Additional Mathematics
Project Work 2
2014
OLIVER5S2
OLIVER
5S2
INTRODUCTION
This project needs to be done to fulfil the terms for Additional Mathematics paper by the Ministry of Education Malaysia. In part of that, the duration for this project work to complete by individually either in a group should not exceed three weeks which the deadline is at 15 August. This time, I have to accomplish this project work about interest rate offered by that finance company in Malaysia and inflation rate that may increase in the future. Besides covering my project work, I have to seek the officer in such finance company near my hometown regarding interest rate for car loans given by them to their client.
The aims of carrying this project work are to enable students to:
a) Apply mathematics to everyday situations and appreciate the importance and the beauty of mathematics in everyday lives;
b) Improve problem solving skills, thinking skills, reasoning and mathematical communication;
c) Develop positive attitude and personalities and intrinsic mathematical values such as accuracy, confidence and systematic reasoning;
d) Stimulate learning environment that enhance effective learning, inquiry-based and team-work;
e) Develop mathematical knowledge in a way which increases students' interest and confidence.
Within the three weeks period, I have to discuss all my finding with my teacher and other partners to find the best way to produce the best project work that can be the best guidance for those who want to know about financing.
I hope that this project work will make me more mature in dealing with financing agency beside it teaches me more dedicated in life.
ACKNOWLEDGEMENT
First of all, I would like to thank to God for giving us energy, strength and health to carry out this project work.
Next, I would like to thank to my school for giving me the opportunity to produce this project work. School also provides me space to discuss and carry out this project work.
Not forgetting to my beloved parents who provided everything needed in this project work, such as financial, Internet, books, computer and so on. They contribute their time and courage on sharing their knowledge with us. Their support may elevate the strength of mind to me to do this project work efficiently.
After that, I would like to express thanks to my Additional Mathematics teacher, Mdm Chong Lee Khim for guiding me throughout this project work. My group had some difficulties in doing this task, but she taught us tolerantly and gave me guidance throughout the journey until we knew what to do. She tried her most excellent as a teacher, to help us until we understand what we supposed to do with the project work
Lastly, as I am doing this project work in a group, I would like to express gratitude to my classmates who shared ideas and providing some help on solving problems. They were cooperative when we combined and discussed together and we help each other until we can finished this project work.
REFLECTION
I would first to thank to God that I have finished my project work in the time given. And also a big thanks to my parent who has give me full moral and financial support to accomplish this project work. Not to forget, thanks to my Additional Mathematics teacher, Mdm Chong Lee Khim who guides me and my friends to finish this project work.
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 interest for car loans. Besides, I manipulated my knowledge in other fields such as banking and economics in this research
I have also learned the beauty of Mathematics in everyday life. Mathematics is the field of study that tends to define by the types of problems it addresses, the methods it uses to address these problems, and the results is achieved. Doing this project work also helps me to re-master my Mathematics knowledge and learn from the mistake of doing methods in problem solving questions.
While planning, I made few tables on interest loan based on monthly instalment given by the bank, weigh against the interest rate from those banks and roll 2 other methods for the calculation. This has trained me that a lot of work should be done such as consideration and provision for repayment before making a loan. I learn this to rationalise my expenses for the family. I must be able to clear the debt within the time given and should not make decision in a haste because of quickness make great waste.
