Presented by…

KHO LIK FA (K)()

CINDY anak BARE()

CHRISYE STEPHANE ANAK NINGKAN()

ELVERNA PRESNEY ANAK JABANG()

SELIA SELIANA CHANDU ANAK DEPA()

MR. JASON LEE YEONG CHERNG

ADDITION

AL MATHEMAT

ICS PROJE

CT WORK 2/201

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GROUP 5USES OF

STATISTICS IN OUR DAILY

ECONOMIC ACTIVITY

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2

CO

NTEN

CHAPTERS TITLES PAGES1 CONTENT 22 APPRECIATION 43 OBJECTIVES 64 INTRODUCTION 85 PART A 116 PART B 157 PART C 198 PART D 249 FURTHER EXPLORATION 27

10 CONCLUSION 2911 REFLECTION 31

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APPRECIATION

First of all, we would like to thank God for giving us energy, strength and health to carry out this project work.

Next, we would like to thank our school for giving us the chance to create this project work. School also provides us space to discuss and carry out this project work.

Not forgetting our beloved parents who provided everything needed in this project work, such as money, Internet, books, computer and so on. They contribute their time and spirit on sharing their experience with us. Their support may raise the spirit in us to do this project work smoothly.

After that, we would like to thank our Additional Mathematics teacher, Mr Jason Lee Yeong Cherng for guiding us throughout this project. When we face some difficulties on doing tasks, he will try his best to teach us patiently until we have done the project work.

Then, we would like to thank the proprietor of the shop who was willing to share their experience on business activity and the experience on saving money with us.

Lastly, we would like to thank our classmates who shared ideas and providing some help on solving problems. We help each other until we finished this project work.

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OBJECTIVES

All of our Form 5 students in whole Malaysia are required to carry out an Additional Mathematics Project Work during mid-term holiday. This project is done in groups of five. Upon completion of the Additional Mathematics Project Work, we are to gain valuable experiences and able to:

Solve routine and non-routine problems.Improve our thinking skills.Knowledge and skills are applied in meaningful ways in solving real-life problems.Expressing ones mathematical thinking, reasoning and communication are highly encouraged and expected.Stimulates and enhances effective learning.Acquire effective mathematical communication through oral and writing and to use the language of mathematics to express mathematical ideas correctly and precisely.Enhance acquisition of mathematical knowledge and skills through problem-solving in ways that increase interest and confidence.Prepare ourselves for the demand of our future undertakings and in workplace.Realise that mathematics is an important and powerful tool in solving real-life problems and hence develop positive attitude towards mathematics.Train ourselves not only to be independent learners but also to collaborate, to cooperate, and to share knowledge in an engaging and healthy environment.Use technology especially the ICT appropriately and effectively.Train ourselves to appreciate the intrinsic values of mathematics and to become more creative and innovative.Realize the importance and the beauty of mathematics.

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INDEX

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INTRODUCTION

An index number is a percentage ratio of prices, quantities or values comparing two time periods or two points in time. The time period that serves as a basis for the comparison is called the base period and the period that is compared to the base period is called the given or current period. A price index measures the change in the money value of an item (or group of items) over time whereas a quantity index measures the non-monetary value of an item (or a group of items) over time. An index number that represents a percentage comparison of the number of cars sold in a given month as compared with that of a base month is a quantity index. A price index represents a comparison of prices between two time periods and, finally, a value index is one that represents a comparison of the total value of production or sales in two time periods without regard to whether the observed difference is a result of differences in quantity, price or both. Index numbers are also differentiated according to the number of commodities or products included in the comparison. A simple index, also known as a relative, is a comparison involving only one item but an index whose calculation is based on several items is known as an aggregate or composite index. A very famous example of a composite index is the Retail Prices Index (RPI), which measures the changes in costs in the items of expenditure of the average household.

In economics and finance, an index is a statistical measure of changes in a representative group of individual data points. These data may be derived from any number of sources, including company performance, prices, productivity, and employment. Economic indices (index, plural) track economic health from different perspectives. Influential global financial indices such as the Global Dow, and the NASDAQ Composite track the performance of selected large and powerful companies in order to evaluate and predict economic trends. The Dow Jones Industrial Average and the S&P 500 primarily track U.S. markets, though some legacy international companies are included. The Consumer Price Index tracks the variation in prices for different consumer goods and services over time in a constant geographical location, and is integral to calculations used to adjust salaries, bond interest rates, and tax thresholds for inflation. The GDP Deflator Index, or real GDP, measures the level of prices of all new, domestically produced, final goods and services in an economy. Market performance indices include the labour market index / job index and proprietary stock market index investment instruments offered by brokerage houses.

