33542561 Additional Mathematics Project Work 3

8/6/2019 33542561 Additional Mathematics Project Work 3

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Additional Mathematics Project

Work 3

Name : Steve Lim Keaw Ann

I/C : 930130-10-5099Class : 5 Local

School : Kolej Tuanku Jaafar


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Additional Mathematics Project Work 3

This Project Is Fully Done By Steve Lim Keaw Ann Page 1

Content Title PageContent 1Acknowledgement & Appreciation 2Objective 3Question of Additional Mathematics Project Work 3 4 ~ 7Answers 8Part 1 a 9 ~ 10Part 1 b,c 11Part 1 d, Part 2 a,b 12

Part 2 c 13Part 2 d(i) 14Part 2 d(ii), e 15 ~ 16Further Exploration 17Reflection 18Illustraion 19 ~ 20


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Acknowledgement and Appreciation

First of all, I would like to say thank you to my friends, teachers and parents forgiving 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.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 project work.

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 completingthis project work.

Thank you everyone.

Yours sincerely,

(Steve Lim Keaw Ann)


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Objective

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 hasprepared for tasks for us with four choices, and I chose the third task. We are to 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 and non-routineproblems

2. Experience classroom environments which are challenging, interesting and meaningfuland hence improve their thinking skills

3. Experience classroom environments where knowledge and skills are applied inmeaningful ways in solving real-life problems

4. Experience classroom environments where expressing ones mathematical thinking,reasoning and communication are highly encouraged and expected

5. Experience classroom environments that stimulates and enhances effective learning6. Acquire effective mathematical communication through oral and writing, and to use the

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

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 problems

and 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 environment

11. Use technology especially the ICT appropriately and effectively12. Train ourselves to appreciate the intrinsic values of mathematics and to become more

creative and innovative13. Realises the importance and the beauty of mathematics


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Question of Additional

Mathematics

Project Work 3 Year

2010


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CURRICULUM DEVELOPMENT DIVISIONMINISTRY OF EDUCATION MALAYSIA

ADDITIONAL MATHEMATICS PROJECT WORK 3/2010

BACKGROUNDEvery 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 begin by estimatingthe demand for the product at various selling prices. Generally, the demand for a productwill increase as the selling price decreases.

PART 1Table 1 shows the various selling prices and estimated demand for a particular computer

component manufactured by a company, Warisan RMN.

Selling Price Per Unit, ,(RM)

Estimated Year demand, ,(units)

75 4500125 3500200 2000250 1000

Table 1

a) Determine the relationship between the demand, , and the selling price, , byplotting a graph based on the values displayed in Table 1. Plotting of the graph canbe done manually, using computer software such as Microsoft Excel or graphing

calculator. Interpret the graph, discus and write a brief explanation on the

relationship 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.


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PART 2In year 2009, Warisan RMN made a profit of RM200,000. The company intends to increaseits production in year 2010, therefore needs a substantial amount of money for capital

investment.As manager of the company, you have to decide on the amount of loan and the period of the 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 months 24 months 36 months 48 months 60 months

10,000 1034.00 617.00 478.00 409.00 467.0015,000 1550.00 925.00 717.00 613.00 550.0020,000 2067.00 1234.00 956.00 817.00 734.0025,000 2584.00 1542.00 1195.00 1021.00 917.0030,000 3100.00 1850.00 1434.00 1225.00 1100.0035,000 3617.00 2159.00 1673.00 1430.00 1284.0040,000 4134.00 2467.00 1912.00 1634.00 1467.0045,000 4650.00 2775.00 2150.00 1838.00 1650.0050,000 5167.00 3084.00 23890.0 2042.00 1834.00

Table 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 inTable 3.

Total LoanRM

Total Interest Incurred (RM)12 months 24 months 36 months 48 months 60 months

10,00020,00030,000

40,00050,000

Table 3

b) 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 obversingthe 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.


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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 1 st January 2010.Assuming that the bank gives an annual interest of 2.5%; determine the amount of the reserve fund at the end of each month until 31 st 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.

REFLECTIONWhile 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 3


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Answers


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Part 1a) As the selling price, increases, the estimated yearly demand, decreases. Thus we

can say that the relationship is inversely proportional as shown below

1 If a against graph is plotted, a straight line will be formed

Graph 1.1 Graph against Based on graph 1.1, the curve of the graph shows a curve, proving the relationship of against is inversely proportional. In which means that as the selling price increases, theestimated yearly demand will decrease.

0

50

100

150

200

250

300

1000 2000 3500 4500


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b) Cost of the computer product = RM50 per unitExpress yearly profit, , in terms of selling price, .

