Mathematics Stage 5 NS5.1.2 Consumer arithmetic. Methods of purchasing

Mathematics Stage 5 NS5.1.2 Consumer arithmetic Part 5 Methods of purchasing

Acknowledgments The Centre for Learning Innovation gratefully acknowledges the following owners of copyright material for permission to reproduce their work. Extracts from Mathematics Syllabus Years 7-10 Board of Studies, NSW Unit overview 2002 p iii-v, Part 1 pp 3, Part 2 pp 3, Part 3 pp 3, 4, Part 4 pp 3, 4, Part 5 p 3. Screenshots from Excel, used by permission Microsoft Corporation. Part 4 pp. 19-20, 48. COMMONWEALTH OF AUSTRALIA Copyright Regulations 1969 WARNING This material has been reproduced and communicated to you on behalf of the New South Wales Department of Education and Training (Centre for Learning Innovation) pursuant to Part VB of the Copyright Act 1968 (the Act). The material in this communication may be subject to copyright under the Act. Any further reproduction or communication of this material by you may be the subject of copyright protection under the Act. CLI Project Team acknowledgement: Writer: Jim Stamell Editor: Ric Morante Illustrator(s): Thomas Brown, Tim Hutchinson Desktop Publishing: Gayle Reddy Version Date: November 8, 2004 Revision Date: August 5, 2005 Revision Date: September 20, 2005 All reasonable efforts have been made to obtain copyright permissions. All claims will be settled in good faith. Published by Centre for Learning Innovation (CLI) 51 Wentworth Rd Strathfield NSW 2135 Copyright of this material is reserved to the Crown in the right of the State of New South Wales. Reproduction or transmittal in whole, or in part, other than in accordance with provisions of the Copyright Act, is prohibited without the written authority of the Centre for Learning Innovation (CLI). State of New South Wales, Department of Education and Training 2005.

Contents Part 5 Introduction Part 5...3 Indicators...3 Preliminary quiz...5 Best buys...9 Further best buys...15 Methods of payment 1...17 Methods of payment 2...21 GST...23 Term payment...27 Suggested answers Part 5...31 Exercises Part 5...35 Part 5 Methods of purchasing 1

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Introduction Part 5 This is the last section on consumer arithmetic and covers best buys, GST and term payments. Though there are many ways of earning and spending money it is important you learn to combine relevant calculations with sound logical thinking so you choose the wisest course for your circumstances. Indicators By the end of Part 5, you will have been given the opportunity to work towards aspects of knowledge and skills including: calculating and comparing the cost of purchasing goods using buying on terms calculating a best buy. By the end of Part 5, you will have been given the opportunity to work mathematically by: realising the total cost and/or hidden costs involved in some types of purchase arrangements making informed decisions relating to purchases and in given situations interpreting the GST on receipts. Source: Extracts from outcomes of the Mathematics Years 7 10 syllabus <www.boardofstudies.nsw.edu.au/writing_briefs/mathematics/mathematics_ 710_syllabus.pdf > (accessed 04 November 2003). Board of Studies NSW, 2002. Part 5 Methods of purchasing 3

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Preliminary quiz Before you start this part, use this preliminary quiz to revise some skills you will need. Activity Preliminary quiz Try these. 1 The table gives the monthly life insurance premiums for non-smokers. $250 000 policy $500 000 policy Age Male Female Male Female 35 $10.22 $9.14 $16.10 $13.92 40 $11.96 $10.88 $19.58 $17.40 45 $18.49 $15.44 $32.63 $26.54 50 $25.45 $21.10 $46.55 $37.85 55 $42.63 $30.23 $80.91 $56.12 a b What is the monthly premium for a 45-year-old male who takes out a $500 000 policy? A 50-year-old woman takes out a $250 000 policy. How much does she pay each year? c Is the cost for a $500 000 policy twice the cost of a $250 000 policy? Use an example to explain. Part 5 Methods of purchasing 5

d How much more in monthly premium would a 55-year-old male pay than a 55-year-old female to take out a $500 000 policy? e Suggest a reason for males paying a higher premium than females. 2 Calculate 17 1 % of $1250. 2 3 Increase $85 by 22%. 4 Decrease $670 by 15%. 5 Twenty tablets cost $24.60. Calculate the cost of each tablet. 6 To pay off a loan, Terry needs to pay $675 a month for 3 years. How much does Terry pay? 6 NS5.1.2 Consumer arithmetic

