BUKU TEKS MATHEMATICS FORM 3 (DLP)

Chapter 2 Standard Form

Example 12

Calculate the value of each of the following operations. State the answer in standard form.

D î ± + 9.24 × 10± (b) 8.21 × 10– 4 + 1.49 × 10–5
F î –5 – 4.6 × 10– 6

Solution:
D î ± + 9.24 × 10± î ±

î ± CHAPTER 2

î 1 × 10±

î ±

î –2

(b) Method 1 Method 2 SMART

8.21 × 10– 4 + 1.49 × 10–5 8.21 × 10– 4 + 1.49 × 10–5 1. 3UHVV Mode EXWWRQ D
î – 4 + 1.49 × 10–1 × 10–4 IHZ WLPHV XQWLO WKH
î 101 × 10–5 + 1.49 × 10 –5 î – 4 + 0.149 × 10– 4
î – 4 VFUHHQ VKRZV:
î –5 + 1.49 × 10–5 î – 4
Fix Sci Norm
î –5
123
î –5
2. 3UHVV 2 WR FKRRVH
î 1 × 10–5 Sci WKDW LV VWDQGDUG
IRUP
î 1 + (–5)
3. (QWHU QXPEHU RI
î – 4 VLJQL¿FDQW ¿JXUHV V I
QHHGHG IRU H[DPSOH
(c) Method 1 Method 2
4. (QWHU WKH UHTXLUHG
î 10–5 – 4.6 × 10– 6 î –5 – 4.6 × 10–6 RSHUDWLRQ
î –5 – 4.6 × 10–1 × 10–5
î 101 × 10–6 – 4.6 × 10–6 î –5 – 0.46 × 10–5 Ƈ î 5 í î
± î –5 3UHVV Exp í Exp
î –6 – 4.6 × 10– 6 î –5
6FUHHQ GLVSOD\:
± î –6 ( í (

î –6 3UHVV = î 5

î 1 × 10–6 Ƈ î 5 î î
3UHVV Exp î Exp
î 1 + (–6)
6FUHHQ GLVSOD\:
î –5 Exp î Exp

3UHVV = î 10

MIND TEST 2.2b 5. ([WHQG \RXU H[SORUDWLRQ
WR RWKHU RSHUDWLRQV
1. Calculate the value of each of the following operations. State your LQYROYLQJ RWKHU VWDQGDUG
IRUPV
answer in standard form.
6. &RPSDUH WKH UHVXOWV
(a) 2.4 × 104 î 4 (b) 8.2 × 106 – 4.27 × 106 SURGXFHG E\ FDOFXODWRU
F î 7 + 4.98 × 107 (d) 1.2 × 105 î 4 ZLWK DQVZHUV REWDLQHG
(f) 5.7 × 10 + 8.02 × 104 WKURXJK PDQXDO
(e) 5.7 × 108 – 2.4 × 107 FDOFXODWLRQV
(g) 6.5 × 104 í î (h) 5.2 × 10í í î í
(i) 8.74 × 10–5 – 2.65 × 10–5 (j) 4.1 × 10í + 9.5 × 10í
(l) 9.42 × 10– 6 ± î –7
N î í í î í

41

2SHUDWLRQV RI 0XOWLSOLFDWLRQ DQG 'LYLVLRQ TIPS

Example 13 /DZ RI ,QGLFHV
Ƈ 2SHUDWLRQ RI
Solve the following operations. State your answers in standard form.
PXOWLSOLFDWLRQ
D î 5 × 4.9 × 102 (b) 7.5 × 10í × 5 × 10í (A î P î B î Q)
A î B î P + Q
CHAPTER 2 (c) —52.9—××—1100—25 (d) —64.8—××1—100–—6± Ƈ 2SHUDWLRQ RI GLYLVLRQ
(A î P) ÷ (B î Q)
A ÷ B î P ± Q

Solution:

D î 5 × 4.9 × 102 (b) 7.5 × 10í × 5 × 10í (c) —52.9—××—1100—25 (d) —64.8×—×1—01–0—6±
î î 5 + 2 ²52.9± î 5 – 2 ²64.8± î ± ± ±
î î í í î
î 7 î í î
î 1 × 107 î 1 × 10í
î 1 + 7 î 1 + (–9)
î 8 î í

MIND TEST 2.2c

1. Calculate the value of each of the following operations. State your answer in standard form.

(a) 4 × 105 î î 2 (b) 7.5 × 10í × 5 × 10í

(c) î 5 × 4.0 × 102 G î í × 4 × 105

(e) (1.08 × 102) ÷ (2.4 × 104) (f) (9.6 × 10í ) ÷ (1.5 × 10í )

(g) (5.9 × 105) ÷ (2 × 102) (h) (2.58 × 104 · î –4)

2. $ PRELOH VZLPPLQJ SRRO PHDVXUHV FP = FP = 56 cm. BULLETIN
Calculate the maximum volume of water that it can hold in litres. OLWUH FP3
6WDWH \RXU DQVZHU LQ VWDQGDUG IRUP DQG FRUUHFW WR IRXU VLJQL¿FDQW OLWUH P3
¿JXUHV.

3. Syazwani wants to transfer 2 terabytes of data DISCUSSION CORNER
WR SHQ GULYHV ZLWK D FDSDFLW\ RI JLJDE\WHV
:KDW LV WKH PLQLPXP QXPEHU RI JLJDE\WH SHQ %HWZHHQ RSHUDWLRQ RI
drives needed? DGGLWLRQ RU VXEWUDFWLRQ
DQG RSHUDWLRQ RI
*LYHQ PLOOLPHWUH ± PHWUH DQG PLFURPHWUH –6 metre, PXOWLSOLFDWLRQ RU GLYLVLRQ
state 1 millimetre in micrometre. LQYROYLQJ VWDQGDUG IRUP
ZKLFK RSHUDWLRQ LV HDVLHU"
:K\"

42

Chapter 2 Standard Form

How do you solve problems involving numbers in LEARNING
standard form? STANDARD

Example 14 Solve problems involving
numbers in standard form.

A ream of paper contains 800 sheets of paper. The thickness of one sheet of paper is 9.4 × 10–3 cm.
Given the total thickness of n reams of paper is 225.6 cm, calculate the value of n.

Solution: CHAPTER 2

Understanding the problem Implementing the strategy Making a
Number of sheets in 1 ream = 800 conclusion
Thickness of 1 sheet = 9.4 × 10–3 cm Thickness of 1 ream
Thickness of n reams = 225.6 cm = 800 × 9.4 × 10–3 cm Number of
= 7.52 cm reams is 30.
Planning a strategy
‡ Determine the thickness of 1 ream of Thus,
n = —tthh—iicckk—nnee—ssss—ooff—n1—rreea—amm–s
paper. n = —272.—552.6—ccm—m
‡ Q = —tthhi—icckk—nnee—ssss—ooff—n1r–ree—aamm—s n = 30

Example 15

$ SURSHUW\ ¿UP ERXJKW D SLHFH RI ODQG LQ WKH VKDSH RI D ULJKW DQJOHG Q
triangle PQR as shown in the diagram.

(a) Calculate the value of PQ, in metres, and state your answer in 3.5 × 102 m
standard form.

(b) If the cost of one square metre of the land is RM45, calculate the

total cost of the land in RM. P 2.1 × 102 m R

Solution:

Understanding the problem Implementing the strategy

ǻPQR is a right-angled triangle. (a) PQ2 = [(3.5 × 102)2 í î 2)2] m2
QR is the hypotenuse. = [1.225 × 105 í î 4] m2
= (7.84 × 104) m2
Planning a strategy
PQ = ¥(7.84 × 104) m2
(a) Calculate PQ using Pythagoras
theorem. = 2.8 × 102 m

(b) Calculate the area of land in the ( ) ( ) E $UHD RI ǻPQR = —21 × 2.1 × 102 m× 2.8 × 102 m
shape of ǻPQR. Multiply total land
area by cost of 1 m2 of land. = 2.94 × 104 m2
Cost of land = 2.94 × 104 × RM45

= RM1 323 000.00

Making a conclusion (b) Total cost of land = RM1 323 000.00
(a) Distance PQ = 2.8 × 102 m

43

Example 16 1.2742 × 104 km

The picture shows the Earth with a diameter of 1.2742 × 104 km. Calculate the
surface area of the Earth, in km2. State the answer in standard form correct to four
VLJQL¿FDQW ¿JXUHV >6XUIDFH DUHD RI VSKHUH SU2 and S @

Solution:

CHAPTER 2 8QGHUVWDQGLQJ WKH 3ODQQLQJ D VWUDWHJ\ ,PSOHPHQWLQJ WKH VWUDWHJ\
SUREOHP
x 5DGLXV ²dia²m2²ete²r 5DGLXV RI ( ) —1.2—74—22—× 1—04– km
x Earth is a sphere. Earth
x Diameter of Earth is x Use formula for × 10 km
surface area of sphere
1.2742 × 104 km. to calculate surface Surface area of Earth
x Answer is in standard area of Earth. SU2
> × 10 )2] km2
form correct to four NP2
VLJQL¿FDQW ¿JXUHV. × 108 km2 (4 s.f.)

0DNLQJ D FRQFOXVLRQ
Surface area of Earth is 5.101 × 108 km2

MIND TEST 2.2d

1. The average daily water consumption in a residential area is 6 950 m . Calculate the total water
FRQVXPSWLRQ LQ FXELF PHWUHV LQ WKH UHVLGHQWLDO DUHD IRU )HEUXDU\ 6WDWH WKH DQVZHU LQ
VWDQGDUG IRUP FRUUHFW WR WKUHH VLJQL¿FDQW ¿JXUHV.

2. 5.791 × 107 km

6XQ 0HUFXU\ (DUWK 1HSWXQH

1.496 × 108 km

4.495 × 109 km

The picture above shows the estimated distance of three planets in the solar system from the

6XQ RQ D FHUWDLQ GD\ &DOFXODWH WKH GL൵HUHQFH LQ GLVWDQFH LQ NP EHWZHHQ

(a) Mercury and Earth (b) 0HUFXU\ DQG 1HSWXQH (c) (DUWK DQG 1HSWXQH

6WDWH WKH DQVZHUV LQ VWDQGDUG IRUP FRUUHFW WR WKUHH VLJQL¿FDQW ¿JXUHV.

44

Chapter 2 Standard Form

Dynamic Challenge

Test Yourself

1. 5RXQG R൵ WKH IROORZLQJ QXPEHUV DQG GHFLPDOV FRUUHFW WR WKH VLJQL¿FDQW ¿JXUHV VWDWHG LQ WKH
brackets.

D [2] (b) 54 299 [4] (c) 8 999 [2] (d) 295 197 [2] CHAPTER 2

(e) 4 854 [1] (f) 5 > @ J [2] K [1]

L [2] M [1] N > @ (l) 501.724 > @

2. Given P î and Q î 4, calculate the values of the following operations. State
\RXU DQVZHUV LQ VWDQGDUG IRUP FRUUHFW WR WKUHH VLJQL¿FDQW ¿JXUHV.

(a) 2PQ (b) P + Q (c) Q ± P (d) P2 + Q2

( e) — 2PQ– (f) —P P —Q Q– (g) P–2 + Q± (h) Q – P±

3. Complete the following. (b) 5.74 × 10± î –6

(a) 2.5 × 102 + × 104 î ± î × 10
î × 104 + × 104
× 104 î 4 î ± + × 10±

î 4 î ±
î 4
î ±

(c) 1.75 × 102 – 4.2 × 10–1 G î –2 ± î –5

î 2 – 4.2 × 10 × 102 î –2 ± î × 10–2

î 2 – × 102 î –2 – × 10–2

î 2 ± î –2

î 2 î –2

A factory produces 72 thousand packets of chips every
ZHHN ,I WKH IDFWRU\ RSHUDWHV GD\V D ZHHN DQG KRXUV
a day, calculate

(a) the number of packets of chips produced every day.
State your answer in standard form.

(b) WKH DYHUDJH SUR¿W SHU KRXU LI WKH QHW SUR¿W RI RQH
SDFNHW RI FKLSV LV VHQ 6WDWH WKH DQVZHU WR WKH
nearest RM.

45

5. 7KH HVWLPDWHG SRSXODWLRQ RI 0DOD\VLD IRU LV
PLOOLRQ *LYHQ 0DOD\VLD¶V ODQG DUHD LV NP2,
calculate the population density of Malaysia for each
square kilometre for 2018.

State your answer correct to the nearest integer.

CHAPTER 2 Skills Enhancement

1. A newly built community hall required 6 185 pieces of tiles measuring FP î FP for the
ÀRRU.
(a) &DOFXODWH WKH ÀRRU DUHD RI WKH KDOO LQ VTXDUH PHWUHV 6WDWH \RXU DQVZHU LQ VWDQGDUG IRUP
FRUUHFW WR WKUHH VLJQL¿FDQW ¿JXUHV.
(b) Given the cost of one piece of tile is RMl.75, calculate the total cost of the tiles to the

nearest RM.

2. Encik Hanif drove his car from Kota Bharu to Kuala

Terengganu to visit his son. On the way back to Kota Bharu,

Encik Hanif made a stop at Setiu. The map shows the NP
(2 hours 18 minutes)
distance and travelling time of Encik Hanif.
(a) Calculate the average speed, in km h–1, of Encik Hanif’s

car for the journey 114 km
(i) from Kota Bharu to Kuala Terengganu (1 hour 40 minutes)
(ii) from Kuala Terengganu to Setiu

(iii) from Setiu to Kota Bharu 51 km
(1 hour 5 minutes)
6WDWH WKH DQVZHUV FRUUHFW WR WKUHH VLJQL¿FDQW ¿JXUHV.
(b) Encik Hanif is a safety-conscious driver who abides

E\ WKH VSHHG OLPLW ,V WKLV VWDWHPHQW WUXH" 6WDWH \RXU
reasons.