Some indices display market variations that cannot be captured in other ways. For example, the Economist provides a Big Mac Index that expresses the adjusted cost of a globally ubiquitous Big Mac as a percentage over or under the cost of a Big Mac in the U.S. with a U.S. dollar (estimated: $3.57). Norway prices reflect most relatively expensive Big Mac, at an 84% increase over U.S. prices, or $6.5725 U.S. The least relatively expensive Big Mac price occurs in Hong Kong, at a 52% reduction from U.S. prices, or $1.71 U.S. The Big Mac index is used to predict currency values. From this example, it would be assumed that Hong Kong currency is undervalued, and provides a currency investment opportunity.

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An index number is a percentage ratio of prices, quantities or values comparing two time periods or two points in time. The time period that serves as a basis for the comparison is called the base period and the period that is compared to the base period is called the given or current period. A price index measures the change in the money value of an item (or group of items) over time whereas a quantity index measures the non-monetary value of an item (or a group of items) over time. An index number that represents a percentage comparison of the number of cars sold in a given month as compared with that of a base month is a quantity index. A price index represents a comparison of prices between two time periods and, finally, a value index is one that represents a comparison of the total value of production or sales in two time periods without regard to whether the observed difference is a result of differences in quantity, price or both. Index numbers are also differentiated according to the number of commodities or products included in the comparison. A simple index, also known as a relative, is a comparison involving only one item but an index whose calculation is based on several items is known as an aggregate or composite index. A very famous example of a composite index is the Retail Prices Index (RPI), which measures the changes in costs in the items of expenditure of the average household.

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The school Cooperative in one of the schools in your area made a profit of RM 50 000 in the year 2011. The cooperative plans to keep the money in a fixed deposit account in a bank for one year. The interest collected at the end of this period will be the poor students

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PART A

in the school. As a member of Board of Cooperative you are to find the total interest which can be collected from different banks.

Given below are the interest rates offered by 3 different banks: Bank A, Bank B and Bank C. You are to calculate the interest that can be obtained based on the given rates, if the money is to be kept in the bank for a period of one year for monthly auto renewable, three months auto renewable, six months auto renewable and twelve months auto renewable without withdrawal. Compare and discuss which bank will you choose and explain why.

PERIOD BANK A (% p.a.) BANK B (% p.a.) BANK C (% p.a.)1 MONTH 3.10 3.00 3.002 MONTH 3.10 3.00 3.003 MONTH 3.15 3.05 3.054 MONTH 3.15 3.05 3.055 MONTH 3.15 3.10 3.056 MONTH 3.20 3.10 3.107 MONTH 3.20 3.10 3.108 MONTH 3.20 3.10 3.109 MONTH 3.20 3.10 3.10

10 MONTH 3.20 3.10 3.1011 MONTH 3.20 3.10 3.1012 MONTH 3.25 3.15 3.20

Solution

by Geometric Progression Solution

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Tn = arn a = 50 000Bank A

Monthly auto renewable

= RM 50 000 × ( 12 03112 000 )

12

= RM 51 572.21

Interest= RM 51 572.21 – RM 50 000= RM 1 572.21

Three months auto renewable

= RM 50 000 × ( 80638000 )

4

= RM 51 593.70

Interest= RM 51 593.70 - RM 50 000= RM 1 593.70

Six Months auto renewable

= RM 50 000 × ( 127125 )

2

= RM 51 612.80

Interest= RM 51 612.80 – RM 50 000= RM 1 612.80

Twelve months without withdrawal

= RM 50 000 × ( 413400 )

1

= RM 51 625.00

Interest= RM 51 625 – RM 50 000= RM 1 625.00

Bank B

Monthly auto renewable

= RM 50 000 × ( 401400 )

12

= RM

51 520.80

Interest= RM 51 520.80 – RM 50 000= RM 1 520.80

Three months auto renewable

= RM 50 000 × ( 80618000 )

4

= RM 51 542.53

Interest= RM 51 542.53 – RM 50 000= RM 1 542.53

Six months auto renewable

= RM 50 000 × ( 20312000 )

2

= RM 51 562.01

Interest= RM 51 562.01 – RM 50 000= RM 1 562.01

Twelve months without withdrawal

= RM 50 000 × ( 20632000 )

1

= RM

51 575.00

13

Interest= RM 51 575.00 – RM 50 000= RM 1 575.00

Bank C

Monthly auto renewable

= RM 50 000 × ( 401400 )