7 Use the simple interest formula to calculate the interest earned on $7800 invested for 3 years at 4.75% pa simple interest. Check your response by going to the suggested answers section. Part 5 Methods of purchasing 7

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Best buys Do you enjoy shopping? Do you shop in different stores and compare the prices? To obtain value for your money: shop around to compare price and quality be prepared to pay more for good quality items if you want them to last a long time. This especially includes items such as manchester, clothes, electrical appliances and shoes don t pay high prices for things you seldom use or will outgrow or tire of very quickly be careful of cheap bargains from unknown stores. Save!!! Buy one get one free Today only. All items 20% off Sale! Sale! Sale While stocks last. Most of the items you regularly buy are called consumables. Consumables are goods you buy and use regularly, such as food, toiletries, household cleaning materials and petrol. They form an important part of your budget. You can save money by careful shopping for these goods: buy only what you really need; avoid impulse buying perishable items, such as fresh fruit and vegetables, should only be bought in amounts you can use immediately to avoid waste buy fruit and vegetables that are in season so they will be at their cheapest take advantage of special offers to stock up on non-perishable goods at extra low prices for items which come in different sizes of packaging, choose the size which is most economical the best buy! Part 5 Methods of purchasing 9

How can you decide which is the best buy? Here is an example to determine the better buy. Follow through the steps in this example. Do your own working in the margin if you wish. A 455 g jar of Vegemite costs $6.75, while a 910 g jar of Vegemite costs $12. Which is the better buy? Solution There are several ways you can attempt this problem. Method A The large jar is twice the size ( 2 455 g ) of the smaller jar. So two of the smaller jars costs 6.75 2 = $13.50, making it $1.50 more expensive than an equal mass in the larger jar. Hence the larger jar is the better buy. You can t always rely on the larger size to be an exact simple multiple of the smaller size, as was in this case. Method B Calculate the unit cost, that is, the price you would pay for one unit. In this example you can calculate the number of cents per gram of Vegemite. For the 455 g jar: 675 = 1.484 cents per gram. 455 For the 910 g jar: 1200 910 = 1.319 cents per gram. 10 NS5.1.2 Consumer arithmetic

The larger jar is the better buy as the cost for each gram is lower. Although you can t buy just one gram, it does allow you to compare unit costs. Can you see why cents per gram was calculated and not dollars per gram? (The values you obtain are easier to compare.) Method C This is just a variation on the unit cost. In fact, it is the reciprocal of the unit cost. For this method you are calculating how much one cent (or one dollar) will buy. For the 455 g jar: 455 = 0.674 grams for each cent. 675 For the 910 g jar: 910 = 0.758 grams for each cent. 1200 So you get more for each cent with the larger jar so it is the better buy. Remember, the better buy is not always the larger size. And, especially with perishable items, do you get value for money if you buy the larger size but it goes off before you have used it all? Which method you use is up to you, but you need to know what the answers are telling you. Part 5 Methods of purchasing 11

Activity Best buys Try these. 1 A 500 g jar of honey costs $5.47 while a 1.5 kg can of honey costs $15.92. How much do you save by buying the can instead of three jars? 2 A 500 g packet of rice costs $1.10. A 2 kg packet of rice costs $4.75. a How many 500 g packets would you have to buy to get 2 kg? b Which is the better buy: 2 kg of rice in small packets, or one large packet? 3 Cheese is sold in different sized packets. For each of the following calculate the unit cost (cents/gram). 250 grams at $4.34 500 grams at $8.15 750 grams at $13.50 1 kilogram at $17.34 Which mass of cheese is the best buy? Check your response by going to the suggested answers section. 12 NS5.1.2 Consumer arithmetic