Self Mastery
1. The picture shows three planets in the Solar System.

0HUFXU\ 1HSWXQH -XSLWHU
>'LDPHWHU NP@ >'LDPHWHU NP@ >'LDPHWHU NP@

(a) Calculate the surface area, in km2, of all three planets. State the answers in standard form

FRUUHFW WR WKUHH VLJQL¿FDQW ¿JXUHV.
[Surface area of sphere ʌU2 DQG ʌ @
(b) %DVHG RQ \RXU DQVZHU LQ D FDOFXODWH WKH GL൵HUHQFH LQ VXUIDFH DUHD EHWZHHQ WKH ODUJHVW DQG
VPDOOHVW SODQHWV LQ WKH 6RODU 6\VWHP 6WDWH WKH DQVZHU FRUUHFW WR IRXU VLJQL¿FDQW ¿JXUHV.

46

Chapter 2 Standard Form

2.

297 mm 297 mm

70 GSM 80 GSM CHAPTER 2
210 mm 210 mm

7KH GLDJUDP DERYH VKRZV WZR W\SHV RI $ VL]HG SDSHU ZLWK GL൵HUHQW PDVVHV *60 PHDQV
grams per square metre.

Calculate the mass of one piece of A4-sized paper, in grams for

(a) 70 GSM (b) 80 GSM

6WDWH WKH DQVZHUV LQ VWDQGDUG IRUP FRUUHFW WR WKUHH VLJQL¿FDQW ¿JXUHV.

P ROJ EC T

1. Look at the pictures below. Obtain the data relevant to the required measurement. Your
answers should be in standard form.

2. You can surf various websites or refer to reference books to obtain interesting data related
to the pictures below.

(a) Mass (b) Population

(c) Distance (d) Magnitude

3. Obtain other interesting facts that involve calculations in standard form.
3UHVHQW \RXU ¿QGLQJV XVLQJ PXOWLPHGLD DSSOLFDWLRQV.

47

CONCEPT MAP

6WDQGDUG )RUP

CHAPTER 2 6LJQL¿FDQW ¿JXUH shows the level 6WDQGDUG IRUP is written as A × Q where
of DFFXUDF\ of a measurement. 1 р A Ͻ and Q is an integer.

$OO GLJLWV DUH VLJQL¿FDQW ¿JXUHV Changing VLQJOH QXPEHUV to
H[FHSW WKH ]HUR EHIRUH WKH ¿UVW QRQ VWDQGDUG IRUP and vice versa.
]HUR GLJLW. D î 5
E î í
D V I E V I F î 4
(c) 1.200 (4 s.f.) (d) 10 518 (5 s.f.) G î í

)RU LQWHJHUV, the value of the %DVLF RSHUDWLRQV (+, –, ×, ÷) involving
VLJQL¿FDQW ¿JXUH IRU ]HUR as the last numbers in standard form.
digit depends on the UHTXLUHG OHYHO RI (a) S × 10Q + T × 10Q
DFFXUDF\. S + T ) × 10Q
D ± V I nearest one) (b) S × 10Q – T × 10Q
E ± V I nearest ten) S – T ) × 10Q
F ± V I nearest hundred) (c) (S × 10P) × (T × 10Q)
G ± V I nearest thousand) S × T ) × 10P + Q
(d) (S × 10P) ÷ (T × 10Q)
5RXQGLQJ R൵ D QXPEHU WR D FHUWDLQ S ÷ T ) × 10P – Q
QXPEHU RI VLJQL¿FDQW ¿JXUHV.
D
V I

2 900 (2 s.f.)
V I
(b) 62.54

60 (1 s.f.)
V I
V I
(c) 0.02704
V I

0.027 (2 s.f.)
V I

48

Chapter 2 Standard Form CHAPTER 2

SELF-REFLECT
$W WKH HQG RI WKLV FKDSWHU , FDQ
1. ([SODLQ WKH PHDQLQJ RI VLJQL¿FDQW ¿JXUH DQG WKXV GHWHUPLQH WKH QXPEHU RI

VLJQL¿FDQW ¿JXUHV RI D QXPEHU
2. 5RXQG R൵ D QXPEHU WR D FHUWDLQ number of VLJQL¿FDQW ¿JXUHV

3. Recognise and write numbers in standard form.

Perform basic arithmetic operations involving numbers in standard form.

5. Solve problems involving numbers in standard form.

EXPLORING MATHEMATICS
1. Get into groups.
2. By using the various sources available, identify several measurement values in daily life that

DUH YHU\ VPDOO RU YHU\ ELJ )RU H[DPSOH,

Hard disk One water molecule One virus
(1 terabyte) (0.1 nanometer) (1 micrometer)

3. 3UHSDUH D UHSRUW RQ \RXU ¿QGLQJV XVLQJ PXOWLPHGLD DSSOLFDWLRQV.
Present your report.
5. Obtain additional information from the presentations of the other groups.
'LVFXVV WKH DGYDQWDJHV RI XVLQJ VWDQGDUG IRUP LQ YDULRXV ¿HOGV.

49

CHAPTER Consumer Mathematics:
Savings and Investments,
3 Credit and Debt

What will you learn?

3.1 6DYLQJV DQG ,QYHVWPHQWV
3.2 &UHGLW DQG 'HEW 0DQDJHPHQW

WWhhyy ddoo yyoouu lleeaarrnn tthhiiss cchhaapptteerr??
‡ .QRZOHGJH RI VDYLQJV DQG LQYHVWPHQWV FDQ KHOS XV

WR PDQDJH RXU ¿QDQFHV
‡ 7KH FRQFHSW RI VDYLQJV DQG LQYHVWPHQWV LV XVHG

LQ EDQNLQJ VWRFNV UHDO HVWDWH EXVLQHVV ¿QDQFH
DFFRXQWLQJ DQG VR RQ

0“ DQ\ D OLWWOH PDNHV D PLFNOH´
7KH DERYH SURYHUE PHDQV LW LV D JRRG KDELW WR
VDYH PRQH\ IRU WKH IXWXUH 6DYLQJ KDELWV WKDW KDYH
EHHQ SUDFWLVHG VLQFH FKLOGKRRG FDQ KHOS D SHUVRQ
FRSH ZLWK DQ\ HPHUJHQF\ ,QYHVWPHQWV PDGH E\ DQ
LQGLYLGXDO PXVW EH LQ D WLPHO\ PDQQHU LQ DFFRUGDQFH
ZLWK WKH FXUUHQW PDUNHW

50

EExxpplloorriinngg EErraa

7KH EDUWHU V\VWHP ZDV SUDFWLVHG EHIRUH WKH XVH RI
PRQH\ LQ WKH HFRQRP\ DQG ZDV WKH HDUOLHVW IRUP RI
EXVLQHVV LQ WKH ZRUOG
+LVWRU\ RI PRQH\ GHYHORSPHQW EHJDQ ZLWK WKH
HYROXWLRQ RI WKH KXPDQ FLYLOLVDWLRQ LWVHOI ZKLFK
ZDV DURXQG %&

KWWS EXNXWHNVNVVP P\ 0DWKHPDWLFV )
([SORULQJ(UD&KDSWHU SGI

WORD B A N K

‡ OLTXLGLW\ ‡ NHFDLUDQ

‡ LQWHUHVW ‡ IDHGDK

‡ GHEW ‡ KXWDQJ

‡ LQWHUHVW UDWH ‡ NDGDU IDHGDK

‡ FUHGLW ‡ NUHGLW

‡ LQYHVWPHQW ‡ SHODEXUDQ

‡ ORDQ ‡ SLQMDPDQ

‡ SHUVRQDO ORDQ ‡ SLQMDPDQ SHULEDGL

‡ UHWXUQ ‡ SXODQJDQ

‡ VDYLQJV ‡ VLPSDQDQ

51

3.1 Savings and Investments

What are savings and investments? LEARNING

Savings UHIHU WR H[FHVV PRQH\ GHSRVLWHG LQ WKH VDIH PRQH\ ER[ RU STANDARD

GUDZHU ([WUD PRQH\ FDQ DOVR EH GHSRVLWHG DW D EDQN WKDW ZLOO SURYLGH Recognise various types of
savings and investments.
UHWXUQV EDVHG RQ LQWHUHVW UDWHV DQG VDYLQJV SHULRGV 7KHUH DUH VRPH

FRPPRQ ZD\V RI VDYLQJ LQ WKH EDQN

Savings Account BULLETIN

CHAPTER 3 ‡ 7KH VDYLQJV DFFRXQW KROGHU FDQ VDYH DQ\ Credit counselling
DPRXQW DFFRUGLQJ WR KLV DELOLW\ and credit agencies
encourage each
‡ 7KH DFFRXQW KROGHU UHFHLYHV WKH LQWHUHVW EDVHG individual to save 10% of
RQ WKH WRWDO DPRXQW DQG GXUDWLRQ RI VDYLQJV their monthly income.

‡ ,QWHUHVW UDWHV DUH ORZHU FRPSDUHG WR ¿[HG

GHSRVLW DFFRXQWV

‡ 7KH DFFRXQW KROGHU FDQ ZLWKGUDZ WKH VDYLQJV DW DQ\ WLPH

‡ 7KH VDYLQJV FDQ EH ZLWKGUDZQ E\ XVLQJ D GHELW FDUG YLD DQ DXWRPDWLF

WHOOHU PDFKLQH $70

Fixed Deposit Account

‡ $ VXP RI PRQH\ LV VDYHG IRU D FHUWDLQ SHULRG RI WLPH VXFK DV PRQWKV
PRQWKV RU \HDU WHQXUH

‡ $ FFRXQW KROGHUV ZLOO EH RIIHUHG PRUH FRPSHWLWLYH LQWHUHVW UDWHV
FRPSDUHG WR VDYLQJV DFFRXQWV

‡ 6DYLQJV FDQQRW EH ZLWKGUDZQ EHIRUH WKH PDWXULW\ GDWH
‡ ,I WKH PRQH\ LV ZLWKGUDZQ EHIRUH PDWXULW\ WKH DFWXDO LQWHUHVW UDWH WKDW

VKRXOG EH UHFHLYHG ZLOO EH UHGXFHG DQG ZLOO EH FDQFHOOHG DW D FHUWDLQ
WLPH
‡ $ VDYLQJV FHUWL¿FDWH ZLOO EH LVVXHG WR WKH DFFRXQW KROGHU

Current Account

‡ 6DYLQJV LQ D FXUUHQW DFFRXQW FDQ EH XVHG IRU SHUVRQDO RU EXVLQHVV
SXUSRVHV

‡ 7KH DFFRXQW KROGHU PD\ PDNH SD\PHQW WR DQRWKHU SDUW\ E\ FKHTXH
‡ 6DYLQJV LQ WKH DFFRXQW ZLOO QRW EH SDLG LQWHUHVW DQG LV VXEMHFWHG WR

VHUYLFH FKDUJHV +RZHYHU WKHUH DUH FHUWDLQ EDQNV WKDW SD\ LQWHUHVW WR
FXUUHQW DFFRXQW KROGHUV
‡ 7KH FXUUHQW DFFRXQW DSSOLFDQW PXVW VXEPLW D UHIHUUDO ZKR LV DQ H[LVWLQJ
FXUUHQW DFFRXQW KROGHU DW WKH VDPH EDQN WR RSHQ WKH DFFRXQW
‡ ,Q DGGLWLRQ WR FKHTXHV QRUPDO ZLWKGUDZDOV DUH XVXDOO\ DOORZHG YLD
GHELW FDUGV DQG RWKHU FKDQQHOV VXFK DV ,QWHUQHW EDQNLQJ WHOHSKRQH
EDQNLQJ DQG VR RQ
‡ 7KH DFFRXQW KROGHU FDQ HQMR\ DQ RYHUGUDIW IDFLOLW\ WKDW LV ZLWKGUDZLQJ
PRQH\ EH\RQG WKH EDODQFH RI WKH GHSRVLW EXW ZLWK LQWHUHVW FKDUJHV

52

Chapter 3 Consumer Mathematics: Savings
and Investments, Credit and Debt

Investment LV DQ DOWHUQDWLYH VWHS IRU IXWXUH UHWXUQV LQ WKH IRUP BULLETIN
RI FXUUHQW LQFRPH DQG FDSLWDO JDLQV 7\SHV RI LQYHVWPHQWV DUH DV
IROORZV There are two types
of investors, that is,
8QLW 7UXVW Investment 6KDUHV aggressive and moderate
investors:
5HDO (VWDWH
Ƈ Aggressive investors
– invest in stock
market.

Ƈ Moderate investors
– buy unit trusts, bonds
and equity funds.

Shares TIPS CHAPTER 3

$ FRPSDQ\ ZLOO LVVXH VKDUHV IRU WKH SXUSRVH RI UDLVLQJ FDSLWDO Luxury Stocks (Blue
$Q LQGLYLGXDO ZKR SXUFKDVHV VKDUHV IURP D FRPSDQ\ LV WKH RZQHU RI Chip Stocks) are stocks
WKH FRPSDQ\ XQGHU FHUWDLQ FRQGLWLRQV 7KH VKDUHKROGHUV ZLOO UHFHLYH of large companies
UHWXUQV LQ WKH IRUP RI GLYLGHQGV DQG FDSLWDO JDLQV with track records of
excellent business such
as Maybank, TNB and
Petronas.