12

= RM 51 520.80

Interest= RM 51 520.80 – RM 50 000= RM 1 520.80

Three months auto renewable

= RM 50 000 × ( 80618000 )

4

= RM 51 542.53

Interest= RM 51 542.53 – RM 50 000= RM 1 542.53

Six months auto renewable

= RM 50 000 × ( 20312000 )

2

= RM 51 562.01

Interest= RM 51 562.01 – RM 50 000= RM 1 562.01

Twelve months without withdrawal

= RM 50 000 × ( 129125 )

1

= RM

51 600.00

Interest= RM 51 600 – RM 50 000= RM1 600.00

PeriodInterest (RM)

Bank A Bank B Bank CMonthly auto renewable RM 1 572.21 RM 1 520.80 RM 1 520.80

Three months auto renewable RM 1 593.70 RM 1 542.53 RM 1 542.53Six months auto renewable RM 1 612.80 RM 1 562.01 RM 1 562.01

Twelve months without withdrawal RM 1 625.00 RM1 575.00 RM1 600.00

Therefore, we will choose Bank A because the interest of Bank A is higher than Bank B and C.

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15

PAR

(a) The Cooperative of your school plans to provide photocopy service to the students of your school. A survey was conducted and it is found out that rental for a photo copy machine is RM 480 per month, cost for a rim of paper (500 pieces) is RM 10 and the price of a bottle of toner is RM 80 which can be used to photocopy 10 000 pieces of paper.

(i) What is the cost to photocopy a piece of paper?

Solutionby Mathematical Solution

Rental for photocopy machine/month= RM 480

Cost for a rim of paper (500 pieces)= RM 10

Price of a bottle of toner (10 000 pieces)= RM 80

Cost for a photocopy of a piece of paper

= RM 80+RM 480+[( 10 000

500 )(RM 10 )]

10 000= RM 0.076

(ii) If your school cooperative can photocopy an average of 10 000 pieces per month and charges a price of 10 cent per piece, calculate the profit which can be obtained by the school cooperative.

Solutionby Mathematical Method

Charge of a piece of photocopy of a paper= RM 0.10

Cost for a photocopy of a piece of paper= RM 0.076

Profit obtained= (RM 0.10 – RM 0.076)(10 000)= RM 240

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PAR

(b) For the year 2013, the cost for photocopying 10 000 pieces of paper increased due to the increase in the price of rental, toner and paper as shown in table below:

Cost 2012 (RM) Cost 2013 (RM)Rental 480 500Torner 80 100Paper 200 240

(i) Calculate the percentage increase in photocopying a piece of paper based on the year 2012, using two different methods.

Solution

METHOD 1by Mathematical Solution

Cost of photocopy of a piece of paper in 2013

= RM 100+RM 500+RM 240

10 000= RM 0.084

Percentage increase

= 0.084−0.076

0.076 x 100%

= 10.5263%

METHOD 2by Price Index Solution

I = P1

P0

x 100 Ῑ� = ∑ IW

∑W

Price Index, I Weightage, W

Rental625

625

Toner 125 5Paper 120 12

Ῑ =

( 6256 ) (25 )+(125 ) (5 )+(120 ) (12 )

25+5+12

= 25015

252 = 111.17

Percentage increase

= (RM 0.076x111.17

100 )– RM 0.076

RM 0.076

x

100%= 10.5263%

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(ii) If the school cooperative still charge the same amount for photocopying a piece of paper, how many pieces of paper should the cooperative photocopy in order to get the same amount of profit?

Solutionby Mathematical Solution

Pieces of paper should cooperative photocopy

= 240

(0.10−0.084 )

= 240

0.016= 15 000 pieces

(iii) If the cooperative still maintain to photocopy the same amount of paper per month, how much profit can Cooperative obtain?

Solutionby Mathematical Solution

Profit obtained= (RM 0.10)(10 000) – (RM 0.084)(10 000)= RM 160

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PAR

The population of the school is increasing. As a result, the school cooperative needs more space for keeping the increasing amount of stock. Therefore the school cooperative plans to expand the store-room.

It is estimated that cost for renovation is RM 150 000. Make a conjecture on which is a better way for the school cooperative to pay, whether to pay the whole lump sum in cash or keep the RM 150 000 in a fixed deposit account at a rate of 6% p.a. in a bank then borrow the RM 150 000 from a bank and pay for the hire purchase for a period of 10 years with a interest rate of 4.8% p.a. and withdraw monthly to pay for the hire purchase every beginning of a month. Make a conclusion and give your reason.