When you are comparing prices you are assuming the quality is the same. If the quality is different, then comparing prices would not give you a good indication of which is the better value for your money. When it comes to comparing three or more sizes, the unit method is often easier. The following exercises will allow you to develop the ideas in this session further. Go to the exercises section and complete Exercise 5.1 Best buys. In the next session you will develop these ideas further. Part 5 Methods of purchasing 13

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Further best buys When making once-only purchases the principle of buy only as much as you need should normally apply. However sometimes it is cheaper to buy more than you need to take advantage of cheaper bulk prices. Here is one such situation. Follow through the steps in this example. Do your own working in the margin if you wish. Holly needs 9 buttons for a shirt. They are sold individually for 20 cents each or on cards of 5 for 85 cents. Which is the cheapest way of buying nine buttons: 9 individual buttons at 20 cents each? a card of 5 plus 4 individual buttons? or 2 cards of 5, which gives a spare button? Solution The nine separate buttons cost, 9 20 = 180 cents = $1.80 1 card + 4 buttons cost, 85 + 4 20 = 165 cents = $1.65 2 cards of 5 cost, 2 85 = 170 cents = $1.70 Holly decides to pay the cheapest, 1 card + 4 buttons at $1.65. Although it is the cheapest, an extra 5 cents to buy 2 cards and have a spare button is probably the best buy. Do you agree? Part 5 Methods of purchasing 15

Activity Further best buys Try these. 1 The cost of ink cartridges for a computer printer are: black, $25.95; colour, $19.95 for each. (Each of the three colours is sold separately.) Jim needed to purchase a black cartridge, and three colour (cyan, magenta, and yellow) cartridges. a Calculate the total cost if he were to buy the four cartridges separately. b If he buys the four cartridges in one pack he can purchase them for $82.50. How much can he save by buying a pack? c The store manager advises Jim that if he were to buy five ink cartridges separately he would receive a 10% discount on the total sale. How much would he pay if he bought the five cartridges? (Assume he buys an extra black.) d What should Jim buy? Explain. Check your response by going to the suggested answers section. Now put some of your learning into practice. Go to the exercises section and complete Exercise 5.2 Further best buys. 16 NS5.1.2 Consumer arithmetic

Methods of payment 1 In modern society there are a number of methods of payment used to buy goods and pay for services. Some methods of payment include: cash, cheque, credit card, electronic funds transfer/point of sale (eftpos), lay-by, loan, hire purchase, and term payment. Over the past few years there have been many changes in banking. Now many people conduct their banking transactions with a card via automatic tellers (ATMs). Most of these outlets provide 24-hour service. These same cards, by which you deposit and withdraw money from your account, may also be used to purchase goods. You, as the consumer, have a number of choices available. You may purchase the goods and debit your account for the cost of the goods using electronic funds transfer/point of sale (eftpos). This also allows you to withdraw extra cash if you wish. These cards are referred to as debit cards, as the amount is debited against your account at the time of the transaction. For example: you may fill your car with petrol, pay for it using eftpos and ask for an additional sum of cash (cash out). The total amount will be deducted from your bank account at the time of purchase. You may purchase the goods on credit, buy now, pay later, using a credit card. For example, you buy a compact disc player using your interest free period credit card. At the end of the month a statement arrives showing the purchase. If the account is settled before the closing date, then no interest charges will apply. If you pay only part of the account then interest charges will apply to the outstanding balance (unpaid amount). Most banks now charge a yearly fee for credit cards with an interest free period. Credit cards have a credit limit, the maximum amount of credit available to you at any one time. This credit limit restricts Part 5 Methods of purchasing 17