Unit Trust BULLETIN

7UXVW IXQG LV FRQWUROOHG E\ D XQLW WUXVW FRPSDQ\ WKDW LV PDQDJHG Ƈ ,QYHVWPHQW UHWXUQV
E\ D TXDOL¿HG SURIHVVLRQDO PDQDJHU LQ WKH ¿HOG RI LQYHVWPHQW 7KRVH comprise current income
ZKR KDYH QR NQRZOHGJH RI WKH SXUFKDVH RI VKDUHV FDQ JHW KHOS IURP and capital gains.
WKH XQLW WUXVW FRPSDQLHV WR PDQDJH WKHLU PRQH\ 8QLW WUXVW FRPSDQLHV
FROOHFW PRQH\ IURP LQYHVWRUV DQG WKH PRQH\ LV LQYHVWHG LQ YDULRXV Ƈ 5HWXUQ RQ FXUUHQW
SRWHQWLDO FRPSDQLHV ZLWK WKH DLP RI SURYLGLQJ UHWXUQV WKDW EHQH¿W income – rents,
LQYHVWRUV dividends, bonus
shares.
Real Estate
Ƈ &DSLWDO JDLQV ±
,QYHVWPHQWV RQ LPPRYDEOH DVVHWV VXFK DV UHVLGHQWLDO KRXVHV additional or increased
VKRSV ODQG DQG RWKHUV DUH LQYHVWPHQWV LQ UHDO HVWDWH ,QYHVWRUV VKRXOG investment value from
FRQVLGHU YDULRXV DVSHFWV EHIRUH LQYHVWLQJ its original amount. For
example, stock prices
)DFWRUV WR EH FRQVLGHUHG LQ UHDO HVWDWH LQYHVWPHQW DUH HFRQRPLF rose from RM2.00
VLWXDWLRQV LQFRPH JHQHUDWLQJ FDSDELOLWLHV WKDW LV UHQW ORFDWLRQ DQG to RM2.20, thus the
SURSHUW\ SURVSHFWV LQ WKH IXWXUH ,QGLYLGXDOV ZKR LQYHVW LQ UHDO HVWDWH addition of RM0.20
ZLOO UHFHLYH DQ LQYHVWPHQW UHWXUQ LQ WKH IRUP RI UHQW DQG FDSLWDO JDLQV was an increase in
investment value.

QU I Z

Is the purchase of life
insurance and health
insurance considered
as an investment or
savings?

53

Brainstorming 1 In groups

Aim: 7R LGHQWLI\ W\SHV RI VDYLQJV DQG LQYHVWPHQWV

Steps:

1. *HW LQWR JURXSV RI ¿YH RU VL[ VWXGHQWV (DFK JURXS VKRXOG VWDWH WKH W\SHV RI VDYLQJV DQG
LQYHVWPHQWV DFFRUGLQJ WR WKH VWDWHPHQWV JLYHQ DQG H[SODLQ WKH FKDUDFWHULVWLFV RI WKH VDYLQJV
DQG LQYHVWPHQWV VSHFL¿HG

2. 7KH LQIRUPDWLRQ FROOHFWHG VKRXOG EH SUHVHQWHG LQ WKH IRUP RI UHSRUWV DV VKRZQ EHORZ

Type of Type of Description
savings investment

1. (QFLN 5L]DO VDYHV D WRWDO RI 50 LQ 6DYLQJV DFFRXQW ± WKH
DPRXQW RI PRQH\ VDYHG
CHAPTER 3 WKH EDQN 6DYLQJV LV VPDOO DQG FDQ EH
ZLWKGUDZQ DW DQ\ WLPH

2. &LN =HWL LV D GHDOHU ZKR NHHSV D VXP RI
PRQH\ LQ WKH EDQN ZLWK WKH LQWHQWLRQ RI
LVVXLQJ D FKHTXH WR SD\ WKH FUHGLWRU

3. 0UV 5DQL XVHV WKH PRQH\ UHFHLYHG
IURP KHU IDWKHU WR EX\ D VKRSORW

4. 3XDQ )DULGDK VDYHG D VXP RI 50
LQ WKH EDQN WR ¿QDQFH WKH HGXFDWLRQ RI
KHU FKLOGUHQ LQ WKH IXWXUH

5. 0U /HH ERXJKW XQLWV RI XQLW
WUXVWV

6. 0V 6KDURQ ERXJKW XQLWV RI %DQN
2UNLG %HUKDG VKDUHV ZRUWK 50
SHU VKDUH RQ WKH .XDOD /XPSXU 6WRFN
([FKDQJH

Discussion:
6WDWH WKH DGYDQWDJHV DQG GLVDGYDQWDJHV RI HDFK W\SH RI VDYLQJV DQG LQYHVWPHQWV

)URP %UDLQVWRUPLQJ LW LV IRXQG WKDW VDYLQJV DQG LQYHVWPHQWV DUH GLIIHUHQW

MIND TEST 3.1a

1. :KDW LV WKH SXUSRVH RI DQ LQGLYLGXDO
V VDYLQJV"
2. <RXU IDWKHU KDV 50 DQG KDV QRW XVHG LW IRU D ORQJ WLPH :KDW LV \RXU DGYLFH WR KLP"

([SODLQ \RXU DQVZHU
3. %HVLGHV PHUFKDQWV ZK\ DUHQ
W PRVW SHRSOH LQWHUHVWHG LQ RSHQLQJ D FXUUHQW DFFRXQW"

54

Chapter 3 Consumer Mathematics: Savings
and Investments, Credit and Debt

:KDW GR \RX XQGHUVWDQG DERXW WKH EHQH¿WV RI VDYLQJV" LEARNING
STANDARD

,QWHUHVW IRU VDYLQJV DUH UHZDUGV SDLG E\ ¿QDQFLDO LQVWLWXWLRQV VXFK DV Perform calculations
EDQNV WR GHSRVLWRUV 7KH LQWHUHVWV FDQ EH GLYLGHG LQWR WZR W\SHV QDPHO\ involving simple interest
simple interest DQG compound interest and compound interest
for savings, and hence
Simple interest explain the impact of
changes in period, rate
6LPSOH LQWHUHVW LV D UHZDUG JLYHQ WR WKH GHSRVLWRU DW D FHUWDLQ UDWH RQ WKH of interest or return and
GHSRVLW DPRXQW SULQFLSDO IRU D FHUWDLQ SHULRG RI WLPH LQ \HDUV compounding frequency
on the future value of
savings.

Example 1 CHAPTER 3

(QFLN =DLQDO GHSRVLWHG 50 DW %DQN %XQJD 5D\D ZLWK DQ LQWHUHVW UDWH RI SHU DQQXP +RZ
PXFK LV WKH LQWHUHVW HDUQHG E\ (QFLN =DLQDO DIWHU \HDU"

Solution:

7KH SULQFLSDO GHSRVLWHG E\ (QFLN =DLQDO LV 50 6R RI 50 LV

5 0 î ² ± 50 TIPS
$IWHU \HDU WKH LQWHUHVW HDUQHG E\ (QFLN =DLQDO LV
,QWHUHVW 50 î Rate is given in percentage
50 form. Thus, we must divide
the rate by a hundred. If
7KH VLPSOH LQWHUHVW FDQ EH FDOFXODWHG XVLQJ WKH IROORZLQJ IRUPXOD the time is given in months,
do not forget to change
to year by dividing by 12
months.

I 3UW

I LV WKH LQWHUHVW, P LV WKH SULQFLSDO U LV WKH UDWH DQG W LV WKH WLPH LQ \HDUV

Example 2

(QFLN %DGUXO GHSRVLWV 50 LQ D EDQN ZLWK DQ LQWHUHVW UDWH RI SHU DQQXP IRU D SHULRG RI
\HDUV &DOFXODWH WKH WRWDO LQWHUHVW WKDW (QFLN %DGUXO ZLOO UHFHLYH IRU WKH \HDU SHULRG

Solution:

P U ² ± W


7KXV LQWHUHVW I 3UW
5 0 î ² ± î


50

55

Example 3 Jenis-jenis Faedah

0V :RQJ GHSRVLWV 50 LQ %DQN 0XUQL ZLWK DQ LQWHUHVW UDWH RI SHU DQQXP &DOFXODWH WKH
DPRXQW RI LQWHUHVW 0V :RQJ ZLOO UHFHLYH DIWHU PRQWKV

Solution:

I 3UW
5 0 î ² ± î ²
50

CHAPTER 3 What is the impact on the simple interest as a result of changing the savings period?

7KH FKDQJHV LQ VDYLQJV SHULRG LQ D EDQN JLYH GLIIHUHQW UHWXUQV

Example 4

(QFLN 1D]ULQ GHSRVLWV 50 LQ %DQN 'HVD ZLWK DQ LQWHUHVW UDWH RI SHU DQQXP &DOFXODWH WKH
WRWDO VDYLQJV RI (QFLN 1D]ULQ DIWHU KH KDV VDYHG IRU
D \HDUV E \HDUV

Solution:
7KH IRUPXOD IRU FDOFXODWLQJ WKH LQWHUHVW I 3UW
3ULQFLSDO 50
,QWHUHVW UDWH

D \HDUV E \HDUV

,QWHU HVW 5 0 î ² ± î 50 ,QWHU HVW 50 î ² ± î 50


7RWDO VDYLQJV DW WKH HQG RI WKH VHFRQG \HDU 7RWDO VDYLQJV DW WKH HQG RI WKH WKLUG \HDU

50 50 50 50

50 50

%DVHG RQ WKH H[DPSOH DERYH LW LV IRXQG WKDW WKH ORQJHU WKH VDYLQJV SHULRG DW WKH EDQN WKH KLJKHU
WKH DPRXQW RI LQWHUHVW HDUQHG 7KHUHIRUH WKH ¿QDO DPRXQW RI VDYLQJV DOVR LQFUHDVHV

What is the impact if the given interest rates differ for the same principal?

Dad, what is the The total annual
impact on the total returns received will
annual returns if surely be different.
interest rates are

different for the
same principal?

56

Chapter 3 Consumer Mathematics: Savings
and Investments, Credit and Debt

Example 5 QU I Z

0UV 9DQPDWK\ GHSRVLWV D VXP RI 50 LQ D EDQN :KDW LV WKH DPRXQW Why is a fixed deposit
account given a higher
RI 0UV 9DQPDWK\
V VDYLQJV DIWHU \HDU LI WKH LQWHUHVW UDWH JLYHQ LV interest rate than a
savings account?
D SHU DQQXP E SHU DQQXP

:KDW LV WKH GLIIHUHQFH EHWZHHQ WKH DPRXQWV RI LQWHUHVW HDUQHG E\
0UV 9DQPDWK\ LQ WKH DERYH VLWXDWLRQV"

Solution:

Total Interest Savings period Total interest Total savings
(years) after 1 year
savings rate 5 05 0 î ² ± î
5 05 0 î ² ± î 50 50
50 50 CHAPTER 3

50 50 50
50

7KH GLIIHUHQFH EHWZHHQ WKH WRWDO LQWHUHVWV UHFHLYHG LV 50 ± 50 TIPS The
50 higher the
The higher return
%DVHG RQ ([DPSOH IRU WKH VDPH SULQFLSDO ZKHQ WKH LQWHUHVW UDWHV the interest
LQFUHDVH WKH WRWDO VDYLQJV DW WKH HQG RI WKH \HDU DOVR LQFUHDVHV rate The
lower the
Compound interest The lower return
the interest
rate

&RPSRXQG LQWHUHVW LV LQWHUHVW WKDW LV FDOFXODWHG EDVHG RQ WKH RULJLQDO SULQFLSDO DQG DOVR WKH
DFFXPXODWHG LQWHUHVW IURP WKH SUHYLRXV SHULRG RI VDYLQJV
&RPSRXQG LQWHUHVW LV GLIIHUHQW IURP VLPSOH LQWHUHVW LQ WHUPV RI WKH DPRXQW RI VDYLQJV WR EH
XVHG IRU LQWHUHVW FDOFXODWLRQ
)RU FRPSRXQG LQWHUHVW WKH IUHTXHQF\ RI FRPSRXQGLQJ RQ WKH SULQFLSDO FDQ EH GLIIHUHQW )RU
H[DPSOH FRPSRXQGHG RQFH D \HDU RU RQFH HYHU\ PRQWKV DQG VR RQ
5HIHUULQJ WR ([DPSOH D LI (QFLN 1D]ULQ LV JLYHQ FRPSRXQG LQWHUHVW ZKLFK LV FRPSRXQGHG
RQFH D \HDU ZKDW LV KLV VDYLQJV DW WKH HQG RI WKH VHFRQG \HDU"

,Q WKH ¿UVW \HDU WKH DPRXQW RI LQWHUHVW UHFHLYHG LV
5 0 î ² ± 50

7KXV WKH DPRXQW RI VDYLQJV DW WKH HQG RI WKH ¿UVW \HDU LV 50 Scan the QR Code or
visit http://bukutekskssm.
)RU WKH VHFRQG \HDU WKH DPRXQW RI VDYLQJV XVHG IRU LQWHUHVW my/Mathematics/F3/
FDOFXODWLRQ LV 50 SULQFLSDO ¿UVW \HDU LQWHUHVW Chapter3Compund.pdf for
7KXV LQWHUHVW DW WKH HQG RI WKH VHFRQG \HDU LV more information about
compound interest.
50 î ² ± 50

7KHUHIRUH WKH DPRXQW RI (QFLN 1D]ULQ
V VDYLQJV DW WKH HQG RI WKH VHFRQG
\HDU LV
50 50 50

57

,Q JHQHUDO WKH IRUPXOD IRU FDOFXODWLQJ FRPSRXQG LQWHUHVW LV

QW
MV P ²QU Q Q XPEHU RI SHULRGV WKH LQWHUHVW LV
FRPSRXQGHG SHU \HDU

MV PDWXUHG YDOXH W WHUP LQ \HDUV

P SULQFLSDO

U \HDUO\ LQWHUHVW UDWH

CHAPTER 3 %DVHG RQ (QFLN 1D]ULQ
V H[DPSOH LW ZDV IRXQG WKDW
P U Q W

7KXV WKH DPRXQW RI (QFLN 1D]ULQ
V VDYLQJV DW WKH HQG RI WKH VHFRQG \HDU LV

MV P ²QU QW
5 0 ² ²



50
50

Example 6

$W WKH EHJLQQLQJ RI D \HDU 0UV /LHZ )RRQJ VDYHV 50 LQ KHU VDYLQJV DFFRXQW ZLWK D UDWH RI
SHU DQQXP DQG FRPSRXQGHG HYHU\ PRQWKV :KDW LV 0UV /LHZ )RRQJ¶V WRWDO VDYLQJV DW WKH HQG
RI WKH WKLUG \HDU"

Solution: QU I Z

P U ² ± Q W What is the impact on
the total cumulative
M V P QW returns, if the
—QU compounding rate
increases in a year?

