projec addmath 2010

8/9/2019 projec addmath 2010

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AdditionalMathematics ProjectWork 3

Name : Steve Lim Keaw

AnnI/C : 930130-10-5099Class : 5 LocalSchool : Kolej TuankuJaafarContentAdditional Mathematics Project Work 3This Project Is Fully Done By Steve Lim Keaw AnnPage 1TitlePageContent

1Acknowledgement & Appreciation2Objective3Question of Additional Mathematics Project Work 34 ~7Answers8Part 1 a9 ~ 10Part 1 b,c11

Part 1 d, Part 2 a,b12Part 2 c13Part 2 d(i)14Part 2 d(ii), e15 ~ 16Further Exploration17Reflection18

Illustraion19 ~ 20Additional Mathematics Project Work 3This Project Is Fully Done By Steve Lim Keaw AnnPage 2Acknowledgement and AppreciationFirst of all, I would like to say thank you to my friends, teachers and parentsforgiving me their full support in making this project successful.

Not forgotten to my family for providing everything, such as money, to buy anythingthat are related to this project work and their advise, which is the most needed

for thisproject. Internet, books, computers and all that act as my source to complete this project.


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They also supported me and encouraged me to complete this task so that I will notprocrastinate in doing it.

Then I would like to thank my teacher, Mr Hussin Bin Sahid for guiding me and myfriends throughout this project. We had some difficulties in doing this task, but he taught us

patiently and gave me guidance throughout the journey until we knew what to do.He triedhis best to help us until we understand what we supposed to do with the projectwork.

Besides that, my friends who were doing this project with me and shared our ideas.They were helpful that when we combined and discussed together, we had this taskcompleted in just a glimpse of an eye.Last but not least, any party which involved either directly or indirect in completing

this project work.Thank you everyone.Yours sincerely,(Steve Lim Keaw Ann)Additional Mathematics Project Work 3This Project Is Fully Done By Steve Lim Keaw AnnPage 3Objective

We, as the students taking Additional Mathematics are required to carry out a project work whilewe are in Form 5. This year the Curriculum Development Division, Ministry of Education has

prepared for tasks for us with four choices, and I chose the third task. We areto choose andcomplete ONLY one task based on our area of interest. This project can be done in groups orindividually, but each of us are expected to submit an individually written report. Uponcompletion of the Additional Mathematics Project Work, we are to gain valuable experiences andable to:1. Apply and adapt a variety of problem solving strategies to solve routine andnon-routineproblems2. Experience classroom environments which are challenging, interesting and meaningfuland hence improve their thinking skills3. Experience classroom environments where knowledge and skills are applied inmeaningful ways in solving real-life problems4. Experience classroom environments where expressing ones mathematical thinking,

reasoning and communication are highly encouraged and expected5. Experience classroom environments that stimulates and enhances effective learning6. Acquire effective mathematical communication through oral and writing, and touse the

language of mathematics to express mathematical ideas correctly and precisely7. Enhance acquisition of mathematical knowledge and skills through problem- solving in


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ways that increase interest and confidence8. Prepare ourselves for the demand of our future undertakings and in workplace9. Realises that mathematics is an important and powerful tool in solving real-life problemsand hence develop positive attitude towards mathematics.10. Train ourselves not only to be independent learners but also to

collaborate, to cooperate and to share knowledge in an engaginghealthy environment11. Use technology especially the ICT appropriately and effectively12. Train ourselves to appreciate the intrinsic values of mathematics and to become morecreative and innovative13. Realises the importance and the beauty of mathematicsAdditional Mathematics Project Work 3This Project Is Fully Done By Steve Lim Keaw AnnPage 4

Question of

AdditionalMathematicsProjectWork 3 Year2010,and the selling price,,(RM)Estimated Year demand,,(units)

754500125350020020002501000Table 1a) Determine the relationship between the demand,Additional Mathematics Project Work 3This Project Is Fully Done By Steve Lim Keaw AnnPage 5CURRICULUM DEVELOPMENT DIVISIONMINISTRY OF EDUCATION MALAYSIAADDITIONAL MATHEMATICS PROJECT WORK 3/2010BACKGROUND

Every business requires some form of investment and a sufficient number of customers tobuy its products or services that give profits on a continuous basis. When pricing experts seta selling price for a new product, their goal is to maximize profits. They beginby estimating

the demand for the product at various selling prices. Generally, the demand fora productwill increase as the selling price decreases.