purchases to less expensive items. So a television or washing machine may be bought using a credit card, but a car or house could not. A number of larger stores offer their own credit cards. These cards may be used for purchases within stores of the one organisation. A monthly statement is issued showing details of purchases, credits and payments. A minimum payment is required by the due date, and any outstanding amount will attract interest at the specified rate. Cash advances are not available on store credit cards. The above information will now be used in this example. Follow through the steps in this example. Do your own working in the margin if you wish. Simon receives his credit card statement for February. The closing balance is $2579.64. He cannot pay the full balance but does pay off $1150 by the due date. a How much will attract interest charges? b If interest is charged at 0.04952% per day on the outstanding balance, how much interest will Simon pay if he is 21 days overdue in paying the balance? Solution a 2579.64 1150 = $1429.64 will attract interest. b Using the simple interest formula, I = PRT I = 1429.64 0.04952 21 100 = $14.87 (Don t forget to change the daily percentage interest rate to a decimal by dividing by 100.) The lesson to be learned from this is pay any outstanding balances by the due date to avoid paying interest. If the full balance is not paid prior to the closing date, then the minimum payment (usually a small percentage of the total) must be made and 18 NS5.1.2 Consumer arithmetic

interest will be charged on the remaining balance. This credit charge will be shown on the following monthly statement. Activity Methods of payment 1 Try these. 1 Joanne s closing balance on her Felix Bros account is $4128.40. The minimum payment due is 2.5% of the closing balance, or $25, whichever is the greater. a What is the minimum amount Joanne must pay? b The annual interest rate on this card is 16.8%. Calculate the daily interest rate as a percentage, correct to six decimal places. (1 year = 365.25 days.) c Assuming she pays the minimum amount by the due date, and the balance exactly two weeks later. Calculate the interest she will be charged. Check your response by going to the suggested answers section. You have been practising questions on using credit cards. Now check that you can solve these kinds of problems by yourself. Part 5 Methods of purchasing 19

Go to the exercises section and complete Exercise 5.3 Methods of payment 1. In the next section you will consider further methods of purchasing goods. 20 NS5.1.2 Consumer arithmetic

Methods of payment 2 A lay-by sale is an agreement between a customer and a retailer for the sale of goods where the purchase price is paid over a fixed period of instalments. Goods on lay-by must be set aside and stored separately to other goods, and be clearly identified. Should the customer terminate the lay-by agreement as the result of any default, the retailer may return lay-by goods to stock, and retain a portion of the instalments paid to cover any expenses incurred. This example shows how lay-by works. Follow through the steps in this example. Do your own working in the margin if you wish. Alide bought a piece of jewellery at a store marked at $450 on 22nd April. Store policy is that a deposit of 20% be made initially followed by regular payments with the whole amount not taking more than 8 weeks. a b c d By which date must the item be completely paid for? Calculate the deposit. Alide made the following weekly payments: $50, $55, $40, $60. How much has she paid off the loan? What average weekly payment must she make in the last four weeks so the jewellery is completely paid off by the due date? Part 5 Methods of purchasing 21

Solution a Adding 8 weeks to 22 nd April gives 17 th June. b Deposit is 20 450 = $90 100 c Total is 90 (deposit) + 50 + 55 + 40 + 60 = $295 d She has still 450 295 = $155 to pay. So in 4 weeks she needs to average 155 = $38.75 per week. 4 Interest is not charged on lay-by, and the customer cannot pick it up until it is completely paid off. There is no limit on how much a customer can pay at any regular interval, although many stores expect a payment at least fortnightly. Activity Methods of payment 2 Try these. 1 Vicky bought a vacuum cleaner at a store marked at $850 on 14th June. Store policy is that a deposit of 15% be made initially followed by regular payments with the whole amount not taking more than 12 weeks. a By which date must the item be completely paid for? b Calculate the deposit. c Vicky made the following weekly payments: two payments of $50 each, $55, three payments of $75 each, and $90. How much has she paid off the loan? 22 NS5.1.2 Consumer arithmetic

d What average weekly payment must she make in the remaining weeks so the vacuum cleaner is completely paid off by the due date? Check your response by going to the suggested answers section. Lay-by is a useful way of buying items as it allows the customer to pay as much as they can afford at any time. It also ensures the item is available when the customer has completely paid off the cost. And if the item is paid off earlier, then the customer can pick it up before the agreement expires. There is a variety of different ways, and costs involved in, purchasing goods. Remember, the seller will always try and make it convenient for you to buy their product. Your job is to see where, and if, there are hidden costs and whether you are prepared to pay them. Alternately, you may need to come to some other arrangement to buy the goods you want. GST On most items bought in Australia a GST (Goods and Services Tax) of 10% applies. The price indicated on the item includes this GST. Suppose a retailer puts a price on a good of $100. He needs to add 10% of $100 (=$10) as the GST, to give a sale price for the item of $110. retailer s price for the item (10 parts) GST $10 $10 $10 $10 $10 $10 $10 $10 $10 $10 $10 selling price of item (11 parts) Part 5 Methods of purchasing 23