² ²




50

Example 7

$ EDQN RIIHUV D LQWHUHVW UDWH SHU DQQXP IRU VDYLQJV LQ D ¿[HG GHSRVLW BULLETIN
DFFRXQW ,I 3XDQ :DKLGDK VDYHV 50 DW WKH EHJLQQLQJ RI WKH
\HDU KRZ PXFK PRQH\ LV LQ KHU ¿[HG GHSRVLW DFFRXQW DW WKH HQG RI WKH ,QÀDWLRQ DOVR DIIHFWV
\HDU LI WKH LQWHUHVW LV FRPSRXQGHG the value of the
D RQFH HYHU\ PRQWKV" E RQFH D PRQWK" FXUUHQF\ ,I WKH LQÀDWLRQ
rate increases, the
Solution: purchasing power of
P U ² ± W RM1 will reduce.

M V P —QU QW

58

Chapter 3 Consumer Mathematics: Savings
and Investments, Credit and Debt

(a) n (b) n
Thus, Thus,

( )MV ²0.0²5 ( ) M V ²0 .0² 5
4
50 50

From Example 7, it was found that when the compounding frequency increases, the future value of
savings also increases.

Example 8

0U &KDUOHV GHSRVLWHG 50 LQ D ¿[HG GHSRVLW DFFRXQW DW %DQN %HUMD\D IRU \HDUV ZLWK DQ CHAPTER 3
interest rate of 6% per annum. What is the difference between the amount of interest Mr Charles
earned if he was given compound interest (compounded once every 4 months) compared to simple
interest?

Solution:

Simple interest Compound interest

Interest, I Prt ( )MV P —nr nt
( ) ²0.0²6
5500 î ² 6 ± î


50

Total accumulated interest
50 ± 50 50

Thus, the difference in the amount between simple interest and compound interest (compounded
once every 4 months) is

50 ± 50 50

%DVHG RQ ([DPSOH LW LV FOHDU WKDW VDYLQJV ZLWK FRPSRXQG LQWHUHVW JLYH KLJKHU UHWXUQV WKDQ VDYLQJV
with simple interest.

Islamic Banking

0DOD\VLD SUDFWLVHV D GXDO EDQNLQJ V\VWHP 7KH\ DUH FRQYHQWLRQDO EDQNLQJ V\VWHP DQG ,VODPLF
EDQNLQJ V\VWHP

Islamic Banking System

%DVHG RQ 5LVN LV %DVHG RQ WKH Does not specify rate of return
Islamic law managed SULQFLSOH RI MXVWLFH on early stage of savings.
according
(syarak). KDODO DQG SUR¿W 7KH UHDO UDWH RI UHWXUQ LV NQRZQ
to the sharing and without upon maturity.
agreement.
usury.

59

Example 9 BULLETIN

(QFLN 2VPDQ VDYHG 50 LQ D VDYLQJV DFFRXQW LQ DQ ,VODPLF EDQN The principle of wadiah
DFFRUGLQJ WR WKH SULQFLSOH RI ZDGLDK IRU \HDU %\ WKH HQG RI WKH \HDU Property or cash received
KH UHFHLYHG D VXP RI 50 DV D UHWXUQ IURP WKH VDYLQJV $Q with the agreement of the
DGGLWLRQDO 50 LV D KLEDK JLIW IURP WKH EDQN &DOFXODWH WKH customer to be deposited
SHUFHQWDJH RI KLEDK REWDLQHG E\ (QFLN 2VPDQ in the bank. The bank
is responsible for the
Solution: security of the property or
the money.

3 HUFHQWDJH RI KLEDK ²5²0² ² ± î LV RQO\ D UHIHUHQFH IRU
50 VDYLQJV DQG LV QRW ¿[HG

CHAPTER 3 MIND TEST 3.1b

1. 3XDQ 1DWKDQLD GHSRVLWHG 50 LQWR KHU VDYLQJV DFFRXQW WKDW JLYHV DQ LQWHUHVW UDWH RI
SHU DQQXP DQG FRPSRXQGHG TXDUWHUO\ +RZ PXFK LV 3XDQ 1DWKDQLD
V VDYLQJV DW WKH HQG RI WKH
¿IWK \HDU"

2. 0U &KRQJ GHSRVLWHG 50 LQWR KLV VDYLQJV DFFRXQW WKDW JLYHV DQ LQWHUHVW UDWH RI
SHU DQQXP DQG FRPSRXQGHG RQFH HYHU\ KDOI \HDU +RZ PXFK LV 0U &KRQJ
V VDYLQJV DW WKH HQG
RI WKH WKLUG \HDU"

3. 3XDQ $PLQDK GHSRVLWHG 50 LQWR KHU VDYLQJV DFFRXQW WKDW JLYHV DQ LQWHUHVW UDWH RI
SHU DQQXP DQG FRPSRXQGHG PRQWKO\ +RZ PXFK LV 3XDQ $PLQDK
V VDYLQJV DW WKH HQG RI WKH
VHFRQG \HDU"

What do you understand by return on investment (ROI)? LEARNING
STANDARD

5HWXUQ RQ LQYHVWPHQW UHIHUV WR WKH UHWXUQ YDOXH RI HDFK ULQJJLW LQYHVWHG Perform calculations
E\ WKH LQYHVWRU ,Q RWKHU ZRUGV UHWXUQ RQ LQYHVWPHQW LV DOVR D UDWLR RI involving the value of
SUR¿W RU ORVV GHULYHG IURP DQ LQYHVWPHQW return on investments, and
hence explain the factors
,Q JHQHUDO LQYHVWRUV SUHIHU WR DVVHVV WKH UHWXUQ RQ LQYHVWPHQW LQ that affect the return
SHUFHQWDJH 5HWXUQ RQ LQYHVWPHQW ZLOO UHÀHFW WKH SUR¿W RU ORVV DFKLHYHG on investments and its
E\ LQGLYLGXDO LQYHVWRUV LQ LQYHVWPHQW impacts.

$Q LQYHVWPHQW LV FRQVLGHUHG SUR¿WDEOH ZLVH LQYHVWPHQW ZKHQ WKH BULLETIN
SUHVHQW YDOXH RI WKH LQYHVWPHQW DQG WKH DPRXQW RI UHWXUQ UHFHLYHG LV
PRUH WKDQ WKH YDOXH RI WKH RULJLQDO LQYHVWPHQW School cooperatives
declare dividends at the
6LPLODUO\ ZKHQ WKH DPRXQW RI UHWXUQ DQG WKH SUHVHQW YDOXH RI HQG RI HDFK ¿QDQFLDO
WKH UHWXUQ LV OHVV WKDQ WKH YDOXH RI WKH RULJLQDO LQYHVWPHQW WKHQ WKH year. The declared
LQYHVWPHQW LV XQSUR¿WDEOH dividend determines
the return value of the
7KH IRUPXOD IRU FDOFXODWLQJ UHWXUQ RQ LQYHVWPHQW LV shares purchased by
each member of the
cooperative.

5HWX UQ RQ LQYHVWPHQW ²²²²7R²WDO² UH²WX±UQ² ²²± î
9DOXH RI LQLWLDO LQYHVWPHQW

60

Chapter 3 Consumer Mathematics: Savings CHAPTER 3
and Investments, Credit and Debt

,Q DGGLWLRQ LQYHVWRUV DOVR KDYH DQ H[SHFWHG UDWH RI UHWXUQ IURP DQ LQYHVWPHQW )RU H[DPSOH DQ
LQYHVWRU H[SHFWV D UDWH RI UHWXUQ RI RQ WKHLU LQYHVWPHQW +RZHYHU WKH UHDO UDWH RI UHWXUQ WR EH
UHFHLYHG PD\ QRW EH DV H[SHFWHG
,QYHVWPHQW LQVWUXPHQWV FRQVLVW RI WKH XQLW WUXVW VKDUHV UHDO HVWDWH DQG VR RQ (DFK RI WKHVH
LQYHVWPHQW LQVWUXPHQWV ZLOO EULQJ UHWXUQV

Unit Trust

8QLW WUXVW LV D JRRG LQYHVWPHQW DOWHUQDWLYH IRU PHGLXP WHUP LQYHVWPHQW WR \HDUV DQG ORQJ
WHUP RYHU \HDUV
,QYHVWPHQWV LQ XQLW WUXVWV DUH ORZ ULVN DV WKH\ DUH PDQDJHG E\ SURIHVVLRQDO IXQG PDQDJHUV
UHJXODWHG E\ WKH VHFXULWLHV FRPPLVVLRQ DQG DOVR PRQLWRUHG E\ %DQN 1HJDUD 0DOD\VLD
,QYHVWPHQWV LQ XQLW WUXVWV DOORZ LQYHVWRUV WR GLYHUVLI\ WKHLU LQYHVWPHQWV ZLWK D VPDOO FDSLWDO
%HORZ LV WKH UHWXUQ IRU XQLW WUXVWV

Return for Unit Trusts

Dividends 8VXDOO\ UHFHLYHG Bonus shares DUH DGGLWLRQDO Capital gain
DW WKH HQG RI WKH ¿QDQFLDO \HDU VKDUHV WKDW DUH JLYHQ IUHH WR LQFUHDVH LQ VKDUH SULFH
ZKHQ VKDUHV DUH VROG
DQG FDOFXODWHG EDVHG RQ WKH H[LVWLQJ VKDUHKROGHUV
PRQH\ LQYHVWHG

Example 10

2Q -DQXDU\ 3XDQ 6LWL LQYHVWHG XQLWV YDOXHG DW 50 SHU XQLW LQ $PDQDK 6DKDP
%XPLSXWHUD $6% )RU WKH ¿QDQFLDO \HDU HQGLQJ 'HFHPEHU $PDQDK 6DKDP %XPLSXWHUD
SDLG D GLYLGHQG RI 2Q -DQXDU\ 3XDQ 6LWL VROG DOO WKH VKDUHV VKH RZQHG DW 50 SHU
XQLW :KDW LV WKH UHWXUQ RQ LQYHVWPHQW IRU 3XDQ 6LWL"

Solution:

Steps for calculating dividend

,QLWLDO FDSLWDO î 50
50

' LYL GHQG ² ± î XQLWV î 50

50

,QFUHDVH LQ VKDUH SULFH 50 ± 50 50

&DSLWDO JDLQ 50 î XQLWV

50

7RWDO UHWXUQ 50 50 50

5HWXUQ RQ LQYHVWPHQW ²5²0 ² ² î
50

7KH UHWXUQ RQ LQYHVWPHQW EHQH¿WV 3XDQ 6LWL DV VKH UHFHLYHV WZR W\SHV RI UHWXUQV QDPHO\ GLYLGHQG
DQG FDSLWDO JDLQ IURP DQ LQFUHDVH LQ VKDUH YDOXH IURP 50 WR 50

61

What do you understand about return on investment for real estate?

,QYHVWPHQW LQ UHDO HVWDWH LV RQH RI WKH LQYHVWPHQWV WKDW EULQJ UHWXUQV LQ WKH IRUP RI UHQW DQG FDSLWDO
JDLQV :KHQ D SURSHUW\ LV UHQWHG WKH RZQHU LQYHVWRU RI WKH SURSHUW\ ZLOO UHFHLYH UHWXUQ LQ
WKH IRUP RI UHQW ,I WKH SURSHUW\ LV VROG WKH RZQHU LQYHVWRU ZLOO UHFHLYH FDSLWDO JDLQ RU FDSLWDO
ORVV

Real Estate

CHAPTER 3Land House Commercial Lot

Returns
Returns
Returns

Rental and Rental and Rental and
capital gain capital gain capital gain

Example 11 BULLETIN

(QFLN <XVXI ERXJKW D VKRSORW DW D SULFH RI 50 RQ -DQXDU\ Stamp duty
LQ %DQJL +H SDLG RI WKH VKRSORW
V SXUFKDVH SULFH RI Tax imposed on
50 7KH VKRSORW ZDV UHQWHG IURP -DQXDU\ 2Q documents or letters
'HFHPEHU KH VROG WKH VKRSORW IRU 50 7KH ORDQ with legal, commercial
DPRXQW VWLOO RZHG WR WKH EDQN ZDV 50 0HDQZKLOH WKH DPRXQW RU ¿QDQFLDO LPSOLFDWLRQV
WKDW KDV EHHQ DPRUWLVHG WR WKH EDQN ZDV 50 2WKHU FKDUJHV under the First Schedule,
LQYROYHG LQ WKH VDOH DQG SXUFKDVH WUDQVDFWLRQV DUH DV IROORZV of Stamp Act 1949.

Legal cost 50 Legal cost
Stamp duty (during sale and purchase) 50 Payment to lawyer to
Agent’s commission 50 perform the transfer of
property for the buyer.

Commission
Fee paid by the property
seller to the agent for the
sale of real estate.