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PART 1Table 1 shows the various selling prices and estimated demand for a particular computercomponent manufactured by a company, Warisan RMN.Selling Price Per Unit,,by

plotting a graph based on the values displayed in Table 1. Plotting of the graphcanbe done manually, using computer software such as Microsoft Excel or graphingcalculator. Interpret the graph, discus and write a brief explanation on therelationship between the demand of the selling price of the computer componentsmanufactured by the company.b) Assuming that production cost of the component is RM 50 per unit, express theyearly profit,, in terms of the selling price,

.Comment on your answer.[Note: Total Profit = Total Sales Total Cost]c) Use two or more methods to determine the maximum profit and the correspondingselling price. Explain your answers.d) Further, determine the number of the computer components to be manufactured bythe company in order to gain maximum profit.Additional Mathematics Project Work 3This Project Is Fully Done By Steve Lim Keaw AnnPage 6PART 2

In year 2009, Warisan RMN made a profit of RM200,000. The company intends to inc

reaseits production in year 2010, therefore needs a substantial amount of money for capitalinvestment.As manager of the company, you have to decide on the amount of loan and the period ofthe loan to be taken for the purpose mentioned above.Table 2 shows part of a monthly repayment schedule for a commercial loan from bank A

LoanAmount(RM)Monthly Payment (RM)12 months24 months36 months48 months60 months10,0001034.00617.00478.00409.00467.00

15,0001550.00925.00


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717.00613.00550.0020,0002067.001234.00956.00

817.00734.0025,0002584.001542.001195.001021.00917.0030,0003100.001850.001434.00

1225.001100.0035,0003617.002159.001673.001430.001284.0040,0004134.002467.001912.001634.00

1467.0045,0004650.002775.002150.001838.001650.0050,0005167.003084.0023890.02042.001834.00Table 2

a) Based on Table 2, Calculate the total amount of interest incurred for each choise of repayment period and their corresponding amount of loan. Tabulate the values in Table 3.Total LoanRMTotal Interest Incurred (RM)12 months24 months36 months48 months

60 months

10,000 20,000 30,000 40,000 50,000


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Table 3b) Based on your findings in (a) calculate the average interest rate per month.Tabulateyour results and comment on your findings.

c) Further, tabulate the amount of yearly repayment for each choice of repaymentperiod up to 5 years for loan amounts from RM10,000 to RM 100,000. By obversing

the total annual payment for 12 months, show that the annual payment for loanamount of RM10,000, RM15,000, RM20,000 and so on form a progression.Additional Mathematics Project Work 3This Project Is Fully Done By Steve Lim Keaw AnnPage 7

d) The company allocated only 20% of the profit made in the year 2009 on loanrepayment period per annum. Assume that the company continues to make anannual profit of RM200,000 in the following years.(i)

Based on your table in (c), determine the maximum amount of loan, in

multiples of RM5000, for each choice of repayment period: 1 year, 2 years, 3years, 4 years and 5 years.(ii)Hence, determine which loan option should the company take, and elaborateon your reasons.

e) The company has set aside a reserve fund of RM 50,000 in a bank and earns monthlyinterest beginning 1st January 2010.Assuming that the bank gives an annual interest of 2.5%; determine the amount ofthe reserve fund at the end of each month until 31st December 2010.FURTHER EXPLORATION

Look into other commercial loans or other financial sources available in the market that maybe utilized by the company for its capital investment. (Example: Overdraft, Islamic Loan)Discuss the advantage and disadvantages of the different types of loans available.REFLECTION

While you were conducting the project, what have you learnt? What moral values did youpractice? Represent your opinions or feelings creatively through usage of symbols,illustrations, drawings or even in a song.Extracted from Additional Mathematics Project Work 3Additional Mathematics Project Work 3This Project Is Fully Done By Steve Lim Keaw AnnPage 8Answersagainstincreases, the estimated yearly demand,decreases. Thus wecan say that the relationship is inversely proportional as shown below

1If a


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Additional Mathematics Project Work 3This Project Is Fully Done By Steve Lim Keaw AnnPage 9Part 1a) As the selling price,

graph is plotted, a straight line will be formedGraph 1.1 GraphagainstBased on graph 1.1, the curve of the graph shows a curve, proving the relationship ofagainstis inversely proportional. In which means that as the selling price increases, the

estimated yearly demand will decrease.0501001502002503001000200035004500, (Units)

Reciprocal ofagainst1graph is plotted, a straight line curve is obtainedSelling price per unit ,,(RM)Estimated Yearly Demand,Additional Mathematics Project Work 3This Project Is Fully Done By Steve Lim Keaw AnnPage 10However, if awhich is7545000.000212535000.00032002000