From this diagram you should be able to see that if you divide the selling price of an item carrying GST by 11 you can work out how much GST has been added. Follow through the steps in this example. Do your own working in the margin if you wish. A lawnmower is advertised as $495. Calculate the GST you pay on this item. Solution GST = 495 11 = $45 When you buy this item, $45 in GST goes to the Federal Government and the retailer keeps the remaining $450. Activity Methods of payment 2 Try these. 2 A refrigerator is marked at a store for $1375. Calculate the GST included. 3 A retailer needs to make $580 when he sells a television set. a How much GST must he add onto this amount to give the sale price? b How much is the sale price? 24 NS5.1.2 Consumer arithmetic

Check your response by going to the suggested answers section. Not all items carry a GST. You can find a list of items that are exempt by going to the Australian Taxation Office website. Access related sites on GST by visiting the CLI webpage <http://www.cli.nsw.edu.au/kto12>. Select Mathematics then Stage 5.2 and follow the links to resources for this unit NS5 Numbers then select NS5.1.2 Consumer arithmetic, Part 5. Now practise this learning more by doing the exercises. Go to the exercises section and complete Exercise 5.4 Methods of payment 2. Part 5 Methods of purchasing 25

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Term payment Expensive items such as cars, boats, and houses cannot usually be bought using credit cards. Payment for these items is generally made over an extended period of time through regular instalments (payments). What are some of the options for obtaining money to pay for these? You could apply for a loan from a bank, building society, friendly society, credit union, insurance company, or finance company. Alternatively, you may approach family or friends. With the possible exception of family and friends, all of the others will charge you interest on the loan. So not only will you have to pay back the capital (money borrowed) but also the interest. Financial institutions will require you to make regular payments, probably monthly, over the period of the loan. Another option is hire purchase. Hire purchase also involves the making of regular instalments or payments. A hire purchase agreement means that the goods are considered hired until the final instalment or payment has been made; only then is the purchaser said to own the goods. When borrowing money you need to: read the terms of the agreement carefully calculate the cost of the goods look at all possible alternatives select the agreement most suited to your needs. Many sellers, in their endeavour to get your business, will offer terms for you to buy certain, more expensive, items. Part 5 Methods of purchasing 27

Here is an example of such a situation. Follow through the steps in this example. Do your own working in the margin if you wish. A car dealer offers Tim the following terms for the $35 000 car he wants to buy: $7000 deposit and 36 monthly instalments of $1025. a b c d e What percentage is the deposit to the cost price of the car? How much will he pay for the car under these terms? How much interest would he pay? How long will it take Tim to own the car? Calculate the annual interest rate charged on the amount borrowed. Solution a b c d The deposit forms Total cost = deposit + instalments Total = 7000 + 36 1025 = $43 900 The extra money is paid is interest. Interest is 43 900 35 000 = $8900. 7000 100 = 20% of the car s value. 35 000 It will take him 36 months (3 years) before the car is fully paid off. e As he already made a $7000 deposit, he owes $28 000. The interest charged on this amount is $8900. Using the simple interest formula you can calculate the simple interest rate, r. I = P r 100 T 8900 = 28 000 r 100 3 8900 = 840 r r = 8900 840 = 10.56% pa 28 NS5.1.2 Consumer arithmetic