62

Chapter 3 Consumer Mathematics: Savings
and Investments, Credit and Debt

7KH WRWDO UHQW FROOHFWHG WKURXJKRXW WKH SRVVHVVLRQ RI WKH VKRSORW LV 50 &DOFXODWH WKH UHWXUQ
RQ LQYHVWPHQW REWDLQHG E\ (QFLN <XVXI

Solution:

7RWDO UHQW 50
&DSLWDO JDLQ 50 ± 50 ± 50 ± 50 ± 50
± 50 ± 50
50

7RWDO UHWXUQ 50 50
50

5 HWX UQ R Q LQYHV WPHQW ²5500² ² ² ² î CHAPTER 3




Example 12

(QFLN +XVVHLQ ERXJKW D KRXVH RQ -DQXDU\ LQ
&KHUDV DW 50 DQG FOHDUHG GRZQ SD\PHQW RI
50 +H H[SHFWV D UHWXUQ RI RYHU \HDUV

(QFLN +XVVHLQ VROG WKH KRXVH DW D SULFH RI 50 DIWHU KDYLQJ RZQHG WKH KRXVH IRU \HDUV
7KH ORDQ DPRXQW DPRUWLVHG WR WKH EDQN ZDV 50 'XULQJ WKDW SHULRG KH PDQDJHG WR HDUQ D
UHQW RI 50 2WKHU H[SHQVHV LQFXUUHG DUH DV IROORZV

Stamp duty (during sale and purchase) 50
Agent's commission 50
Legal cost during sale and purchase 50

:KDW LV WKH UHWXUQ RQ LQYHVWPHQW IRU (QFLN +XVVHLQ IRU \HDUV" 'LG KH DFKLHYH KLV H[SHFWDWLRQ WR
JHW D UHWXUQ RI "

Solution:

5HWXUQ RQ LQYHVWPHQW

5HQW &DSLWDO JDLQ

50 50 ± 50 ± 50 ± 50 ± 50 ± 50

50 50

50

5 HWX UQ RQ LQYHVWPHQW ±55±00±± ± ± ± ± ± ± =


(QFLN +XVVHLQ PDQDJHG WR REWDLQ D UDWH RI UHWXUQ
RI 7KLV UDWH H[FHHGV WKH H[SHFWHG UDWH RI
UHWXUQ RI

63

,Q UHDO HVWDWH LQYHVWPHQW WKHUH DUH IDFWRUV WKDW DIIHFW WKH UHWXUQ RQ LQYHVWPHQW 7KH IDFWRUV WKDW DIIHFW
UHWXUQ RQ LQYHVWPHQW DUH DV IROORZV

CHAPTER 3 Location

The economic situation ‡ 7KH SURSHUWLHV WKDW DUH
VWUDWHJLFDOO\ ORFDWHG QHDU D
‡ 7KH FRXQWU\
V JRRG HFRQRPLF YDVWO\ GHYHORSHG FLW\ FHQWUH
VLWXDWLRQ ZLOO LQFUHDVH UHDO KDYH KLJKHU SULFHV FRPSDUHG
HVWDWH SULFHV EHFDXVH WKH WR SURSHUWLHV LQ UXUDO DUHDV
GHPDQG IRU UHDO HVWDWH ZLOO
LQFUHDVH

Factors that
affect the return
on investment on

real estate

Political situation

‡ $ VWDEOH SROLWLFDO VLWXDWLRQ ZLOO LQFUHDVH GHPDQG IRU UHDO HVWDWH
‡ 7KLV ZLOO LQGLUHFWO\ LQFUHDVH UHDO HVWDWH SULFHV
‡ 3ROLWLFDO LQVWDELOLW\ ZLOO UHGXFH GHPDQG IRU UHDO HVWDWH DQG

LQGLUHFWO\ FDXVH WKH IDOO RI UHDO HVWDWH SULFHV

64

Chapter 3 Consumer Mathematics: Savings
and Investments, Credit and Debt

MIND TEST 3.1c

1. :KDW LV WKH PHDQLQJ RI UHWXUQ RQ LQYHVWPHQW RU 52,"
2.

+ 2Q -DQXDU\ 0U 0RVHV ERXJKW D KRPHVWD\ DW D SULFH RI 50 CHAPTER 3
+ 7KH GDLO\ UHQWDO UDWH LV 50
+ 2Q DYHUDJH WKH KRPHVWD\ ZLOO EH RFFXSLHG IRU GD\V LQ D PRQWK
D &DOFXODWH WKH PRQWKO\ UHQWDOV
E & DOFXODWH WKH UHWXUQ LI WKH KRPHVWD\ LV VROG IRU 50 DW WKH HQG RI WKH \HDU

3. 2Q -DQXDU\ 5DKLP LQYHVWHG LQ XQLWV RI $PDQDK 6DKDP %XPLSXWHUD $6%
VKDUHV YDOXHG DW 50 SHU XQLW )RU WKH ¿QDQFLDO \HDU HQGLQJ 'HFHPEHU $6%
SDLG D GLYLGHQG RI

+RZ PXFK LV WKH GLYLGHQG UHFHLYHG E\ 5DKLP IRU WKDW \HDU"

What factors should be considered before making LEARNING
an investment? STANDARD

7KUHH IDFWRUV WKDW VKRXOG EH WDNHQ LQWR DFFRXQW E\ DQ LQYHVWRU Compare and contrast
SULRU WR PDNLQJ DQ LQYHVWPHQW DUH DV IROORZV potential risks, return
and liquidity of various
types of savings and
investments.

Potential investment risk 7KH XQFHUWDLQW\ WKDW ORVVHV PD\ EH LQFXUUHG IURP WKH
LQYHVWPHQWV PDGH

The level of return 3UR¿W HQMR\HG E\ LQYHVWRUV IURP LQYHVWPHQWV

Liquidity aspect 5HODWLQJ WR KRZ VRRQ WKH LQYHVWPHQW RU VDYLQJV FRXOG EH
FDVKHG RXW

65

7KH WDEOH EHORZ VKRZV WKH FRPSDULVRQ RI YDULRXV W\SHV RI VDYLQJV DQG TIPS
LQYHVWPHQWV E\ LQGLYLGXDOV LQ WHUPV RI ULVN OHYHOV UHWXUQ OHYHOV DQG
OLTXLGLW\ OHYHOV One way to reduce
investment risk is
Type of Risk Return Liquidity to diversify one's
investment level level level investment portfolio.
This helps to offset risks
6DYLQJ 5LVN IUHH /RZ +LJK from each investment
and thus further
)L[HG GHSRVLWV 5LVN IUHH /RZ +LJK reduce the risk in the
investment portfolio.
&RPSDQ\ VKDUHV +LJK +LJK 0RGHUDWH
BULLETIN
CHAPTER 3 5HDO HVWDWH 0RGHUDWH +LJK /RZ
Portfolio
8QLW WUXVW /RZ 0RGHUDWH +LJK Various levels of
investment type.

MIND TEST 3.1d

1. ([SODLQ WKH UHODWLRQVKLS EHWZHHQ ULVN DQG UHWXUQ RQ LQYHVWPHQW
2. 7KH SRWHQWLDO ULVN RI VDYLQJ LQ D EDQN LV ]HUR DV FRPSDUHG WR LQYHVWPHQW ([SODLQ WKLV

VWDWHPHQW
3. :K\ GR XQLW WUXVWV KDYH D KLJK OLTXLGLW\ OHYHO"
4. 5HDO HVWDWH KDV D PRGHUDWH SRWHQWLDO ULVN ([SODLQ
5.



‡ 50 SHU GD\
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RI VHWWLQJ XS WKLV KRPHVWD\ LV 50
D :KDW W\SH RI LQYHVWPHQW ZDV PDGH E\ (QFLN 2VPDQ"
E 6WDWH WKH SRWHQWLDO ULVNV UHWXUQ DQG OLTXLGLW\ RI WKH LQYHVWPHQW PDGH E\ (QFLN 2VPDQ
F ,Q \RXU RSLQLRQ ZDV WKH LQYHVWPHQW PDGH E\ (QFLN 2VPDQ D ZLVH PRYH" -XVWLI\


66

Chapter 3 Consumer Mathematics: Savings
and Investments, Credit and Debt

What do you understand about cost averaging strategy? LEARNING
STANDARD
&RVW DYHUDJLQJ VWUDWHJ\ LV D WHFKQLTXH FRPPRQO\ SUDFWLVHG E\
LQYHVWRUV ZKR LQYHVW LQ VKDUHV ZLWK D ¿[HG DPRXQW IRU D FHUWDLQ SHULRG Calculate the average
VXFK DV PRQWKO\ TXDUWHUO\ RU \HDUO\ UHJDUGOHVV RI WKH VWRFN PDUNHW cost per share for the
FRQGLWLRQV investment of shares using
the ringgit cost averaging
&RVW DYHUDJLQJ VWUDWHJLHV FDQ KHOS LQYHVWRUV WR EX\ VKDUHV ZLWK D strategy and explain the
ORZHU DYHUDJH FRVW DQG WKH WRWDO QXPEHU RI VKDUHV RZQHG ZLOO EH KLJKHU EHQH¿WV RI WKH VWUDWHJ\
ZLWKLQ WKH VDPH LQYHVWPHQW SHULRG DV RSSRVHG WR EX\LQJ WKHP LQ D
OXPS VXP RU ZLWK D VLQJOH SXUFKDVH

)RU H[DPSOH 3XDQ +DVQL]D KDV 50 DQG EX\V VKDUHV LQ D OXPS VXP IURP 6HPSXUQD CHAPTER 3
&RPSDQ\ DW 50 SHU VKDUH XQLW +HQFH 3XDQ +DVQL]D ZLOO RQO\ KDYH XQLWV RI VKDUHV
XQLWV RI VKDUHV î 50 50 +RZHYHU WKH VLWXDWLRQ ZLOO EH GLIIHUHQW LI 3XDQ
+DVQL]D GHFLGHV WR EX\ VKDUHV EDVHG RQ FRVW DYHUDJLQJ VWUDWHJ\

7KH WDEOH EHORZ VKRZV 3XDQ +DVQL]D
V LQYHVWPHQW FKDUW LQ D \HDU EDVHG RQ FRVW DYHUDJLQJ VWUDWHJ\
IRU EX\LQJ VKDUHV RQ D PRQWKO\ EDVLV

0RQWK Investment 8QLW SULFH 50 Number = —In—ve—sUtmn—iet–np—trai—cmeo—u—nt
DPRXQW 50 of unit
-DQXDU\
)HEUXDU\
0DUFK

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0D\
-XQH
-XO\
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6HSWHPEHU
2FWREHU
1RYHPEHU
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QXPEHU RI XQLWV RZQHG

:LWK WKH FRVW DYHUDJLQJ VWUDWHJ\ JLYHQ DERYH 3XDQ +DVQL]D HDUQHG XQLWV E\ LQYHVWLQJ
50

Cost averaging strategy TIPS

Average Cost = Investment amount When you use cost
Number of share averaging strategy to
units owned invest in shares, the
cost of the shares you
Average cost = R—M—617—2401—0–0 = RM1.78 have bought will not
per share unit be the highest price
nor will it be the lowest
price.

67

Example 13
Below are two investors who plan to invest in shares using different strategies.

I would like to invest I want to invest a lump
RM20 000 to buy shares sum of RM20 000 to buy
and would accumulate the Pelita Company shares
shares in the designated
months by spending the at RM2.00 a unit.

same amount
of money.

CHAPTER 3 Mrs Esther Wong Puan Linda

Shares acquired by Mrs Esther Wong in the designated months:

Month January March May August December
2.10 2.00
Shares price per 2.00 1.80 1.60
unit (RM)

(a) Calculate the average cost per unit and the number of shares owned by Puan Linda and Mrs
Esther Wong.

(b) Who is a wise investor? Justify your answer.

Solution:

(a) Puan Linda
Total shares = —R—M2—0—00—0 = 10 000 share units
RM2.00
Average cost per share = ——R—M—20—00–0––––
10 000 share units
= RM2.00

Mrs Esther Wong Total investment Price per unit ( RM) Number of share unit

Month 4 000 2.00 2 000 units
January 4 000 1.80 2 222 units
March 4 000 1.60 2 500 units
4 000 2.10 1 904 units
May 4 000 2.00 2 000 units
August 20 000 10 626 share units
December

Total shares = 10 626 share units
Average cost per share = 1—R0M—622—60 u—0n0i—0ts

= RM1.88

(b) Mrs Esther Wong is a wise investor for practising the cost averaging strategy that helped her to
accumulate more shares with the same amount of money.

68

Advantage Chapter 3 Consumer Mathematics: Savings
of the cost and Investments, Credit and Debt
averaging
strategy for Able to take advantage of the unit price changes
investors ‡ :KHQ WKH VWRFN SULFH LV ORZ PRUH XQLWV RI VKDUHV FDQ EH SXUFKDVHG
‡ ,QGLUHFWO\ KHOSV LQYHVWRUV WR KDYH PRUH VKDUHV LQ WKH ORQJ WHUP
The average cost of a share unit bought by an investor can be reduced in CHAPTER 3
the long term.

1RW LQÀXHQFHG E\ HPRWLRQV
‡ ,QYHVW FRQVLVWHQWO\ RQ D SHULRGLF EDVLV WKH VDPH DPRXQW RI PRQH\

ZLWKRXW EHLQJ LQÀXHQFHG E\ HPRWLRQV FDXVHG E\ VKDUH SULFH ÀXFWXDWLRQ

Lower the risk of loss
‡ 7RWDO LQYHVWPHQW LV FDUULHG RXW RQ D UHJXODU DQG FRQVLVWHQW PDQQHU

which helps investors to purchase based on current situation and avoid
losses associated with lump sum investment.

MIND TEST 3.1e

1. What do you understand about the cost averaging strategy in purchasing shares?
2. Below are two investors who invested using different strategies.

Investor 1 Mr Derick invested a lump sum of RM24 000 to purchase
Wawasan shares at RM2.00 per share unit.

Investor 2 Encik Sulaiman has RM24 000 and invested consistently on a
periodic basis RM2 000 each month to purchase Wawasan shares.

Month Jan Feb March April May June July Aug Sept Oct Nov Dec

Share price 1.60 2.10 1.50 2.20 2.00 2.00 1.60 1.70 1.80
per unit 2.00 1.80 1.70
(RM)

The table above shows the share price bought by Encik Sulaiman on a monthly basis.
(a) Who is a wise investor? Justify your answer.
(b) Calculate the average cost per share unit and the number of shares owned by Encik

Sulaiman.
(c) State the advantages of using cost averaging strategy in purchasing shares.