= 50 Where is the total profit, is the selling price per unit and is the estimated yearlydemand.For example below

Selling Price PerUnit, , (RM)

Estimated YearlyDemand, , (Units)

Total Sales ( ) Total Cost(50 )

Profit( = )75 4500 337,500 225,000 112,500

125 3500 437,500 175,000 262,500200 2000 400,000 100,000 300,000250 1000 250,000 50,000 200,000

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 the

previous one.

c) First method to determine the maximum profit is to produce a lot of computer

component 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 inmind that excessive production does not guarantee a 100% reward. If production istoo high and the demand for the certain product is low, it might cause losses due tolack of demand. Therefore, an advice for new companies is to produce minimum butrewarding amount of product. After the company gains the users trust, then thecompany can start producing huge amount of product. However, provision should bemade for demand and economic crisis. Then only a maximum profit can be

determined.The second method is profit maximization. It is a process by which a firm determinesthe price and output level that returns the greatest profit. There are severalapproaches to this problem. The total revenue - total cost method relies on the factthat profit equals revenue minus cost, and the marginal revenue marginal costmethod is based on the fact that total profit in a perfectly competitive marketreaches its maximum point where marginal revenue equals marginal cost. Any costsincurred 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
http://en.wikipedia.org/wiki/Pricehttp://en.wikipedia.org/wiki/Output_%28economics%29http://en.wikipedia.org/wiki/Profit_%28economics%29http://en.wikipedia.org/wiki/Marginal_revenuehttp://en.wikipedia.org/wiki/Marginal_costhttp://en.wikipedia.org/wiki/Marginal_costhttp://en.wikipedia.org/wiki/Perfectly_competitivehttp://en.wikipedia.org/wiki/Corporationhttp://en.wikipedia.org/wiki/Fixed_costhttp://en.wikipedia.org/wiki/Variable_costhttp://en.wikipedia.org/wiki/Variable_costhttp://en.wikipedia.org/wiki/Fixed_costhttp://en.wikipedia.org/wiki/Corporationhttp://en.wikipedia.org/wiki/Perfectly_competitivehttp://en.wikipedia.org/wiki/Marginal_costhttp://en.wikipedia.org/wiki/Marginal_revenuehttp://en.wikipedia.org/wiki/Profit_%28economics%29http://en.wikipedia.org/wiki/Output_%28economics%29http://en.wikipedia.org/wiki/Price


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generated. 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. In

order 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

=

Where is 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

= = 12 1034 = 12,408

Table 1.2

b) To calculate the average interest rate per month, a table in drawn and data areinserted. Average rate of interest per month is calculated as follow using the formulabelow.

= 100

Indicatormeans average rate of interest per monthmeans total interest incurred which can be obtained from table 1.2means the total loan and lastly

means the total number of months of repayment

Total Loan

RM

Total interest incurred (RM)

12 months 24 months 36 months 48 months 60 months10,000 2,408 4,808 7,208 9,632 12,02020,000 4,804 9,616 14,416 19,216 24,04030,000 7,200 14,400 21,624 28,800 36,00040,000 9,608 19,208 28,832 38.432 48,02050,000 12,004 24,016 36,004 48,016 60,040


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Total LoanRM

Average rate of interest per month12 months 24 months 36 months 48 months 60 months

10,000 2% 2% 2% 2% 2%

20,000 2% 2% 2% 2% 2%30,000 2% 2% 2% 2% 2%40,000 2% 2% 2% 2% 2%50,000 2% 2% 2% 2% 2%

Table 1.3From the results above, we can conclude that the percentage of interest incurred is2% 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 LoanRM

Total Interest incurred (RM)12 months 24 months 36 months 48 months 60 months

10,000 2,400 4,800 7,200 9,600 12,00015,000 3,600 7,200 10,800 14,400 18,00020,000 4,800 9,600 14,400 19,200 24,00025,000 6,000 12,000 18,000 24,000 30,00030,000 7,200 14,400 21,600 28,800 36,00035,000 8,400 16,800 25,200 33,600 42,00040,000 9,600 19,200 28,800 38,400 48,00045,000 10,800 21,600 32,400 43,200 54,00050,000 12,000 24,000 36,000 48,000 60,00055,000 13,200 26,400 39,600 52,800 66,00060,000 14,400 28,800 43,200 57,600 72,00065,000 15,600 31,200 46,800 62,400 78,00070,000 16,800 33,600 50,400 67,200 84,00075,000 18,000 36,000 54,000 72,000 90,00080,000 19,200 38,400 57,600 76,800 96,000

85,000 20,400 40,800 61,200 81,600 102,00090,000 21,600 43,200 64,800 86,400 108,00095,000 22,800 45,600 68,400 91,200 114,000

100,000 24,000 48,000 72,000 96,000 120,000

Table 1.4

Notes: All interests rate are based on Table 1.3


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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 years

i) The table below shows the maximum amount of profit earn in 5 yearsYear

2009 2010 2011 2012 2013Profit earn forthat year

200,000 200,000 200,000 200,000 200,000

Total profit 200,000 400,000 600,000 800,000 1,000,000Provision forrepayment

40,000 80,000 120,000 160,000 200,000

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 recommend the

company to request a loan of RM50,000. The total amount needed to repay isRM74,000 (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 suggests that 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. Thus it canbe summarised into a table as follows.