Businesses are entitled to charge interest on outstanding balances. After all, Tim has the car but the car dealer has not got all their money. If Tim had the cash, he could have paid for the car outright and avoided interest. He can also check out other sources of finance, too. Activity Term payment Try these. 1 Tim approached his credit union and was offered the $35 000 to buy the car. Interest would be charged at a simple interest rate of 6.2% pa over 4 years. a How much will he pay in interest under these terms? b Should he accept the terms of the car dealer, or his credit union? c How much interest can he save with this option? d Given he accepts the credit union offer, how much must Tim pay each month given equal instalments over this time? Check your response by going to the suggested answers section. While his monthly payments with the credit union are less than the car dealer s offer, Tim is paying it for longer (48 months compared to 36 months). The difference between the two offers is therefore not as great as would first appear. And with the credit union Tim is saved the problem of having to first come up with the $7000 deposit the car dealer needs. Part 5 Methods of purchasing 29

It is worthwhile checking out other sources of finance before committing yourself to buying expensive items. You can summarise the results using the following table: Car dealer Credit union deposit $7000 none monthly instalment $1025 $910 number of monthly payments 36 24 total paid $43 900 $43 680 interest $8900 $8620 amount borrowed $28 000 $35 000 Buying goods on terms raises many questions: does Tim really need a car? is this the most suitable car? does he need the car immediately? can he make do with other means of transport? does he need the car for his job? would Tim be best to wait until he could buy the car for cash? if he were to pay cash for the car could he get a cash discount? has Tim looked at all possible finance options? can he meet the regular repayments? what would happen if his income is reduced or stopped? Go to the exercises section and complete Exercise 5.5 Term payment. 30 NS5.1.2 Consumer arithmetic

Suggested answers Part 5 Check your responses to the preliminary quiz and activities against these suggested answers. Your answers should be similar. If your answers are very different or if you do not understand an answer, contact your teacher. Activity Preliminary quiz 1 a $32.63 b $253.20 c No, you can use any example such as a 35-year old male pays $10.22 for a $250 000 policy, but the same male would pay $16.10 for a $500 000 policy. d $80.91 $56.12 = $24.79 2 3 e Women live longer than men. 17.5 1250 = $218.75 100 22 85 = $18.70, so increase is $85 + $18.70 = $103.70. 100 [Alternatively, calculate 122% of $85 (that is, 100% + 22%).] 4 15 670 = $100.50, so decrease is $670 $100.50 = $569.50. 100 [Alternatively, calculate 85% of $670 (that is, 100% 15%).] 5 Each tablet costs 24.60 20 = $1.23. 6 In 36 months he pays 36 675 = $24 300. 7 I = P r 100 T = 7800 4.75 100 3 = $1111.50 Part 5 Methods of purchasing 31

Activity Best buys 1 Three jars cost 3 5.47 = $16.41. Savings 16.41 15.92 = $0.49. 2 a 4 packets b Four small packets cost 4 $1.10 = $4.40. It is cheaper to buy the four smaller packets. 3 The unit costs are: (250 grams) 1.736 cents/gram; (500 grams) 1.63 cents/gram; (750 grams) 1.8 cents/gram; (1 kilogram) 1.734 cents/gram. The best buy is the 500 g cheese. Activity Further best buys 1 a 25.95 + 3 19.95 = $85.80 b Saving is 85.80 82.50 = $3.30 c 2 black and 3 colours cost 2 25.95 + 3 19.95 = $111.75. With the 10% saving he pays 0.9 111.75 = $100.58. d The pack is cheaper than the individual items, but buying five cartridges he pays 100.58 82.50 = $18.08 more, thus effectively buying the $25.95 black cartridge for this price. If Jim uses the printer frequently then the extra black will not go astray and this would be a good buy. If he uses it infrequently he risks the cartridge drying out before he has a chance to use it. Activity Methods of payment 1 1 a Minimum payment is 2.5 4128.40 = $103.21 100 (Note that $25 as the minimum payment applies to amount of $1000 or less.) b Daily interest rate is 16.8 365.25 = 0.045996% c Interest charged is (4128.40 103.21) 0.045996 100 14 = $25.92 (You could calculate the balance before finding the interest.) 32 NS5.1.2 Consumer arithmetic