69

How do you solve problems involving savings and LEARNING
investments? STANDARD

Solve problems involving
savings and investments.

Example 14

(QFLN =DLGL 0U /HRQJ DQG 0U 1DYLQ KDG UHWLUHG IURP WKHLU MREV DQG HDFK UHFHLYHG 50 DV
gratuity from their company. They use different investment methods to invest.

Who is a wise investor?

CHAPTER 3 Apartment (QFLN =DLGL ERXJKW D PHGLXP FRVW DSDUWPHQW LQ .DMDQJ
worth RM150 000 and receives a rental of RM800 per
Encik Zaidi PRQWK 7KH EDODQFH LV NHSW LQ D ¿[HG GHSRVLW DFFRXQW
with an interest rate of 4% per annum.

Mr Leong invested RM400 000 in Manis Company shares
at RM2.00 per unit. The company declared a dividend of
8% for that year.

Mr Leong

0U 1DYLQ GHSRVLWHG 50 LQWR D VDYLQJV DFFRXQW
with an interest rate of 1% per annum. The balance
50 LV NHSW LQ D ¿[HG GHSRVLW DFFRXQW DW
interest rate per annum.

Mr Navin

70

Chapter 3 Consumer Mathematics: Savings
and Investments, Credit and Debt

Solution:
Encik Zaidi

Level of risk 7KH OHYHO RI ULVN IRU SURSHUW\ DSDUWPHQWV DQG ¿[HG GHSRVLWV LV ORZ

Return on Receives a return on investment in the form of rent and interest.
investment
Rental Savings interest Return on investment (ROI)

RM800 × 12 = RM9 600 —4— × RM250 000 ROI = —RM—1–9––6–0–0– × 100%
100 RM400 000

= RM10 000 = 4.9%

Liquidity Savings are easily converted to cash while property takes time to sell.

Mr Leong CHAPTER 3

Level of risk The level of risk in buying shares is high.

Return on Receives dividends and bonuses depending on the performance of the company
investment LQYHVWHG LQ ,I KH VHOOV KLV VKDUHV LW LV XQFHUWDLQ WKDW KH ZLOO EH DEOH WR VHOO WKH

shares at a higher price compared to the purchase price. This depends on the

economic situation and performance of the company stock at that period.

Dividend = 400 000 × —8– ROI = —RM—3–2––0–0–0– × 100%
100 RM400 000

= RM32 000 = 8%

Liquidity Moderate.

Mr Navin

Level of risk 7KH OHYHO RI ULVN IRU ERWK VDYLQJV DQG ¿[HG DFFRXQW DUH ORZ

Return on Receives a return on investment in the form of interest only.
investment Savings interest Fixed deposit interest Return on investment (ROI)

RM200 000 × —1– —1040– × RM200 000 ROI = —R—M–1–0–0–0–0– × 100%
100 RM400 000

= RM2 000 = RM8 000 = 2.5%

Liquidity Savings are easily turned into cash.

‡ 0U /HRQJ LV D ZLVH LQYHVWRU EHFDXVH KLV UHWXUQ RQ LQYHVWPHQW YDOXH LV KLJKHU WKDQ (QFLN =DLGL
DQG 0U 1DYLQ

‡ ,Q WKLV H[DPSOH (QFLN =DLGL 0U /HRQJ DQG 0U 1DYLQ HDFK XVHV WKH VDPH DPRXQW RI FDSLWDO
which is RM400 000. The effectiveness of their investments can be compared based on their
returns for the year respectively.

71

CHAPTER 3 MIND TEST 3.1f
1. The following are two investors who invested their gratuity.

0U 5DVDPDQLH UHFHLYHG 50 DV JUDWXLW\ IURP KLV FRPSDQ\ +H ERXJKW D GRXEOH
VWRUH\ VKRS LQ %DQJL 6HODQJRU DQG UHFHLYHV D PRQWKO\ UHQWDO RI 50

Monthly rental
RM3 500

(QFLN 1LN ,]ZDQ UHFHLYHG 50 DV JUDWXLW\ IURP KLV FRPSDQ\ +H VDYHV 50
LQ D ¿[HG GHSRVLW DFFRXQW DW D FRPPHUFLDO EDQN ZLWK DQ LQWHUHVW UDWH RI SHU DQQXP +H DOVR
bought share units worth RM150 000.
$W WKH VDPH WLPH (QFLN 1LN ,]ZDQ ERXJKW VKDUHV LQ &HSDW 0DMX &RPSDQ\ ZRUWK 50
The balance of the gratuity is used to buy a medium-cost apartment in Ampang and he
receives a monthly rental of RM1 200.

Monthly rental
RM1 200

D ([SODLQ WKH LQYHVWPHQW ULVN OHYHO RI ERWK LQGLYLGXDOV
(b) Who is a wise investor? Justify your answer.
(c) What factors need to be considered before investing in real estate?

2. ,Q 0U :RQJ ERXJKW D KRXVH DW 50 +H SDLG GRZQ SD\PHQW DQG WKH EDODQFH
ZDV SDLG WKURXJK D ORDQ $IWHU \HDUV 0U :RQJ GHFLGHG WR VHOO WKH KRXVH DW 50 7KH
IROORZLQJ DUH WKH H[SHQVHV LQYROYHG

Monthly instalment amount paid RM666 000
Stamp duty RM15 000
Agent’s commission RM8 000
Other expenses RM18 000

Calculate the return on investment for Mr Wong.

72

Chapter 3 Consumer Mathematics: Savings
and Investments, Credit and Debt

3.2 Credit and Debt Management

What do you understand about credit and debt? LEARNING
STANDARD
7KH ZRUG FUHGLW KDV VHYHUDO PHDQLQJV ,Q WKH ¿QDQFLDO ZRUOG credit
means a contractual agreement between the supplier (for instance a Explain the meaning
EDQN RU ¿QDQFLDO LQVWLWXWLRQ DQG WKH FRQVXPHU 7KH FRQVXPHU FDQ of credit and debt, and
borrow money from the supplier for any use or purchase and agree hence describe the wise
WR UHSD\ ZLWKLQ D FHUWDLQ SHULRG ,Q VKRUW FUHGLW LV D SRVWSRQHPHQW RI management of credit
payment facility provided by the supplier to the consumer. and debt.

)RU H[DPSOH EDQNV RIIHU FUHGLW IDFLOLWLHV WR CHAPTER 3
FXVWRPHUV LQ WKH IRUP RI FUHGLW FDUGV ,I WKH FXVWRPHU RU
FUHGLW FDUG RZQHU XVHV WKH FUHGLW FDUG LQ D WUDQVDFWLRQ WKH
EDQN ZLOO SD\ WKH VHOOHU ¿UVW DQG WKH FXVWRPHU ZLOO SD\

back the bank within a certain period of time.

&UHGLW FDQ DOVR PHDQ WKH DPRXQW RI PRQH\ WKDW FDQ EH ERUURZHG )RU H[DPSOH IRU FUHGLW FDUG
LI WKH FUHGLW FDUG OLPLW LV 50 WKHQ WKH FDUG RZQHU KDV WKH DELOLW\ WR EX\ JRRGV RU PDNH
transactions up to RM10 000 with the card.

Debt XVXDOO\ PHDQV DQ DPRXQW WKDW KDV EHHQ ERUURZHG EXW KDV QRW EHHQ VHWWOHG ,I D WUDQVDFWLRQ
LV PDGH XVLQJ D FUHGLW FDUG WKH FUHGLW ZLOO EH FRQYHUWHG LQWR GHEW

Personal budget is the estimated income and
H[SHQGLWXUH RI DQ LQGLYLGXDO IRU D JLYHQ SHULRG 7KH SUDFWLFH
of making personal budget is strongly encouraged so that
an individual can

(a) plan spending prudently

(b) avoid overspending

(c) save

How do you manage credit and debt wisely?

‡ &UHGLW FDUG XVHUV QHHG WR VHWWOH WKH GHEW SD\PHQW ZLWKLQ WKH SHULRG VWLSXODWHG E\ WKH EDQN WR
HQMR\ LQWHUHVW IUHH SHULRG

‡ 3D\ WKH RXWVWDQGLQJ EDODQFH OLVWHG RQ WKH FUHGLW FDUG VWDWHPHQW
‡ 7KH PLQLPXP DPRXQW SDLG E\ WKH FUHGLW FDUG KROGHU SURYLGHV RSSRUWXQLW\ IRU WKH EDQN WR

charge interest on the balance and may also incur late payment charges.
‡ 3D\ ZLWKLQ WKH FDVK GLVFRXQW SHULRG IRU SD\PHQW RI GHEWV

73

CHAPTER 3 Example 15

(QFLN 6\HG ERXJKW DQ DLU FRQGLWLRQHU DW 50 RQ -XO\ +H ODFNHG 50 LQ FDVK EXW
KDV D %DQN &HPHUODQJ FUHGLW FDUG +H ZDV DZDUH WKDW WKH VKRUWDJH RI FDVK FRXOG EH SDLG DW WKH HQG
of the month when he received his salary.
(a) Which credit facility can be used by Encik Syed to overcome the shortage of money?
E 6WDWH WKH DGYDQWDJHV DQG GLVDGYDQWDJHV RI WKH SD\PHQW PHWKRG \RX VSHFL¿HG LQ DQVZHU D

Solution:

(a) Encik Syed can use the credit card facility.
(b) The use of credit cards is more convenient if Encik Syed repays his credit within the interest-

IUHH SHULRG WR DYRLG DQ\ H[WUD FKDUJHV

Brainstorming 2 In groups

Aim: The impact of using credit card in buying goods online.

Steps:
1. *HW LQWR JURXSV RI IRXU RU ¿YH
2. Surf any website related to the topics of discussion for more information.
3. The information collected should be presented using an appropriate thinking map to the

class.
4. The best thinking map will be displayed in the mathematics corner.

Discussion:
What is the impact of purchasing goods online?

)URP %UDLQVWRUPLQJ LW LV IRXQG WKDW SXUFKDVLQJ JRRGV RQOLQH FDQ FDXVH FRQVXPHUV WR VSHQG
H[WUDYDJDQWO\ DQG JHW LQWR GHEW 7KXV EH SUXGHQW ZKHQ EX\LQJ JRRGV RQOLQH

74

Chapter 3 Consumer Mathematics: Savings
and Investments, Credit and Debt

MIND TEST 3.2a

1. What does a personal loan mean? NICOL REFRIGERATOR
2. Many people are bankrupt due to credit cards
RM3 200

HEBAT ELECTRICAL SHOP

What are the ways to overcome the situation above?

3. 3XDQ =XUDLGDK ZDQWV WR EX\ D UHIULJHUDWRU DW +HEDW (OHFWULFDO 6KRS EXW VKH
ODFNV 50 LQ FDVK +HEDW (OHFWULFDO 6KRS SURYLGHV LQVWDQW ORDQV IRU
purchases with an interest rate of 4% per annum. Puan Zuraidah also has a
credit card. Which credit facility should be used by Puan Zuraidah and state
its advantages?

What do you understand about the advantages and LEARNING CHAPTER 3
disadvantages of credit cards? STANDARD

The use of credit cards is increasingly common today. As a consumer Investigate and describe
it is important for us to realise and understand the advantages and the advantages and
disadvantages of using credit cards. disadvantages of credit card
and ways to use it wisely.

Advantages of credit card Disadvantages of credit card

‡ &UHGLW FDUGKROGHUV FDQ HQMR\ D UHZDUG ‡ ,QFXU FKDUJHV VXFK DV DQQXDO IHHV ¿QDQFH
system in the form of cash rebate or point FKDUJHV LQWHUHVW FDVK DGYDQFH LQWHUHVW
redemption. charges and late payment charges.

‡ 'RHV QRW UHTXLUH XV WR FDUU\ D ORW RI FDVK ‡ 2YHUVSHQGLQJ
‡ (DV\ DQG HI¿FLHQW SD\PHQW PHWKRG ‡ 6RPH VWRUHV GR QRW DFFHSW FUHGLW SD\PHQW
‡ &RQYHQLHQFH RI EX\LQJ JRRGV DQG VHUYLFHV

online.

+RZHYHU QRW DOO LQGLYLGXDOV DUH HOLJLEOH IRU D FUHGLW FDUG 7KHUH DUH VHYHUDO FRQGLWLRQV WKDW DQ
applicant must adhere to.

‡ \HDUV ROG DQG DERYH
‡ 0LQLPXP LQFRPH RI 50 SHU DQQXP DQG PHHWV RWKHU UHTXLUHPHQWV VHW E\ WKH EDQN
‡ 5HTXLUHV VDODU\ VOLS RU VXSSRUWLQJ GRFXPHQWV

Credit card users must comply with the obligations as a credit card user when signing the credit
card application form.

‡ 'R QRW JLYH FUHGLW FDUG GHWDLOV WR VWUDQJHUV
‡ 5HPHPEHU WKH SLQ QXPEHU DQG GR QRW UHFRUG WKH SLQ QXPEHU RQ WKH EDFN RI WKH FDUG
‡ &KHFN WKH WUDQVDFWLRQV LQ WKH FUHGLW FDUG VWDWHPHQW UHFHLYHG DW WKH HQG RI WKH PRQWK

75

What do you understand about the impact of minimum LEARNING
payment and late payment on credit card use? STANDARD

7KH FUHGLW FDUGKROGHU ZLOO UHFHLYH D ¿QDQFLDO VWDWHPHQW IRU WKH FUHGLW Investigate and describe
FDUG PRQWKO\ ,Q WKH VWDWHPHQW WKHUH DUH GHWDLOV VXFK DV FUHGLW OLPLW the impact of minimum
VWDWHPHQW GDWH ODWHVW DPRXQW PLQLPXP SD\PHQW DPRXQW W\SH RI and late payments for
charges and so on. credit card usage.

