21
Total at the end of month (one month period) Bank A Bank B Bank C 3.10% 3.00% 3.00% 1 50129.17 50125 50125 2 50258.67 50250.31 50250.31 3 50388.5 50375.94 50375.94 4 50518.67 50501.88 50501.88 5 50649.18 50628.13 50628.13 6 50780.02 50754.7 50754.7 7 50911.2 50881.59 50881.59 8 51042.72 51008.79 51008.79 9 51174.59 51136.32 51136.32 10 51306.79 51264.16 51264.16 11 51439.33 51392.32 51392.32 12 51572.21 51520.8 51520.8 Total at the end of month (3 month period) Bank A Bank B Bank C 3.15% 3.05% 3.05% 3 50393.75 50381.25 50381.25 6 50790.6 50765.41 50765.41 9 51190.58 51152.49 51152.49 12 51593.7 51542.53 51542.53 Total at the end of month (6 month period) Bank A Bank B Bank C 3.20% 3.10% 3.10% 6 50800 50775 50775 12 51612.8 51562.01 51562.01 Total at the end of month ( one year period) Bank A Bank B Bank C 3.25% 3.15% 3.20% 12 51625 51575 51600

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Page 1: add maths project work 2012 full answer(correction)

Total at the end of month (one month period) Bank A Bank B Bank C

3.10% 3.00% 3.00%1 50129.17 50125 501252 50258.67 50250.31 50250.313 50388.5 50375.94 50375.944 50518.67 50501.88 50501.885 50649.18 50628.13 50628.136 50780.02 50754.7 50754.77 50911.2 50881.59 50881.598 51042.72 51008.79 51008.799 51174.59 51136.32 51136.3210 51306.79 51264.16 51264.1611 51439.33 51392.32 51392.3212 51572.21 51520.8 51520.8

Total at the end of month (3 month period) Bank A Bank B Bank C

3.15% 3.05% 3.05%3 50393.75 50381.25 50381.256 50790.6 50765.41 50765.419 51190.58 51152.49 51152.4912 51593.7 51542.53 51542.53

Total at the end of month (6 month period) Bank A Bank B Bank C

3.20% 3.10% 3.10%6 50800 50775 5077512 51612.8 51562.01 51562.01

Total at the end of month ( one year period) Bank A Bank B Bank C

3.25% 3.15% 3.20%12 51625 51575 51600

PART B

Page 2: add maths project work 2012 full answer(correction)

(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?

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 of paper ) = RM 80

By Mathematical solution :

Cost needed = RM 480 + RM 80 + RM 200 (RM 10 × 20 rim)

= RM 760

Cost to photocopy a piece of paper

= RM 760 ÷ 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.

Page 3: add maths project work 2012 full answer(correction)

Solution :

Charge to photocopy per piece = RM 0.10

Cost to photocopy a piece of paper = RM 0.076

By Mathematical solution :

Profit obtained = (RM 0.10 - RM 0.076) (10 000)

= RM 240

(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)

Page 4: add maths project work 2012 full answer(correction)

Rental 480 500

Toner 80 100

Paper 200 240

(i) Calculate the percentage increase in photocopying a piece of paper based on the year 2012,

using two different methods.

Solution :

Method 1 : Mathematical solution

Cost to photocopy a piece of paper in year 2013

= RM 500 + RM 100 + RM 240

= RM 840

Percentage increase

= 840−760

760 × 100%

= 10.53

Therefore, the percentage increase is 10.53%.

Method 2 : Price Index solution

I = P1 x 100 , Ῑ = ΣIWP0 ΣW

Page 5: add maths project work 2012 full answer(correction)

I rental = 500480

× 100 = 104.167

I toner = 10080

× 100 = 125

I paper = 240200

× 100 = 120

Ῑ = (104.167×480 )+ (105× 80 )+(120×200)

480+125+120= 110.53%

(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?

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?

Solution :

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

= RM 1 000 –RM 840

= RM 160

Page 6: add maths project work 2012 full answer(correction)

PART C

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 :

Conjecture in table form

MONTH MONEY

LEFT

TOTAL

MONEY

PAID

MONTH MONEY

LEFT

TOTAL

MONEY

PAID

MONTH MONEY

LEFT

TOTAL

MONEY

PAID

1 148150 1850 41 99166.80 75850 81 39368.39 149850

2 147040.75 3700 42 97812.63 77700 82 37715.23 151700

3 145925.95 5550 43 96451.70 79550 83 36053.81 153550

4 144805.58 7400 44 95083.95 81400 84 34384.08 155400

5 143679.61 9250 45 93709.37 83250 85 32706.00 157250

6 142548.01 11100 46 92327.92 85100 86 31019.53 159100

7 141410.75 12950 47 90939.56 86950 87 29324.62 160950

8 140267.80 14800 48 89544.26 88800 88 27621.25 162800

9 139119.14 16650 49 88141.98 90650 89 25909.35 164650

10 137964.74 18500 50 86732.69 92500 90 24188.90 166500

11 136804.56 20350 51 85316.35 94350 91 22459.84 168350

12 135638.58 22200 52 83892.93 96200 92 20722.14 170200

13 134466.78 24050 53 82462.40 98050 93 18975.75 172050

Page 7: add maths project work 2012 full answer(correction)

