtime for which he is paid time and a half. a Calculate Jim s gross weekly pay. b Jim has his private health cover deducted from his gross pay. The annual contribution is $879. Calculate the amount deducted weekly from Jim s pay. c Jim pays 5.5% of his gross pay into superannuation. Calculate the amount of Jim s superannuation contribution. d If Jim also pays $85.90 in tax, calculate his net wage. 3 Ruth has a total income of $700 per week. She has expenses of $90 for her mortgage, $90 for her bills, $80 for entertainment, $50 for car running costs, $5 for groceries and $30 for medical needs. Calculate the amount that Ruth can allocate for savings in her budget. 4 Amy has to budget for the following bills. Electricity $5 every months Telephone $0 per quarter Insurance $6.50 per month Rates $050 per year Calculate the amount that Amy should budget each week to pay all of these bills. 5 A washing machine has a pre-tax price of $575. Calculate the amount of GST payable on the washer, if it is levied at a rate of 0%. 6 Calculate the amount of GST payable on each of the following items (prices given are pre-tax): a a cooked chicken at $9.95 b a bike at $475 c a chocolate costing $3.50 d a haircut priced at $4.75 e a $6.75 train ticket. 7 A round of golf usually costs $5 before tax. Calculate the total cost of the game after the 0% GST is added. 8 The total cost of a plane flight was $453.0, including GST. Calculate the actual cost of the flight without the tax. 9 Vicky invests $400 at 5% p.a. for 3 years with interest compounded annually. Calculate the compounded value of the investment at the end of the term. E E E F F G G G G H