0.00052501000


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0.001Graph 1.2 Graphagainst1In graph 1.2, the graph shows a straight line when it is plotted

against1. It actuallymeans the same as graph 1.1.0501001502002503000.00020.0003

0.00050.001

Series 1Column1Column2is the estimated yearlydemand.For example belowSelling Price PerUnit,, in terms of selling price,

.=50Whereis the total profit,is the selling price per unit andAdditional Mathematics Project Work 3This Project Is Fully Done By Steve Lim Keaw AnnPage 11b) Cost of the computer product = RM50 per unitExpress yearly profit,, (RM)Estimated YearlyDemand,, (Units)Total Sales (

)Total Cost


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(50)Profit(=

)754500337,500225,000112,5001253500437,500175,000262,500

2002000400,000100,000300,0002501000250,00050,000200,000

Table 1.1Based on Table 1.1 calculation has been made to calculate the total profit using

theformula=

. It was found that the maximum profit can be obtained iswhen the selling price is RM200 per unit. Thus, Warisan RMN should sell eachcomputer component at a price of RM 200 to ensure the amount of user buying thecomponent is at maximum to produce maximum profit. Although, the selling pricewas RM75 and the demand was 4500, the profit earned is still not as high as theprevious one.c) First method to determine the maximum profit is to produce a lot of computercomponent at a time. However, the company should ensure that they have alreadygained a place in the users heart so that they will purchase. This keeps the demand

running on and on thus preventing wastage of natural resources. We should keep in mind that excessive production does not guarantee a 100% reward. If productionis too high and the demand for the certain product is low, it might cause losses due to lack of demand. Therefore, an advice for new companies is to produce minimum butrewarding amount of product. After the company gains the users trust, then the

company can start producing huge amount of product. However, provision should be

made for demand and economic crisis. Then only a maximum profit can bedetermined.The second method is profit maximization. It is a process by which a firm determ


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inesthe price and output level that returns the greatest profit. There are severalapproaches to this problem. The total revenue total cost method relies on thefactthat profit equals revenue minus cost, and the marginal revenuemarginal costmethod is based on the fact that total profit in a perfectly competitive marketreaches its maximum point where marginal revenue equals marginal cost. Any costs

incurred by a firm may be classed into two groups: fixed cost and variable cost.Fixedcosts are incurred by the business at any level of output, including zero output.These may include equipment maintenance, rent, wages, and general upkeep.Variable costs change with the level of output, increasing as more product is=Whereis total interest,is the total month for monthly payment and

forthe number of months.For example loan amount of RM10,000 for 12 months payment where eachmonth repayment is RM1034.00=

= 121034Additional Mathematics Project Work 3This Project Is Fully Done By Steve Lim Keaw AnnPage 12generated. Materials consumed during production often have the largest impact onthis category. Total cost is the total when fixed cost and variable cost are combined.

d) Referring to table 1.1, the maximum profit is obtained at the selling price of 200. Inorder to obtain maximum profit, the selling price should be allocated in betweenRM125 and RM250. This is because the highest profit is in between the selling priceof RM125 and RM250.PART 2a) The total interest incurred is calculated through the formula below=12,408Table 1.2

b) To calculate the average interest rate per month, a table in drawn and data a

reinserted. Average rate of interest per month is calculated as follow using the formula


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below.= 100

Indicatormeans average rate of interest per monthmeans total interest incurred which can be obtained from table 1.2means the total loan and lastlymeans the total number of months of repaymentTotal LoanRMTotal interest incurred (RM)

12 months24 months36 months48 months60 months10,0002,4084,8087,2089,63212,02020,0004,804

9,61614,41619,21624,04030,0007,20014,40021,62428,80036,00040,0009,60819,20828,83238.43248,02050,00012,00424,01636,00448,01660,040Additional Mathematics Project Work 3This Project Is Fully Done By Steve Lim Keaw AnnPage 13

Total LoanRMAverage rate of interest per month


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12 months24 months36 months48 months60 months10,0002%

2%2%2%2%20,0002%2%2%2%2%30,0002%

2%2%2%2%40,0002%2%2%2%2%50,0002%2%

2%2%2%

Table 1.3From the results above, we can conclude that the percentage of interest incurredis2% for each period of repayment. Besides, the total amount of interest needed topay exceeds the loan when the total repayment months are 60. Thus, this meansthat the percentage of interest incurred is same for all loan regardless of therepayment period.c)Total LoanRMTotal Interest incurred (RM)12 months24 months36 months48 months60 months10,0002,4004,8007,2009,60012,000