Public Bank
Loan interest
2.5% per annum
Loaned value
(RM)
Monthly instalment according to the lengths (RM)
48
60
72
84
96
108
78 000
1787.50
1462.50
1245.83
1091.07
975.00
884.72
75 000
1718.75
1406.25
1197.92
1049.11
937.50
850.69
72 000
1650.00
1350.00
1150.00
1007.14
900.00
816.67
69 000
1581.25
1293.75
1102.08
965.18
862.50
782.64
66 000
1512.50
1237.50
1054.17
923.21
825.00
748.61
63 000
1443.75
1181.25
1006.25
881.25
787.50
714.58
60 000
1375.00
1125.00
958.33
839.29
750.00
680.56
57 000
1306.25
1069.75
910.42
797.32
712.50
646.53
54 000
1237.50
1012.50
862.50
755.36
675.00
612.50
51 000
1168.75
956.25
814.58
713.39
637.50
578.47
PART 1 (a)
Maybank
Loan interest
2.7% per annum
Loaned value
(RM)
Monthly instalment according to the lengths (RM)
48
60
72
84
96
108
78 000
1800.50
1475.50
1258.83
1104.07
988.00
897.72
76 000
1754.33
1437.67
1226.56
1075.76
962.67
874.70
74 000
1708.17
1399.83
1194.28
1047.45
937.33
851.69
72 000
1662.00
1362.00
1162.00
1019.14
912.00
828.67
70 000
1615.83
1324.17
1129.72
990.83
886.67
805.65
68 000
1569.67
1286.33
1097.44
962.52
861.33
782.63
66 000
1523.50
1248.50
1065.17
934.21
836.00
759.61
64 000
1477.33
1210.67
1032.89
905.90
810.67
736.59
62 000
1431.17
1172.83
1000.61
877.60
785.33
713.57
60 000
1385.00
1135.00
968.33
849.29
760.00
690.56
AmBank
Loan interest
3.15% per annum
Loaned value
(RM)
Monthly instalment according to the lengths (RM)
48
60
72
84
96
108
78 000
1829.75
1504.75
1288.08
1133.32
1017.25
926.97
75 000
1759.38
1446.88
1238.54
1089.73
978.13
891.32
72 000
1689.00
1389.00
1189.00
1046.14
939.00
855.67
69 000
1618.63
1331.13
1139.46
1002.55
899.88
820.01
66 000
1548.25
1273.25
1089.92
958.96
860.75
784.36
63 000
1477.88
1215.38
1040.38
915.38
821.63
748.71
60 000
1407.50
1157.50
990.83
871.79
782.50
713.06
57 000
1337.13
1099.63
941.29
828.20
743.38
677.40
54 000
1266.75
1041.75
891.75
784.61
704.25
641.75
51 000
1196.38
983.88
842.21
741.02
665.13
606.10
PART 1 (b)
I have survey and pick out 3 of my favourite banks which are Public Bank, Maybank and Ambank, this shows that the loan interest are vary between these 3 banks which are 2.5%, 2.7% and 3.15% respectively. The lower the interest rate given by the bank, the better the savings I can get when I borrow the bank loan. As you can see, the lowest interest is given by Public Bank and the highest interest is given by Ambank and Maybank interest is slightly in the middle between those 2 banks. Some bank offer high interest rate to earn much profits and interest change without prior notice because of economy factors.
I extremely advise my father to take bank loan from Public Bank because of a number of reasons. I highly prioritise the loan interest offer by 3 banks and I like better to choose Public Bank because it has the least interest rate rather than another bank. This is also because my father does not have to forfeit much loan every month and he can have much savings for another uses.
Even though Public Bank is located quite far away from my hometown, my father can rationalise his savings by using it for his transportation fuels to go to and back from the bank. My father also does not have to go to the bank every week because he only goes to the bank when he requires assistance.
Plus, I am considering that banking with Public Bank is also much easier and convenient compared to another bank. They also treat their clients the way that they have to and the administrator is very user-friendly. Public Bank is also well-known among my father's friends and relatives so that they can encourage him to gives good satisfaction to the bank.
PART 1 (c)
Your father wants to loan RM60, 000.00. By using at least two methods, find the values paid for the car if your father chooses instalment for 4 years, 5 years, 6 years, 7 years, 8 years and 9 years. Show your working clearly and perform your findings in table.