Activity Methods of payment 2 1 a 6 th September (a calendar may be useful to determine this) b Deposit is 15 850 = $127.50 100 c Paid 127.50 + 2 50 + 55 + 3 75 + 90 = $597.50 850 597.50 d She has 5 weeks to go, so average = 5 = $50.50 2 GST is 1375 11 = $125 3 a 10 580 = $58 b Sale is 580 + 58 = $638 100 Activity Term payment 1 a I = 35 000 6.2 100 4 = $8680 b c d credit union because he will pay less interest. save 8900 8680 = $220 in interest. He will pay $35 000 + $8680 = $43 680 over 4 years. Each month he will pay 43 680 48 = $910. Part 5 Methods of purchasing 33

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Exercises Part 5 Exercises 5.1 to 5.5 Name Teacher Exercise 5.1 Best buys 1 A 50 g jar of coffee costs $4.22, while a 150 g jar of the same coffee costs $12.10 and a 250 g jar costs $19.09. How much do you save by buying: a one 150 g jar instead of 3 small jars? b one 250 g jar instead of 5 small jars? 2 Red salmon comes in three sizes: 105 g for $6.42; 210 g for $8.56; 420 g for $12.38 a Which is the cheapest way to buy 420 g red salmon? b By how much is this cheaper than the most expensive way? Part 5 Methods of purchasing 35

c Suggest reasons why people would choose to buy the 105 g size. 3 A 40 g pack of sultanas costs 65 cents and a 1 kg bag of sultanas costs $6.16. How much will you save if you buy a 1 kg bag of sultanas instead of the small packs? 4 A 750 ml bottle of lemonade costs 99 cents while a 1250 ml bottle of lemonade costs $1.75. Which is the better buy? 36 NS5.1.2 Consumer arithmetic

5 For each of the following work out the unit price for each size. List the sizes in order of best buy value. a Cans of baked beans: (unit cost in cents/gram) A B C 130 g for $1.52 cents 225 g for $2.74 cents 440 g for $3.96 cents Order of best buy is b Washing powder is sold as follows: A B C D 750 g for $4.25 1 kg for $4.95 1.5 kg for $6.35 3 kg for $10.95 Order of best buy is Part 5 Methods of purchasing 37

Exercise 5.2 Further best buys 1 Penelope needs 9 litres of paint for the walls in three rooms. She is deciding whether she will paint them all off white or each room a different colour with some trim on the ceiling. At the hardware/paint discount store prices are: 500 ml can $18.20 1 L can $25.95 4 L can $43.95 10 L can $99.00 a Suggest at least two ways in which she can buy the paint she needs. b What is the cheapest way to buy enough paint for her needs? 38 NS5.1.2 Consumer arithmetic

2 In an open plan house Kurt decides to have matching curtains in the lounge, dining and family room areas. The fabric he has selected is sold at: $45 per metre 40% discount for a 100 m roll $62.50 for a 2.4 m drop length. On measuring up, Kurt finds he needs 30 drop lengths of 2.4 m each. a Calculate the total length of fabric required for the 30 drops. b How much would it cost to buy enough fabric by the metre? c How much does it cost to buy 100 m roll of curtain fabric? d How much does it cost to buy 30 drop lengths? e What is the cheapest way of buying the fabric needed? f How many drops must Kurt require so that buying a full roll is cheaper? Part 5 Methods of purchasing 39

3 (Research assignment) Most Australians now have mobile phones. Research the offers made by three different mobile phone providers and determine which is the best plan for your situation. Justify why you chose the plan you settled for. Your decision may include factors other than just costs, such as convenience, after-sale service and so on. Include in your report any brochures provided by the different mobile phone plans. 40 NS5.1.2 Consumer arithmetic

Exercise 5.3 Methods of payment 1 1 Peter owed nothing on his credit card at the end of April. During the month of May he buys the following, using his credit card. 3.5.05 shoes $109.95 12.5.05 wedding gift $120.30 23.5.05 electrical appliance $268.50 24.5.05 restaurant meal $83.25 27.5.05 hotel accommodation $214.80 a What would be the closing balance on his statement for May? b If the minimum payment due is 5% of the closing balance or $25, whichever is the greater, find the minimum payment Peter can make. c On what amount will Peter be charged interest if he pays the minimum amount? Part 5 Methods of purchasing 41