CHAPTER 3 The cardholder should pay the statement balance immediately so TIPS
WKDW QR ¿QDQFLDO FKDUJHV DUH LQFXUUHG %XW EDQNV SURYLGH ÀH[LELOLW\
E\ DOORZLQJ XVHUV WR SD\ LQ D JLYHQ SHULRG NQRZQ DV WKH LQWHUHVW IUHH The credit cardholder must
period. Usually this period is 20 days from the statement date. pay the full statement
balance of the credit card
7R HQMR\ WKLV SULYLOHJH HYHU\ PRQWK WKH FDUGKROGHU PXVW SD\ WKH to enjoy a 20-day interest
total balance of credit card statement or make a minimum payment in free period from the
the interest free period. The minimum payment is usually 5% of the statement date.
WRWDO EDODQFH RI WKH FUHGLW FDUG VWDWHPHQW RU D PLQLPXP RI 50
However, if you pay only
,I WKHUH LV VWLOO D EDODQFH RI WKH ODWHVW DPRXQW XSRQ H[SLU\ RI WKH part of it, you will lose the
LQWHUHVW IUHH SHULRG D ¿QDQFH FKDUJH RU LQWHUHVW ZLOO EH LPSRVHG RQ interest-free period.
the balance based on daily rate. Most banks charge an annual interest
rate of between 15% and 18%.

,Q DGGLWLRQ LI QR SD\PHQW LV PDGH ZLWKLQ WKH LQWHUHVW IUHH SHULRG WKHQ WKH PLQLPXP ODWH SD\PHQW
charge of RM10 or 1% of total outstanding balance as of the statement date will be charged.

Example 16

Encik Ahmad received his credit card statement for January 2019 from Bank Sentosa. The statement
VKRZV WKDW (QFLN $KPDG KDV D FXUUHQW DPRXQW RXWVWDQGLQJ EDODQFH RI 50 ,W LV DVVXPHG
that Encik Ahmad did not use his credit card in February.

(a) What is the minimum payment to be paid?

E ,I KH RQO\ PDNHV D PLQLPXP SD\PHQW IRU -DQXDU\ DQG WKH VWDWHPHQW GDWH LV GD\V IURP WKH
H[SLU\ GDWH RI WKH LQWHUHVW IUHH SHULRG ZKDW LV WKH EDODQFH VKRZQ LQ KLV )HEUXDU\ VWDWHPHQW"

F , I KH PLVVHG KLV SD\PHQW IRU -DQXDU\ ZKDW LV WKH EDODQFH VKRZQ LQ KLV )HEUXDU\ VWDWHPHQW"

Solution: TIPS

(a) Current amount = RM5 200 We should use credit
cards wisely.
( )5% of the current amount = —5– × RM5 200 = RM260
100

7KLV DPRXQW H[FHHGV 50 WKXV WKH PLQLPXP SD\PHQW WR EH SDLG E\ (QFLN $KPDG LV

RM260.

E 2XWVWDQGLQJ EDODQFH 50 ± 50 50
3HULRG VXEMHFW WR ¿QDQFLDO FKDUJHV GD\V ÷ 365) year
,QWHUHVW FKDUJHG 50 î > ÷ 100) × (15 ÷ 365)] = RM36.54

&XUUHQW DPRXQW 2XWVWDQGLQJ EDODQFH LQ )HEUXDU\ 50 50 50

76

Chapter 3 Consumer Mathematics: Savings
and Investments, Credit and Debt

F 2XWVWDQGLQJ EDODQFH 50
3HULRG VXEMHFW WR ¿QDQFLDO FKDUJHV GD\V ÷ 365) year
,QWHUHVW FKDUJHG 50 × > ÷ 100) × (15 ÷ 365)] = RM38.47

( )Late payment charges = —1– î 50 50 50
100
&XUUHQW DPRXQW LQ )HEUXDU\ 50 50 50 50

How do you solve problems involving the use of credit LEARNING
cards? STANDARD

Credit cardholders should be aware of the advantages and disadvantages Solve problems involving
of credit cards. Several factors have to be taken into account before the use of credit cards.
XVLQJ FUHGLW FDUGV VXFK DV WKH EDODQFH RI WKH H[LVWLQJ OLPLW FXUUHQW FDVK
ÀRZ DQG VR RQ CHAPTER 3

Example 17

Ms Chin wants to buy a French made handbag online. She surfs the
,QWHUQHW DQG ¿QGV WZR LQWHUHVWLQJ SURPRWLRQV
(a) Company L in Singapore offers promotional price of SGD250. For SGD250

RUGHUV RXWVLGH 6LQJDSRUH 6*' VKLSSLQJ FKDUJHV DSSO\
(b) Company V in Malaysia offers promotional price of RM799. Delivery is free for all orders to

local addresses.

Ms Chin intends to make payment by credit card and she understands that the bank will charge an
DGGLWLRQDO RQ HDFK WUDQVDFWLRQ IURP DEURDG $VVXPH WKH FXUUHQW H[FKDQJH UDWH IRU 0DOD\VLDQ
ringgit is

RM1 = SGD0.34

$V D ZLVH FRQVXPHU ZKLFK RIIHU VKRXOG 0V &KLQ FKRRVH" -XVWLI\ \RXU FKRLFH

Solution:
Ms Chin should compare the actual price to be paid if buying from the two companies.

(a) Company L:
Promotional price = SGD250 × (1 ÷ 0.34) = RM735.29
Postal charges = SGD50 × (1 ÷ 0.34) = RM147.06

( )Additional charges by bank = RM735.29 × 1—010– = RM7.35

$FWXDO SULFH WR EH SDLG 50 50 50 50

(b) Company V:
Promotional price = RM799
Actual price to be paid = RM799

$OWKRXJK WKH SURPRWLRQDO SULFH RIIHUHG E\ &RPSDQ\ / LV FKHDSHU EXW WKH DFWXDO SULFH SD\DEOH LV
KLJKHU GXH WR WKH DGGLWLRQDO FKDUJHV LQFXUUHG IRU RQOLQH SXUFKDVHV IURP &RPSDQ\ / 6R 0V &KLQ
should buy from Company V to save RM90.70.

77

How do you calculate loan repayment and instalment? LEARNING
STANDARD
Each loan will be charged interest on the loan from the date the loan
was released to the borrower. There are two calculation methods for Calculate the total
ORDQ LQWHUHVW QDPHO\ ÀDW LQWHUHVW UDWH DQG LQWHUHVW RQ EDODQFH amount of loan
repayment and
Total loan balance is the amount deducted from the initial down instalment, with various
payment plus the amount of interest charged. interest rates and
different loan periods.
The monthly instalment is the total amount paid by the borrower to
the bank every month to settle the balance of the loan.

CHAPTER 3 Flat interest

,Q WKH ÀDW LQWHUHVW PHWKRG WKH LQWHUHVW UDWH ZLOO EH FDOFXODWHG RQ WKH RULJLQDO ORDQ DPRXQW RYHU WKH
WHUP RI WKH ORDQ 6R WKH DPRXQW RI LQWHUHVW FKDUJHG SHU PRQWK LV ¿[HG

Example 18

Mrs Lim bought a car worth RM80 000 on credit. She pays 10% down payment and the balance
LV SD\DEOH LQ LQVWDOPHQWV RYHU \HDUV 7KH ÀDW LQWHUHVW UDWH LPSRVHG E\ WKH EDQN LV SHU DQQXP
What is the amount of repayment and monthly instalment payable by Mrs Lim?

Solution:

Loan amount = Purchase price – down payment
= RM80 000 – RM8 000 = RM72 000

,QWHUHVW IRU \HDUV 50 î ²4± î \HDUV 50
100

7RWDO UHSD\PHQW 50 50 50 Total repayment can be calculated
with the formula A = P Prt

Monthly instalment = —R72M—m8—9on2—t8h0s– = RM1 240 per month

Example 19

(QFLN $]ODQ REWDLQHG D SHUVRQDO ORDQ RI 50 IURP %DQN 0XOLD ZLWK DQ LQWHUHVW UDWH RI
per annum. The repayment period is 7 years.

:KDW LV WKH PRQWKO\ LQVWDOPHQW WR EH SDLG E\ (QFLN $]ODQ"

Solution: 7KXV WRWDO UHSD\PHQW
A = P Prt
/RDQ P = RM10 000 ( )A 50 RM10 000 × —4– × 7
100
r = 4% 50 50

t = 7 years = RM12 800

Monthly instalment = —RM—1—2 8—00– = RM152.38
84 months

78

Chapter 3 Consumer Mathematics: Savings
and Investments, Credit and Debt

Interest on balance

,Q DGGLWLRQ WR WKH ÀDW LQWHUHVW EDQNV DOVR RIIHU LQWHUHVW RQ EDODQFH IRU FHUWDLQ W\SHV RI ORDQV ,Q WKH
LQWHUHVW RQ EDODQFH PHWKRG WKH DPRXQW RI LQWHUHVW FKDUJHG HDFK PRQWK RQ WKH ORDQ GHSHQGV RQ WKH
DPRXQW RI WKH ORDQ EDODQFH IRU WKDW PRQWK 6LQFH WKHUH LV PRQWKO\ LQVWDOPHQW SD\PHQW WKH DPRXQW
RI WKH ORDQ EDODQFH ZLOO EH UHGXFHG WKXV WKH DPRXQW RI LQWHUHVW IRU HDFK PRQWK ZLOO DOVR EH UHGXFHG

+RZHYHU LW VKRXOG EH QRWHG WKDW IRU HYHU\ LQVWDOPHQW SDLG HDFK PRQWK WKH SULRULW\ LV JLYHQ WR VHWWOH
WKH LQWHUHVW DPRXQW LQ WKDW PRQWK DQG WKHQ WKH EDODQFH LV XVHG WR VHWWOH WKH RXWVWDQGLQJ EDODQFH RI
the loan amount.

Example 20

(QFLN +DULWK REWDLQHG D SHUVRQDO ORDQ RI 50 IURP %DQN 0XOLD ZLWK DQ LQWHUHVW UDWH RI CHAPTER 3
on the balance. The repayment period is 7 years while the monthly instalment is RM150.

&DOFXODWH WKH WRWDO DPRXQW RI LQWHUHVW SD\DEOH E\ (QFLN +DULWK IRU WKH ¿UVW WKUHH PRQWKV

Solution: Scan the QR Code or
visit http://bukutekskssm.
First month my/Mathematics/F3/
First month interest = RM10 000 × —6 – × —1 Chapter3InterestRate
Calculation.pdf for more
100 12 information about loan
= RM50.00 ZLWK ÀDW LQWHUHVW DQG
interest on debts.
/RDQ DW WKH HQG RI ¿UVW PRQWK 50 50
= RM10 050

%DODQFH DIWHU ¿UVW LQVWDOPHQW 50 ± 50
= RM9 900

Second month
Balance of the loan at the beginning of second month = RM9 900
Second month interest = RM9 900 × —6– × —1

100 12
= RM49.50

/RDQ DW WKH HQG RI VHFRQG PRQWK 50 50
= RM9 949.50

Balance after second instalment = RM9 949.50 – RM150
= RM9 799.50

Third month
Balance of the loan at the beginning of third month = RM9 799.50
Third month interest = RM9 799.50 × —6– × —1

100 12
= RM49.00

/RDQ DW WKH HQG RI WKLUG PRQWK 50 50
= RM9 848.50

Balance after third instalment = RM9 848.50 – RM150
= RM9 698.50

7RWDO LQWHUHVW IRU WKH ¿UVW WKUHH PRQWKV LV 50 50 50 50

79

How do you solve problems involving loans? LEARNING
Example 21 STANDARD

Solve problems involving
loans.

Ameera wants to buy a car and has paid a deposit of RM4 800. The balance will be settled through
a vehicle loan.

RM48 000

CHAPTER 3 State the advantages and disadvantages of the vehicle loan chosen by Ameera.

Solution:

Advantages Disadvantages
‡ 5HSD\PHQW RI YHKLFOH ORDQ LQ PRQWKO\ ‡ 7KH FDU ZLOO EH UHSRVVHVVHG LI

instalments allows Ameera to own the car. instalments are not made.
‡ 'RHV QRW UHTXLUH D OXPS VXP SD\PHQW ‡ 7KH WRWDO DPRXQW RI UHSD\PHQW LV KLJK

due to interest charged on the loan.

Example 22 TIPS

0U 9LQFHQW LV D WHDFKHU ZLWK D PRQWKO\ LQFRPH RI 50 +H GHFLGHV Do not borrow money
WR EX\ D QHZ FDU WR FRPPXWH WR ZRUN +H FRQWDFWV WZR EDQNV WR JHW from unlicensed
D ORDQ RI 50 ,Q DGGLWLRQ KH QHHGV 50 WR FRYHU RWKHU moneylenders as the
H[SHQVHV HYHU\ PRQWK loan:
Ƈ ZLOO EH PDGH DFFRUGLQJ
The following are loan packages offered by two banks to Mr Vincent.
to their own terms and
Loan details Bank A Bank B conditions.
Loan amount RM40 000 RM40 000 Ƈ LPSRVHV YHU\ KLJK
Payment period interest charges which
,QWHUHVW UDWH 9 years 6 years is compounded daily.
Guarantor 4.5 % 5% Ƈ H[SRVHV \RX DQG \RXU
1RW UHTXLUHG family to danger if you
Required make late payment.
Ƈ IRUFHV \RX WR PDNH
an additional loan to
repay previous loan.

Suggest to Mr Vincent which bank is better suited for his car loan. State your reasons.

Solution:

Understanding the problem Planning a strategy

The amount of monthly instalments ‡ &DOFXODWH PRQWKO\ LQWHUHVW
payable by Mr Vincent provided that it is ‡ &DOFXODWH PRQWKO\ LQVWDOPHQW SD\DEOH
not burdensome.