PUBLIC BANK
Duration
Interest Rates
Yearly Interest
Yearly Amount
4 years
2.5% per annum
RM 1375
RM 66 000
5 years
RM 1125
RM 67500
6 years
RM 958.33
RM 69000
7 years
RM 839.29
RM 70500
8 years
RM 750
RM 72000
9 years
RM 680.56
RM 73500
METHOD 1: Percentage
4 years = 48 months
4×2.5100×60000+60000
=10100×60000+60000
=6000+60000
=6600048
=1375
5 years = 60 months
5×2.5100×60000+60000
=12.5100×60000+60000
=7500+60000
=6750060
=1125
6 years = 72 months
6×2.5100×60000+60000
=15100×60000+60000
=9000+60000
=6900072
=958.33
7 years = 84 months
7×2.5100×60000+60000
=17.5100×60000+60000
=10500+60000
=7050084
=839.29
8 years = 96 months
8×2.5100×60000+60000
=20100×60000+60000
=12000+60000
=7200096
=750
9 years = 108 months
9×2.5100×60000+60000
=22.5100×60000+60000
=13500+60000
=73500108
=680.56
PART 2 (a)
Pie Chart
Bar graph
PART 2 (b)
Term lengths typically by those banks in this country are at range between 48 and 108 months. The most suitable length of instalment for car that I will choose is the shortest possible, which is 4 years, or usually expressed in months, such as a 48-month term. This is because the longer the loans mean lower monthly payments. But I will be paying more to the bank in terms of finance charges. That's why unless I can find an outstanding deal, most financial people say to go with the shortest loan is more feasible.
As to compare, the annual interest and the annual amount, the annual interest value become less following the year and the annual amount value increases as the year increases even if the interest rates are fixed at all over the monthly instalments. I can always take out a longer-term and just pay it off ahead of schedule. But, some lenders might charge an early termination fee for doing so. Plus, I am paying the bulk of the interest rate charges in the initial years of the loan.
Even though, there are some banks offered the increasing of interest rates along with the years too, and that causes more money wasted when I pay the loan to the bank as they collect much profits the interest rates given. As I repeat this again, although the longer the month terms picked, they are becoming increasingly common. So the conclusion is the shortest monthly instalment is more practical for me.
PART 2 (c)
Electricity – 9%
Electricity charge increases by 10%
=10%100×9%
=0.9%
=0.9%+9.0%
=9.9%
New electricity charge – 5.5%
=9.9100×4500
=RM445.50
Savings become decreases, currently at 15%
=15100×4500
=RM675.00
=15%-0.9%
=14.1%
=14.1100×4500
=RM634.50
The increases of electricity charge affect the family expenditure through savings.
FURTHER EXPLORATION
(a)
Overall expenditure;
In 2014
T1=RM1000
In 2020
T7=10001.0046
Tn=arn-1T1=aa=2500r=100.4%100=1.004T7=RM1024.24
Tn=arn-1
T1=a
a=2500
r=100.4%100=1.004
Food (2014)
=46100×1000
=RM460
Food (2020)
=46100×1024.24
=RM471.15
Transportation (2014)
=27100×1000
=RM270
Transportation (2020)
=27100×1024.24
=RM276.54
Bill of water (2014)
=2100×1000
=RM20
Bill of water (2020)
=2100×1024.24
=RM20.48
Bill of electricity (2014)
=8100×1000
=RM80
Bill of electricity (2020)
=8100×1024.24
=RM81.94
Telecommunications (2014)
=17100×1000
=RM170
Telecommunications (2020)
=17100×1024.24
=RM174.12
Family's expenditures for year 2014
Expenditures
%
RM
Food
46
460.00
Transportation
27
270.00
Bill of water
2
20.00
Bill of electricity
8
80.00
Telecommunications
17
170.00
Family's expenditures for year 2020
Expenditures
%
RM
Food
46
471.15
Transportation
27
276.54
Bill of water
2
20.48
Bill of electricity
8
81.95
Telecommunications
17
174.12
(b)
2014 – RM4500
2015 – RM4725
2016 – RM4961.25
2017 – RM5209.31
2018 – RM5469.78
2019 – RM5742.27
2020 – RM6029.38
The increment is not satisfied with the percentage of family expenditure. The value of family expenditure becomes higher when the both of the income and the percentage of increase high.