Table 1.6

Period of Repayment(Year)

Year Profit ForThat Year TotalProvisionFor

Repayment

TotalLoan RM TotalInterestincurred

TotalAmount of Repayment

RM1 2009 200,000 40,000 30,000 7,200 37,2002 2010 200,000 80,000 50,000 24,000 74,0003 2011 200,000 120,000 65,000 46,800 111,8004 2012 200,000 160,000 80,000 76,800 156,8005 2013 200,000 200,000 90,000 108,000 198,000


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ii) 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 a

burden 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 yearsor 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 payRM3,300 per month. Besides, we can make use of the loan by investing tomake new computer components which can be very profitable.

e) SituationThe company has set aside a reserve fund of RM50,000 in a bank an earns monthlyinterest beginning 1 st January 2010.Interest rate: 2.5%Problem: Amount of the reserve fund at the end of each month until 31 st 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.


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Month Amount of Moneyin the beginning of

the month

Amount of Interest (RM)

Total Amount Of Money at the end

of the monthJanuary 50,000 104.17 50,104.17February 50,104.17 104.17 50,208.34March 50,208.34 104.17 50,312.51April 50,312.51 104.17 50,4146.68May 50,416.68 104.17 50,520.85June 50,520.85 104.17 50,625.02July 50,625.02 104.17 50,729.19August 50,729.19 104.17 50,833.36September 50,833.36 104.17 50,937.53October 50,937.53 104.17 51,041.70November 51,041.70 104.17 51,145.87

December 51,145.87 104.13 51,2501 Year 50,000 1,250 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 RM1041

6which is an infinite number. To make it rational

number, I made some adjustment where the first 11 months will receive RM104.17as interests and the last month which is December we will receive an interests of RM104.13. Sum it up we will get RM1,250 (RM104.1711 + RM103.13 =RM1,250)


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FURTHER EXPLORATIONRHB Bank SME Bank Bumiputra Bank

Fast credit decision, uponreceipt of fulldocumentation

Quick "Yes" or "No" toyour application

Simple documentationrequirements

27 easily accessibleCommercial BankingBusiness Centres and awide network of branchesthroughout Malaysia

Prompt and friendlycustomer service

In line with theGovernment's call tosupport SME businessesnationwide

Uses a transparent andobjective credit scoringapproach

Fastest turnaround timefor Loans up to RM 1

Million A comprehensive range of financial products andservices

Holistic approach to creditapproval with emphasis onyour business experience,payment history andaccount activity patterns

No collateral required - Youdon't have to pledge yourassets to be eligible, onlyguaranteefrom your directors and/orshareholders is/are required.

Easy to apply - No need toget 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 toRM 500,000 - You choosethe sum that suits yourbusiness needs.

Flexible repayment tenure -

You can choose a period of repayment between 1 to 5years.

Non-Collateralize , noguarantor required &CCRIS/CTOS/FIS alsocan apply

Government servants &private sector staffs( Bhd / Sdn Bhd / Enterprise )

Pensioner or SOCSO Those who are

blacklisted with anybank financial

institutions - also canapply CRITERIA : SALARY

MUST BE CREDITEDTHROUGH BANK

Specialized & designedfor Bumiputra workingin KL & Selangor

Guaranteed the lowestinstallment plan in town

Loan up to 3-5 times of

salary / 10000 / higher -subjected to terms andconditions

Instant approval within30 minutes

Bring us your documentas follow :-

3 months latest payslip 3 months latest bank

statement Employment

confirmation letter Utilities bill


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REFLECTION

Throughout the project while I was conducting it, I learned many stuff. This includeson 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 fields such as accounting and economics inthis 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 Warisan RMN. I wasrequired to make decision on making loans so that the company is able to increase its

production 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 of workshould be done such as consideration and provision for repayment before making a loan.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 moreconfident when doing something. I also learned to be disciplined in terms of punctuality,doing project and not least to avoid plagiarism.

In a nutshell, I have learned something about the future and how serious can it be if we 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.


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Everything comes with a plan. Without a plan, we will fail. Just like the saying goes, we dont

plan to fail but we fail to plan.


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A perfectly good business plan is a must to be done to have a long-lasting and profitable

business.

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33542561 Additional Mathematics Project Work 3

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