14 133289.11 25900 54 81024.71 99900 94 17220.63 173900

15 132105.56 27750 55 79579.83 101750 95 15456.74 175750

16 130916.08 29600 56 78127.73 103600 96 13684.02 177600

17 129720.67 31450 57 76668.37 105450 97 11902.44 179450

18 128519.27 33300 58 75201.71 107300 98 10111.95 181300

19 127311.86 35150 59 73727.72 109150 99 8312.51 183150

20 126098.42 37000 60 72246.36 111000 100 6504.07 185000

21 124878.92 38850 61 70757.59 112850 101 4686.60 186850

22 123653.31 40700 62 69261.38 114700 102 2860.03 188700

23 122421.58 42550 63 67757.69 116550 103 1024.33 190550

24 121183.69 44400 64 66246.48 118400 104 192400

25 119939.60 46250 65 64727.71 120250 105 194250

26 118689.30 48100 66 63201.35 122100 106 196100

27 117432.75 49950 67 61667.35 123950 107 197950

28 116169.91 51800 68 60125.69 125800 108 199800

29 114900.76 53650 69 58576.32 127650 109 201650

30 113625.27 55500 70 57019.20 129500 110 203500

31 112343.39 57350 71 55454.30 131350 111 205350

32 111055.11 59200 72 53881.57 133200 112 207200

33 109760.38 61050 73 52300.98 135050 113 209050

34 108459.19 62900 74 50712.48 136900 114 210900

35 107151.48 64750 75 49116.04 138750 115 212750

36 105837.24 66600 76 47511.62 140600 116 214600

37 104516.43 68450 77 45899.18 142450 117 216450

38 103189.01 70300 78 44278.68 144300 118 218300

39 101854.95 72150 79 42650.07 146150 119 220150

40 100514.23 74000 80 41013.32 148000 120 222000

223850

Page 8: add maths project work 2012 full answer(correction)

Conclusion

Pay the whole lump sum in cash of RM 150 000 is a better way than keep the RM 150 000 in a

fixed deposit account at a rate of 6% p.a. in a bank then borrow the money from bank and pay for

the hire purchase. After 103th month, there is no more money left in the bank. Hence, the money

left for 17th months need to pay from other sources.

PART D

Page 9: add maths project work 2012 full answer(correction)

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 :

Compound interest

Interest which is calculate not only the intial principal but also the accumulated interest of prior

periods. Compound interest differs from simple interest in that sample interest is calculated

solely as a percentage of the principal sum.

Simple interest

The interest calculate on principle sum, not compounded on earned interest.

Year Compound interest

3.5% per year

Simple interest

5 % per year

1 51750 52500

2 53561.25 55000

3 55435.89 57500

4 57376.15 60000

5 59384.31 62500

6 61462.76 65000

7 63613.96 67500

8 65840.44 70000

9 68144.86 72500

10 70529.93 75000

11 72998.48 77000

12 75553.43 80000

Page 10: add maths project work 2012 full answer(correction)

13 78197.80 82500

14 809347.00 85000

15 83767.43 87500

16 86699.29 90000

17 89733.76 92500

18 92874.45 95000

19 96125.05 97500

20 99489.40 100000

21 102971.56 102500

22 106575.56 105000

Page 11: add maths project work 2012 full answer(correction)

FURTHER EXPLORATION

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 :

Method : Geometric Progression

a = RM 5 000 , r = 1.08

Tn > 50 000

(5 000)(1.08n-1) > 50 000

1.08n-1 > 50 0005 000

1.08n-1 > 10

log10 1.08n-1 > log10 10

(n-1) log10 1.08> log10 10

n-1 > log1010

log101.08

n-1 > 29.92

n > 30.92

Therefore, n = 31 , when he is 30 years old

Page 12: add maths project work 2012 full answer(correction)

REFLECTION

Add Maths Here Comes The Winner

With you…… huuuu……uuuu…… (add maths)

With you…… huuuu……uuuu…… (add maths)

It’s hard for us to start at first,

It make me didn’t sleep tight (ggrrrr)

Cause your puzzle was my mission

make me flying in confusion

But I always believe in Magic

is believing in myself,

Song Title : Add Maths Here Comes The Winner

Singer, Composer and lyrics officially by :

Nursyazreen bt Wahid Marican (5KA)

Page 13: add maths project work 2012 full answer(correction)

if they can find the solution,

You’ll see, i can make anything happen

*Chorus

Grab my calculator

Eat and drink all were later

Mind start to pressure

In room, find the answer

Cause no one will ever see me quit

and I simply won't

If I start something

I will finish it and do it well

Finally it’s the time, come on!

When the answers are on my lawn-awn-awn,

Remember a winner never stop trying

Page 14: add maths project work 2012 full answer(correction)

Cause the price of victory is high-high-high

but so are the rewards.

*Chorus

Grab my calculator

Eat and drink all were later

Mind start to pressure

In room find the answer

No one will ever see me quit, because I simply won't.

If I start something, I will finish it and do it well

Remember…..

A winner never stop trying……

Cause the price of victory is high……

Page 15: add maths project work 2012 full answer(correction)

But so are the rewards…….

[THE END]