(c) I will not encourage my father to accept the offer. This is because small difference in the interest rate can make a big difference to the payments over time. As the interest rate of credit card charged at 0.4% monthly, calculation shows that the interest rate yearly is at 4.8%. That is a very large portion of value. This could waste much money than any other type of loans. Buying a credit card is not recommended because the interest rate is higher than any other loans categories.
As the interest rate of loan increases, the interest of savings decrease because the interest value that need to pay to the bank is usually higher. While the interest of saving is high means that I just need pay low according to the interest loan for credit card.
RM15000 credit card loan with 4.8% annually interest rate for 1 year.
4.8100×15000+1500012=RM15720
RM15000 interest of saving based on 3% annually for 1 year
3100×15000+1500012=RM15450
(d) What you will need first, is a clear idea of where your money is going; then you can look at ways to cut fluff and lower the cost of your required living expense. The fastest way for some people to reduce monthly expenses will be in the area of health, auto and life insurance. Companies that sell those are incredibly competitive. Avoid items, however cheap or appealing, which have a primary effect of causing large and unnecessary spending. Some of these items, such as printers and suits, though rarely vehicles, are helpful to get rid of even if they are not broken.
Avoid or minimize addictive or mind-altering substances, those which are illegal, currently expensive, decrease current productivity, decrease future productivity, cause health problems, or decrease judgment undermining reduction of expenses. Make a shopping list before you go to the store and stick to it. This is especially helpful to impulse buyers. A shopping list gives you a clear idea of what you need and eliminates unnecessary purchases.
Parents should place rules on cell phone use. If your cell phone use is occasional only, consider a pay-as-you-go plan. Do consider, however, that a cheap unlimited data and navigation plan can sometimes save money by allowing instant price comparisons and quality checks. Some mobile phone plans are genuinely good and money-saving; but make sure that you shop around first for the deal that best suits you.
Reference
http://malaysia.deposits.org/providers/maybank.html
http://malaysia.deposits.org/accounts/cimb-bank-1-year-fixed-deposit.html
http://malaysia.deposits.org/accounts/ambank-1-year-fixed-deposit.html
http://www.maybank2u.com.my/calculator/form_hire-purchase-calc.html
https://ringgitplus.com/en/car-loan/
HISTORY
History of statistics
Statistics is the study of the collection, organization, analysis, interpretation and presentation of data. It deals with all aspects of data including the planning of data collection in terms of the design of surveys and experiments. When analyzing data, it is possible to use one of two statistics methodologies: descriptive statistics or inferential statistics.
The History of statistics can be said to start around 1749 although, over time, there have been changes to the interpretation of the word statistics. In early times, the meaning was restricted to information about states. This was later extended to include all collections of information of all types, and later still it was extended to include the analysis and interpretation of such data. In modern terms, "statistics" means both sets of collected information, as in national accounts and temperature records, and analytical work which require statistical inference.
Statistical activities are often associated with models expressed using probabilities, and require probability theory for them to be put on a firm theoretical basis: see History of probability.
A number of statistical concepts have had an important impact on a wide range of sciences. These include the experiments and approaches to statistical inference such as Bayesian inference, each of which can be considered to have their own sequence in the development of the ideas underlying modern statistics.