(You can give your solution in table form, Excel or graph)

Solution

by Excel

Months

Saving Balance

(RM)

Total Loans To Be Pay

(RM)1 148150.00 1850.002 147040.75 3700.003 145925.95 5550.004 144805.58 7400.005 143679.61 9250.006 142548.01 11100.007 141410.75 12950.008 140267.80 14800.009 139119.14 16650.00

10 137964.74 18500.0011 136804.56 20350.0012 135638.58 22200.0013 134466.78 24050.0014 133289.11 25900.0015 132105.56 27750.0016 130916.08 29600.00

17 129720.67 31450.0018 128519.27 33300.0019 127311.86 35150.0020 126098.42 37000.0021 124878.92 38850.0022 123653.31 40700.0023 122421.58 42550.00

Months

Saving Balance

(RM)

Total Loans To Be Pay

(RM)24 121183.69 44400.0025 119939.60 46250.0026 118689.30 48100.0027 117432.75 49950.0028 116169.91 51800.0029 114900.76 53650.0030 113625.27 55500.0031 112343.39 57350.0032 111055.11 59200.00

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PAR

33 109760.38 61050.0034 108459.19 62900.0035 107151.48 64750.0036 105837.24 66600.0037 104516.43 68450.0038 103189.01 70300.0039 101854.95 72150.0040 100514.23 74000.0041 99166.80 75850.0042 97812.63 77700.0043 96451.70 79550.0044 95083.95 81400.0045 93709.37 83250.0046 92327.92 85100.00

Months

Saving Balance

(RM)

Total Loans To Be Pay

(RM)47 90939.56 86950.0048 89544.26 88800.0049 88141.98 90650.0050 86732.69 92500.0051 85316.35 94350.0052 83892.93 96200.0053 82462.40 98050.0054 81024.71 99900.0055 79579.83 101750.0056 78127.73 103600.0057 76668.37 105450.0058 75201.71 107300.0059 73727.72 109150.0060 72246.36 111000.0061 70757.59 112850.0062 69261.38 114700.0063 67757.69 116550.0064 66246.48 118400.0065 64727.71 120250.0066 63201.35 122100.0067 61667.35 123950.0068 60125.69 125800.0069 58576.32 127650.0070 57019.20 129500.0071 55454.30 131350.0072 53881.57 133200.0073 52300.96 135050.0074 50712.48 136900.0075 49116.04 138750.00

76 47511.62 140600.0077 45899.18 142450.0078 44278.67 144300.0079 42650.07 146150.0080 41013.32 148000.0081 39368.39 149850.0082 37715.23 151700.0083 36053.81 153550.0084 34384.08 155400.00

Months

Saving Balance

(RM)

Total Loans To Be Pay

(RM)85 32706.00 157250.0086 31019.53 159100.0087 29324.62 160950.0088 27621.24 162800.0089 25909.35 164650.0090 24188.90 166500.0091 22459.84 168350.0092 20722.14 170200.0093 18975.75 172050.0094 17220.63 173900.0095 15456.74 175750.0096 13684.02 177600.0097 11902.44 179450.0098 10111.95 181300.0099 8312.51 183150.00

100 6504.07 185000.00101 4686.60 186850.00102 2860.03 188700.00103 1024.33 190550.00104 192400.00105 194250.00106 196100.00107 197950.00108 199800.00109 201650.00110 203500.00111 205350.00112 207200.00113 209050.00114 210900.00115 212750.00116 214600.00117 216450.00118 218300.00

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119 220150.00120 222000.00

223850.00

by Graph

0

20000

40000

60000

80000

100000

120000

140000

160000

Months

∴ Pay RM 150 000 in cash is better than keep the RM 150 000 in a fixed deposit account at a rate of 6% p.a. then loan RM 150 000 from the other bank and pay with the period of 10 years with the rate of 4.8% p.a..

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23

PAR

The cooperative of the school also has another amount of RM 50 000. The cooperative plans to keep the money in a bank. The bank offered a compound interest rate of 3.5% per annum and a simple interest rate of 5% per annum.

Explain the meaning of “compound interest” and “simple interest”. Suggest a better way of keeping the money in this bank. State a suitable period for keeping the money for each plan. Explain why.

Solution

by Dictionary (source: Oxford Advanced Learner’s Dictionary 6th Edition)

Compound interest

Interest that is paid both on the original amount of money saved and on the interest that has been added to it.

Simple interest

Interest that is paid only on the original amount of money that you invested, and not on any interest that is earned.