15,0003,6007,200


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10,80014,40018,00020,0004,8009,60014,400

19,20024,00025,0006,00012,00018,00024,00030,00030,0007,20014,40021,600

28,80036,00035,0008,40016,80025,20033,60042,00040,0009,60019,20028,80038,400

48,00045,00010,80021,60032,40043,20054,00050,00012,00024,00036,00048,00060,00055,00013,20026,40039,60052,80066,00060,00014,40028,80043,20057,60072,000

65,00015,60031,200


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46,80062,40078,00070,00016,80033,60050,400

67,20084,00075,00018,00036,00054,00072,00090,00080,00019,20038,40057,600

76,80096,00085,00020,40040,80061,20081,600102,00090,00021,60043,20064,80086,400

108,00095,00022,80045,60068,40091,200114,000100,00024,00048,00072,00096,000120,000Table 1.4Notes: All interests rate are based on Table 1.3Additional Mathematics Project Work 3This Project Is Fully Done By Steve Lim Keaw AnnPage 14

d) Profit in year 2009 = RM200,00020% of the profit = RM 40,000Purpose of provision of 20% = loan repaymentAssumption = making the same profit in the same following yearsi)The table below shows the maximum amount of profit earn in 5 years

Year20092010


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201120122013Profit earn forthat year200,000200,000

200,000200,000200,000Total profit200,000400,000600,000800,0001,000,000Provision forrepayment40,000

80,000120,000160,000200,000

Table 1.5If the Warisan RMN chooses to repay in 1 year time, I would recommend them tomake loan of RM 30,000. This is because the amount needed to return back isRM37,200 (RM30,000+RM7,200) including interests. This does not exceed theprovision set by the company.For the second choice of repayment is 2 years time. For this choice, I recommendthecompany to request a loan of RM50,000. The total amount needed to repay is

RM74,000 (RM50,000+RM24,000) inclusive of interests.For the third choice of repayment is 3 years time. I recommend the company torequest a loan of RM65,000. The amount needed to repay is RM111,800(RM65,000+RM46,800)For the fourth choice is to repay within 4 years time. In this case, I suggeststhat aloan of RM80,000 should be made. The amount of money needed to repay isRM156,800 (RM80,000+RM76,800).For the last choice is to pay within 5 years time. I will urge the company to make aloan of RM 90,000. The total repayment amount is RM198,000(RM90,000+RM108,000)In conclusion, all the reason above is within the provision for repayment. Thusit canbe summarised into a table as follows.Table 1.6

Period ofRepayment(Year)YearProfit ForThat Year

TotalProvision

ForRepaymentTotal


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Loan RM

TotalInterestincurred

Total

Amount ofRepaymentRM12009200,00040,00030,0007,20037,20022010

200,00080,00050,00024,00074,00032011200,000120,00065,00046,800111,8004

2012200,000160,00080,00076,800156,80052013200,000200,00090,000108,000198,000Additional Mathematics Project Work 3This Project Is Fully Done By Steve Lim Keaw AnnPage 15ii)

Based on the the company, Warisan RMN situation, the firm needs asubstantial amount of money for capital investment. Therefore, I, as themanager of the company, should choose the best choice for the companythus can make more profit from the loan and the repayment should not be aburden to the company. Based on the Table 1.6, we can see that the amountof repayment does not exceed the provision for repayment. Therefore, Iwould choose to make a loan of RM90,000 with a repayment within 5 years

or 60 months. In this case, the total interests incurred is RM108,000. Whenwe sum it up, the total is RM198,000. For RM198,000, we can divided into 60months which is the repayment period. So in that case, we need to pay


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RM3,300 per month. Besides, we can make use of the loan by investing tomake new computer components which can be very profitable.e) Situation

The company has set aside a reserve fund of RM50,000 in a bank an earns monthlyinterest beginning 1st January 2010.Interest rate: 2.5%

Problem: Amount of the reserve fund at the end of each month until 31st December2010.