2 Kerrie s bank charges interest on cash advances and outstanding credit card balances at 17% pa a What is this as a monthly interest rate (to four decimal places)? b How much interest will Kerrie pay on an outstanding balance of $507 for one month? 3 Teresa s bank charges interest on outstanding balances as follows: 1.83% of outstanding balance plus 0.05027% of this balance per day until repaid. Teresa had an outstanding balance of $156.93 for 17 days. Calculate the credit charges payable. 42 NS5.1.2 Consumer arithmetic

4 The closing balance of Emma s Mastercard is $814.60. The minimum payment is 5% of closing balance, or $25, whichever is the greater. The credit charge on the outstanding balance is 2% of the outstanding amount plus 0.05575% per day of this amount until paid in full. a What is the minimum payment due? b What is the balance owing if Emma makes the minimum payment? c What is the credit charge if this balance is outstanding for 23 days? Part 5 Methods of purchasing 43

Exercise 5.4 Methods of payment 2 1 A car is on sale for $27 940. Calculate the GST included. 2 A retailer needs to make $1600 when he sells a computer. The retailer paid $1900 to the manufactures for the computer. a How much GST must he add onto this amount to give the sale price? b How much is the sale price? 3 Write down the name of one electrical appliance, and its cost price, as you may see it at a store or advertised in a newspaper or brochure. Use this information to calculate the GST that applies on this appliance. 4 The GST on an item is $387. Calculate the sale price of that item. 44 NS5.1.2 Consumer arithmetic

5 Zita pays off the full amount due on her bankcard at the end of April. Her statement for the month of May shows a total of $781.54 in purchases and a payment of $327.90. What is the closing balance for May? 6 Quentin gets a $150 cash advance using his credit card. Interest is charged from the date of the transaction until paid in full. Quentin repays the cash advance after 21 days. What will be his credit charge calculated at the daily rate of 0.05301%? 7 Cecilia s credit union has a minimum payment of 2.5% or $20, which ever is the greater, on credit card accounts. Cecilia s closing balance for December is $78.23. What is the minimum payment she can make? 8 Cynthia has a credit card with Big Chill Freezer Supplies Ltd. The following credit charges apply to outstanding balances: an initial charge of 1.5% of the balance plus 0.04932% per day until the balance is fully repaid. Calculate the credit charges payable by Cynthia on an outstanding balance of $551.36 for 22 days. Part 5 Methods of purchasing 45

Exercise 5.5 Term payment 1 How much will Dieter pay for a bicycle with a marked price of $376 if he pays $40 deposit and $12.37 per month for 24 months? How much extra will he pay in interest charges? 2 Wanda wants to buy a wetsuit valued at $187. She can pay 10% deposit and 25 weekly repayments of $8. a b What deposit will she pay? How much will she pay altogether? c How much more will she pay under these terms? 46 NS5.1.2 Consumer arithmetic

3 Romeo and Juliette need to buy a fridge. They have chosen a 220 L fridge with a marked price of $1548. The store will arrange finance based on one third deposit and repayments over two years at $24 per fortnight. a By buying the fridge on terms, how much deposit do they pay? b How much will they pay for the fridge altogether? c How much will they have paid in interest charges? 4 Janelle operates a catering business and needs a computer to keep all her records in order. The computer package she wants is on sale for $2599 or 25% deposit and monthly repayments of $92.35 over two years. How much will she pay in interest charges if she buys the computer on terms? Part 5 Methods of purchasing 47

5 Derek has just bought himself a bed, marked at $599, on 15% deposit and fortnightly instalments of $8.50 over 3 years. What saving would he have made if he paid cash? 6 Siân bought a boat for $9700 from a yacht broker. She paid a deposit of $900, extra brokerage costs of $280 and monthly instalments of $268.15 for 5 years. a Calculate the total cost of the boat and use this to find how much interest is charged? b Calculate the annual rate of simple interest charged. Remember to use the interest and the amount owing after the deposit. c She had not expected the maintenance cost to be so expensive and sold the boat for $10 950 soon after the last payment was made. How much did she lose? 48 NS5.1.2 Consumer arithmetic