By Excel

Year

Simple Interest (RM)

Compound Interest (RM)

0 50000 500001 52500 517502 55000 53561.253 57500 55435.894 60000 57376.155 62500 59384.326 65000 61462.777 67500 63613.968 70000 65840.459 72500 68144.87

10 75000 70529.9411 77500 72998.4912 80000 75553.4313 82500 78197.8014 85000 80934.73

Year

Simple Interest (RM)

Compound Interest (RM)

15 87500 83767.4416 90000 86699.3017 92500 89733.7818 95000 92874.4619 97500 96125.0720 100000 99489.4421 102500 102971.5722 105000 106575.5823 107500 110305.7224 110000 114166.4225 112500 118162.2526 115000 122297.9327 117500 126578.3628 120000 131008.6029 122500 135593.9030 125000 140339.69

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PAR

From the table and the graph above,

Simple interest is suitable for savings in a short period. It is because of its interest is higher than compound interest and it is paid only on the original amount of money that you invested, and not on any interest that is earned. For example, when you keep RM50 000 with an interest of 5% of simple interest for 2 years, then you will gain RM 5 000 after two years. So the total amount in the bank is RM 55 000 after two years. When one keeps RM 50 000 with the interest of 3.5 % of compound interest for 2 years, then you will gain RM3 561.25. So the total amount in the bank is RM 53 561.25 after two years.

Compound interest is suitable for savings in a long period. It is because of the original amount of money saved and on the interest that has been added to it. For example, RM50 000 for the plan of 3.5 % of compound interest plan for 21 years then we will have RM 102 971.57 in our saving account. But when one keeps RM 50 000 for the plan of 5 % of simple interest for 30 years, then we will only have RM 102 500 in our savings account.

Therefore, it is better to save in the compound interest plan account for long-term savings and simple interest for short-term savings.

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2 4 6 8 10 12 14 16 18 20 22 24 26 28 300

20000

40000

60000

80000

100000

120000

140000

Simple InterestCompound Interest

99459.44317

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FURTHE

R EXPLORATI

When Ahmad was born, his parents invested an amount of RM 5 000 in the Amanah Saham Bumiputera (ASB) for him. The interest rate offered was 8.0% p.a. At what age will Ahmad have a saving of RM 50 000, if he keeps the money without withdrawal?

Solution

by Geometric Progression

Tn = 50 000

r = 100+8.0

100 = 1.08a = 5 000

Tn = arn-1

Let, Tn > 50 0005 000 (1.08n-1) > 50 000

∴ 1.08n-1 > 10 log 1.08n-1 > log 10(n-1) log 1.08 > log 10

n-1 > log 10

log 1.08 n-1 > 29.92 n > 30.92

The least value of n = 31, age = 30.

by Excel

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FURTHE

R EXPLORATI

Terms, Tn Value of saves Age of Ahmad1 5000 02 5400 13 5832 24 6298.56 35 6802.44 46 7346.64 57 7934.37 68 8569.12 79 9254.65 8

10 9995.02 911 10794.62 1012 11658.19 1113 12590.85 1214 13598.12 1315 14685.97 1416 15860.85 1517 17129.71 1618 18500.09 1719 19980.09 1820 21578.51 1921 23304.79 2022 25169.17 2123 27182.70 2224 29357.32 2325 31705.90 2426 34242.38 2527 36981.77 2628 39940.31 2729 43135.53 2830 46586.37 2931 50313.28 30

∴ Ahmad will have a saving of RM 50 000 at the age of 30.

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CONCLUSION

After doing research, answering the questions, plan a table and some problem solving, we saw that usage of index number is important in our daily business activity. It is not just widely use in the business segment but also in banking skills. We learnt a lot of lesson from this Additional Mathematics Project Work such as banking account skills, loaning technique, counting the cost of a product, predict the future plans of money and so on. Without this, shopkeeper will get a lot of loses in the business activity. We would like to thanks the one who contribute the idea of index number to help us a lot in our business activity together in our daily life.

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After by spending countless hours, days and night to finish this project and also sacrificing our time for chatting and movies in this few weeks, there are several things that we want to say…

Additional Mathematics,The killer subject,But when we study hard,It was so easy to understand…

Additional Mathematics,You look so interesting,So unique from the other subject,That’s why we like you so much…

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REFLECTION

After sacrificing our precious time,Spirit and energy for this project,And now,We realized something important from it!

We really love Additional Mathematics,Additional Mathematics,You are our real friend,You are our family,And you are our life…

WE LOVE ADDITIONAL MATHEMATICS!

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END,BYE...

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