By the 18th century, the term "statistics" designated the systematic collection of demographic and economic data by states. For at least two millennia, these data were mainly tabulations of human and material resources that might be taxed or put to military use. In the early 19th century, collection intensified, and the meaning of "statistics" broadened to include the discipline concerned with the collection, summary, and analysis of data. Today, data are collected and statistics are computed and widely distributed in government, business, most of the sciences and sports, and even for many pastimes. Electronic computers have expedited more elaborate statistical computation even as they have facilitated the collection and aggregation of data. A single data analyst may have available a set of data-files with millions of records, each with dozens or hundreds of separate measurements. These were collected over time from computer activity (for example, a stock exchange) or from computerized sensors, point-of-sale registers, and so on. Computers then produce simple, accurate summaries, and allow more tedious analyses, such as those that require inverting a large matrix or perform hundreds of steps of iteration, that would never be attempted by hand. Faster computing has allowed statisticians to develop "computer-intensive" methods which may look at all permutations, or use randomization to look at 10,000 permutations of a problem, to estimate answers that are not easy to quantify by theory alone.
Johann Heinrich Lambert in his 1765 book Anlage zur Architectonic proposed the semicircle as a distribution of errors:
With -1 < x < 1.
Progression may refer to:
In mathematics:
Arithmetic progression, sequence of numbers such that the difference of any two successive members of the sequence is a constant
Geometric progression, sequence of numbers such that the quotient of any two successive members of the sequence is a constant
In music:
Chord progression, series of chords played in order
Backdoor progression, the cadential chord progression from iv7 to I, or flat-VII7 to I in jazz music theory
Omnibus progression, sequence of chords which effectively divides the octave into 4 equal parts
Ragtime progression, chord progression typical of ragtime music and parlour music genres
Progression, music software for guitarists
In other fields:
Age progression, the process of modifying a photograph of a person to represent the effect of aging on their appearance
Cisternal progression, theory of protein transport through the Golgi apparatus inside a cell
Colour progression, ranges of colour whose values transition smoothly through a hue, saturation, luminance, or any combination of the three
Horizontal progression, the gradual movement from left to right during writing a line of text in Western handwriting
A progressive tax is a tax by which the tax rate increases as the taxable amount increases
Semantic progression, evolution of word usage
Educational progression, an individual's movement through stages of education and/or training
Progress tracking in video games
Astrological progression, used in Horoscopic astrology to forecast future trends and developments.
1. Arithmetic Progression
In mathematics, an arithmetic progression (AP) or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant. For instance, the sequence 5, 7, 9, 11, 13, 15 … is an arithmetic progression with common difference of 2.
If the initial term of an arithmetic progression is and the common difference of successive members is d, then the nth term of the sequence () is given by:
And in general
A finite portion of an arithmetic progression is called a finite arithmetic progression and sometimes just called an arithmetic progression. The sum of a finite arithmetic progression is called an arithmetic series.
The behaviour of the arithmetic progression depends on the common difference d. If the common difference is:
Positive, the members (terms) will grow towards positive infinity.
Negative, the members (terms) will grow towards negative infinity.
2. Geometric Progression
In mathematics, a geometric progression, also known as a geometric sequence, is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio. For example, the sequence 2, 6, 18, 54 ... is a geometric progression with common ratio 3. Similarly 10, 5, 2.5, 1.25 ... is a geometric sequence with common ratio 1/2.
Examples of a geometric sequence are powers rk of a fixed number r, such as 2k and 3k. The general form of a geometric sequence is
Where r 0 is the common ratio and a is a scale factor, equal to the sequence's start value.
CONCLUSION
As the conclusion for this, the increasing of inflation rate in Malaysia does affect the family's expenditures and its monthly income itself. Because value of everything is expected to be higher in the future and continue to higher when the inflation rate increases.
The use of card credit is probably not good for people who have their middle level income every month. The monthly interest rate offer in the credit card is roughly different to any type of loans. People should not be encouraged to have a credit card loan because much money will be wasted by paying the interest rate to the bank.
We need to know how to save money because it can be use at another time. People should avoid over spending and try to be rational when buying something. We should think on what should do and whether to react it or not.
Family's monthly expenditure
Family's monthly expenditure
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