From the situation above, we can conclude that the amount of money in the bankincreases by 2.5% per annum. Thus the information can be shown in a table form asfollows.Additional Mathematics Project Work 3This Project Is Fully Done By Steve Lim Keaw AnnPage 16Month

Amount of Moneyin the beginning ofthe monthAmount ofInterest (RM)

Total Amount OfMoney at the endof the monthJanuary50,000104.1750,104.17

February50,104.17104.1750,208.34March50,208.34104.1750,312.51April50,312.51104.1750,4146.68May50,416.68104.1750,520.85June50,520.85104.1750,625.02July50,625.02104.1750,729.19August

50,729.19104.1750,833.36


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September50,833.36104.1750,937.53October50,937.53104.17

51,041.70November51,041.70104.1751,145.87December51,145.87104.1351,2501 Year50,0001,250

51,250

The amount of interest obtained for a year is RM1,250. If it would be divided into 12 months, the amount will be RM10416 which is an infinite number. To make itrational number, I made some adjustment where the first 11 months will receiveRM104.17as interests and the last month which is December we will receive an interests ofRM104.13. Sum it up we will get RM1,250 (RM104.1711 + RM103.13 =RM1,250)Additional Mathematics Project Work 3This Project Is Fully Done By Steve Lim Keaw AnnPage 17FURTHER EXPLORATION

RHB BankSME BankBumiputra Bank Fast credit decision, uponreceipt of fulldocumentationQuick "Yes" or "No" toyour applicationSimple documentationrequirements27 easily accessible

Commercial BankingBusiness Centres and awide network of branchesthroughout MalaysiaPrompt and friendlycustomer service In line with the

Government

s call tosupport SME businessesnationwide Uses a transparent andobjective credit scoring

approach Fastest turnaround timefor Loans up to RM 1


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Million A comprehensive range offinancial products andservicesHolistic approach to credit

approval with emphasis on

your business experience,payment history andaccount activity patterns No collateral required You

don

t have to pledge yourassets to be eligible, onlyguaranteefrom your directors and/orshareholders is/are required.Easy to apply No need to

get property valuation reportor transfer money fromother bank orto use FD as security. Fast approval Upon

receiving full andsatisfactory documentationfrom you, drawdown willbe available within 2 weekssubject to approvalconditions. Loan from RM 50,000 to

RM 500,000 You choosethe sum that suits yourbusiness needs.Flexible repayment tenure

You can choose a period ofrepayment between 1 to 5years. Non Collateralize , no

guarantor required &CCRIS/CTOS/FIS alsocan apply Government servants &

private sector staffs( Bhd / Sdn Bhd /Enterprise )Pensioner or SOCSOThose who are

blacklisted with anybank financialinstitutions also can

apply CRITERIA : SALARYMUST BE CREDITED


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THROUGH BANK Specialized & designedfor Bumiputra workingin KL & Selangor Guaranteed the lowestinstallment plan in town Loan up to 3 5 times of

salary / 10000 / highersubjected to terms andconditions Instant approval within30 minutes Bring us your documentas follow : 3 months latest payslip 3 months latest bankstatement E m p l o ym en t

confirmation letterUtilities billAdditional Mathematics Project Work 3This Project Is Fully Done By Steve Lim Keaw AnnPage 18REFLECTION

Throughout the project while I was conducting it, I learned many stuff. This includes on usage of knowledge and ways to conduct the project. While I was conducting the project, I collected information from the internet and brochures from the banks regarding the loans. Besides, I manipulated my knowledge in other fieldssuch as accounting and economics in this research.

However, the most important this I have learnt from this project is to plan before wedo something. In this project, I was regarded as the manager of the firm WarisanRMN. I wasrequired to make decision on making loans so that the company is able to increase itsproduction in the following year, Year 2010. Thus, planning is required and information wasgiven. Bank A provides such a loan and repayment period where we can make our choicewisely.

While planning, I made few tables on total interest incurred, average interest rateper month and also annual payment for the loan. This has taught me that a lot ofworkshould be done such as consideration and provision for repayment before making aloan.We must be able to clear the debt within the time given and should not make decision in ahaste because great haste make great waste.

Besides, I learned how to cooperate with friends. My friends and I discussed aboutthe project and we shared ideas amongst ourselves. This discussion has made me m

oreconfident when doing something. I also learned to be disciplined in terms of punctuality,


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doing project and not least to avoid plagiarism.

In a nutshell, I have learned something about the future and how serious can itbe ifwe make a wrong decision. Moreover, work that we done must be original and not totallyderived from other people. These two images have expressed my opinions from this

project.Additional Mathematics Project Work 3This Project Is Fully Done By Steve Lim Keaw AnnPage 19Everything comes with a plan. Without a plan, we will fail. Just like the sayinggoes, we dontplan to fail but we fail to plan.Additional Mathematics Project Work 3This Project Is Fully Done By Steve Lim Keaw AnnPage 20A perfectly good business plan is a must to be done to have a long lasting and profitable

business.

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