80

Chapter 3 Consumer Mathematics: Savings
and Investments, Credit and Debt

Implementing the strategy

The amount of money repaid The amount of money repaid
to Bank A to Bank B

A = P Prt A = P Prt
A 50 50 î ²140.5±0 î A 50 50 î ²5± î

100

Total money = 50 Ju m la h b a y5ar0bal ik T o ta l money 50 50

repaid = RM 56 200 repaid = RM52 000

Monthly instalment = —RM—5—6—20–0– Monthly instalment = —RM—5—2 —00—0
108 months 72 months

=RM520.37 = RM722.22 CHAPTER 3

Making a conclusion
Mr Vincent should choose Bank A because the monthly instalment for Bank A is lower and less
EXUGHQVRPH WR KLP +RZHYHU GLIIHUHQW SD\PHQW WHUPV UHVXOW LQ GLIIHUHQW DPRXQW RI LQWHUHVW WKDW
ZLOO EH SDLG 7KHUHIRUH 0U 9LQFHQW FRXOG DOVR FKRRVH %DQN % DV WKH WRWDO LQWHUHVW SDLG ZLOO EH
less for Bank B.

Dynamic Challenge

Test Yourself

1. What is savings?
2. 6SHFLI\ IHDWXUHV UHODWHG WR )L[HG 'HSRVLW $FFRXQW
3. Encik Lipong deposits a sum of RM8 000 into Bank Pantas with an interest rate of 4% over 2

years. What is the amount of savings at the end of the second year?

Skills Enhancement
1. +RZ FDQ FRVW DYHUDJLQJ VWUDWHJ\ KHOS DQ LQYHVWRU"
2. ([SODLQ WKH PHDQLQJ RI LQYHVWPHQW LQ UHDO HVWDWH
3. 7KH IROORZLQJ FRQYHUVDWLRQ LV EHWZHHQ 5DPHVK DQG ,VPDLO UHJDUGLQJ WKH SXUFKDVH RI VKDUHV

Ramesh, I have That's great!
just bought You will get
shares of returns from your
BHP Berhad. investment.

([SODLQ WKUHH W\SHV RI UHWXUQ WKDW ZLOO EH UHFHLYHG E\ ,VPDLO

4. The following are two types of investments.

Lee Chong bought 3 000 units of Mokhtar bought 3 000 000 units of unit trusts.
shares of a public limited company.

([SODLQ WKH WZR GLIIHUHQFHV EHWZHHQ WKH WZR W\SHV RI LQYHVWPHQWV DERYH

81

5. (QFLN 6KDK ZDQWV WR GHSRVLW 50 LQWR D ¿[HG GHSRVLW DFFRXQW IRU PRQWKV
7KH IROORZLQJ DUH WKH ¿[HG GHSRVLW LQWHUHVW UDWHV IRU GLIIHUHQW WHUPV RIIHUHG E\ D EDQN WR (QFLN

Shah.

Duration Annual interest rate
1 month 3.0
3 months 3.5
6 months 3.75
9 months 4.00
12 months 4.25

Calculate the amount of interest that will be received by Encik Shah if he is saving for a
9-month term.

CHAPTER 3 6. ,Q (QFLN =DLQDO KROGV XQLWV RI VKDUHV RI 6\DULNDW 9LVLRQ 6GQ %KG ZKLFK LV ZRUWK
50 SHU VKDUH XQLW 'XULQJ WKH \HDU WKH FRPSDQ\ GHFODUHG D GLYLGHQG DQG D ERQXV LVVXH DW
QHZ VKDUH IRU VKDUH XQLWV KHOG $W WKH HQG RI WKH VKDUH SULFH URVH WR 50 SHU XQLW
Calculate

(a) the amount of dividend received by Encik Zainal

(b) the number of bonus share units to be received by Encik Zainal

(c) the number of share units held by Encik Zainal after receiving the bonus shares

7. Complete the following table.

Deposit amount Flat interest Savings period Total interest
(RM) rate (years) accumulated
10 000 5% 2
5 000 1 150
6% 720
4 000

8. 0U .LVKHQGUDQ GHSRVLWV 50 LQWR D ¿[HG GHSRVLW DFFRXQW ZLWK LQWHUHVW UDWH
compounded every 3 months for a period of 3 years. Calculate the amount of interest accrued
after the third year.

Self Mastery

1. 0U 2VZDOG $OSKRQVXV ERUURZHG 50 IURP %DQN <DNLQ WR VWDUW D WDLORULQJ EXVLQHVV LQ
5DZDQJ 7KH EDQN FKDUJHV D ÀDW LQWHUHVW UDWH IRU D UHSD\PHQW SHULRG RI \HDUV +RZ PXFK
LQWHUHVW ZLOO EH SDLG WR WKH EDQN E\ 0U 2VZDOG $OSKRQVXV"

2. 0UV (PLO\ )UDQFLV VDYHV 50 LQ D EDQN %\ WKH HQG RI WKH HLJKWK \HDU WKH PRQH\
FROOHFWHG DPRXQWV WR 50 ,I WKH EDQN SD\V DQ DQQXDO LQWHUHVW RI x% for a year and is
FRPSRXQGHG HYHU\ PRQWKV FDOFXODWH WKH YDOXH RI x.

3. 3XDQ 1RUDLQL 0LWLV GHSRVLWV D FHUWDLQ DPRXQW RI PRQH\ LQWR KHU VDYLQJV DFFRXQW ZKLFK
provides an interest rate of 2% per annum and compounded quarterly. What is the initial deposit
PDGH E\ 3XDQ 1RUDLQL 0LWLV LI WKH PRQH\ FROOHFWHG DW WKH HQG RI WKH ¿IWK \HDU LV 50 "

4. Puan Zaiton bought 1 000 share units of Syarikat Pelita Berhad at RM2.00 per unit. At the end
RI WKH \HDU 6\DULNDW 3HOLWD %HUKDG SDLG D GLYLGHQG RI VHQ SHU XQLW WR DOO LWV VKDUHKROGHUV 7KH
IROORZLQJ \HDU 3XDQ =DLWRQ VROG DOO WKH VKDUHV KHOG ZKHQ WKH VKDUH SULFH URVH WR 50 SHU
unit. Calculate the total return for Puan Zaiton.

82

Chapter 3 Consumer Mathematics: Savings
and Investments, Credit and Debt

5. ( QFLN ,VNDQGDU WDNHV D SHUVRQDO ORDQ RI 50 IURP %DQN &HUJDV ZLWK DQ LQWHUHVW UDWH RI
4% per annum. The repayment term is for 10 years. What is the monthly instalment payable by
(QFLN ,VNDQGDU"

6. Puan Balkis takes a personal loan of RM8 000 from Bank Sentosa with interest rate of 4% per
annum on the balance. The payback period is 4 years while the monthly instalment is RM110.
Calculate the amount of interest payable by Puan Balkis within 2 months.

7. 7KH IROORZLQJ LV D SURPRWLRQDO OHDÀHW RIIHUHG E\ 6HQJ +RQJ &RPSDQ\

79.2 cm 137.1 cm GREAT DEALS! CHAPTER 3

60 inches Television

Cash Price
RM4 000

Instalments
RM120 × 36

7KH IROORZLQJ FRQYHUVDWLRQ WRRN SODFH EHWZHHQ 0DVQDK 5DVDP DQG 1DQDN $OLRQJ DIWHU WKH\
VWXGLHG WKH SURPRWLRQDO OHDÀHW DERYH

Nanak Aliong, I want to buy a television as
advertised in the above leaflet in instalment

because I can only afford a low monthly
payment.

Masnah Rasam, I think it is better
for you to pay in cash rather than

instalment.

(a) What is your view on Masnah Rasam’s opinion?
(b) Calculate the amount of interest paid and the interest rate on this instalment payments.
F ,I \RX ZDQW WR EX\ D WHOHYLVLRQ KRZ ZRXOG \RX SXUFKDVH LW"

8. Ms Kayal borrows from Bank Desa RMX with an interest rate of 5% per annum. The payback
SHULRG LV \HDUV ,I WKH PRQWKO\ LQVWDOPHQW SDLG LV 50 FDOFXODWH WKH DPRXQW RI PRQH\
borrowed by Ms Kayal.

9. 0U 0XUXJDQ KDV ERUURZHG 50 IURP %DQN 2UNLG IRU SHUVRQDO XVH +H ZLOO UHSD\ RYHU
years with a monthly instalment of RM320. Calculate the yearly interest charged by the bank.

10. Puan Sapiah borrowed RM12 000 from a bank with interest rate of 3% per annum for 5 years.
0HDQZKLOH 3XDQ 6KD¿TDK ,UD ERUURZV WKH VDPH DPRXQW RI PRQH\ IURP DQRWKHU EDQN ZLWK D
rate of 4.5% per annum for 5 years. Calculate and state the difference between the total interest
SDLG E\ 3XDQ 6DSLDK DQG 3XDQ 6KD¿TDK ,UD

83

P ROJ EC T

Assume that you have won RM1
PLOOLRQ LQ D SX]]OH FRQWHVW
1. State the way in which you will

invest the money.
2. ([SODLQ ZK\ \RX FKRVH WKLV IRUP

of investment.

CHAPTER 3 CONCEPT MAP
Savings and Investments

Savings Investments

Savings )L[HG Current Shares Unit Real
Account Deposit Account Trust Estate

Account

,QWHUHVW Return on investment

Simple Compound Rent Capital
interest interest gain

Credit Debt
Credit card Loan
,QWHUHVW
84
Flat interest ,QWHUHVW RQ GHEWV

Chapter 3 Consumer Mathematics: Savings CHAPTER 3
and Investments, Credit and Debt

SELF-REFLECT

At the end of this chapter, I can:

1. Recognise various types of savings and investments.

2. Perform calculations involving simple interest and compound interest for
VDYLQJV DQG KHQFH H[SODLQ WKH LPSDFW RI FKDQJHV LQ SHULRG UDWH RI LQWHUHVW RU
return and compounding frequency on the future value of savings.

3. 3HUIRUP FDOFXODWLRQV LQYROYLQJ UHWXUQ RQ LQYHVWPHQWV DQG KHQFH H[SODLQ WKH
factors that affect return on investments and its impacts.

4. &RPSDUH DQG FRQWUDVW SRWHQWLDO ULVNV UHWXUQ DQG OLTXLGLW\ RI YDULRXV W\SHV RI
savings and investments.

5. Calculate the average cost per share for the investment of shares using the ringgit
FRVW DYHUDJLQJ VWUDWHJ\ DQG H[SODLQ WKH EHQH¿WV RI WKH VWUDWHJ\

6. Solve problems involving savings and investments.
7. ([SODLQ WKH PHDQLQJ RI FUHGLW DQG GHEW DQG KHQFH GHVFULEH WKH ZLVH PDQDJHPHQW

of credit and debt.
8. ,QYHVWLJDWH DQG GHVFULEH WKH DGYDQWDJHV DQG GLVDGYDQWDJHV RI FUHGLW FDUG DQG

ways to use it wisely.
9. ,QYHVWLJDWH DQG GHVFULEH WKH LPSDFW RI PLQLPXP DQG ODWH SD\PHQWV IRU FUHGLW

card usage.
10. Solve problems involving the use of credit cards.
11. &DOFXODWH WKH WRWDO DPRXQW RI ORDQ UHSD\PHQW DQG LQVWDOPHQW ZLWK YDULRXV

interest rates and different loan periods.
12. Solve problems involving loans.

EXPLORING MATHEMATICS

<RX FDQ YLVLW WKH &UHGLW &RXQVHOOLQJ DQG 'HEW 0DQDJHPHQW
Agency (AKPK) website to calculate the required period and
the amount of interest payable to settle your credit card debt.

85

4CHAPTER Scale
Drawings

What will you learn?

4.1 Scale Drawings

WWhhyy ddoo yyoouu lleeaarrnn tthhiiss cchhaapptteerr??
‡ 6FDOH GUDZLQJV DUH XVHG WR JLYH DQ LGHD RI REMHFW

measurements or actual distances.
‡ 6FDOH GUDZLQJV DUH IUHTXHQWO\ XVHG LQ DUFKLWHFWXUH

engineering, photography, technological design, and
so on.

Housing developers usually prepare models of
the housing scheme they are going to build.
These models give the buyers an idea of the housing
zone and other facilities provided by the developer.

Also, the plans of the houses to be built are
drawn using a certain scale with measurements
being in proportion to the actual measurements of
the houses. These plan drawings allow buyers to
choose the type of house to buy based on house size,
IDFLOLWLHV DQG DOVR QHHGV DQG D൵RUGDELOLW\ +DYH \RX
ever seen your house plan?

86

EExxpplloorriinngg EErraa

$QJNRU :DW LQ &DPERGLD LV RQH RI WKH IDPRXV
PRQXPHQWV LQ 6RXWKHDVW $VLD ,W ZDV EXLOW E\
6XU\DYDUPDQ ,, DIWHU KLV YLFWRU\ RYHU &KDPSD
DQG VXEVHTXHQWO\ XQLWLQJ .DPSXFKHD 7KLV
monument symbolises the strength and sovereignty
RI 6XU\DYDUPDQ ,,¶V JRYHUQPHQW ,WV KHLJKW LV
PHWUHV DQG LWV DUHD LV KHFWDUHV 7KH DOWDU LV DW WKH
FHQWUH ,W KDV IRXU VWRUH\V ZLWK HYHU\ FRUQHU KDYLQJ
ZDOOV PHDVXULQJ PHWUHV ZLGH DQG PHWUHV
long built from laterite and sandstones sourced
ORFDOO\ &DUYLQJV GHSLFWLQJ VWRULHV IURP 5DPD\DQD
and Mahabharata epics decorate the walls.

KWWS EXNXWHNVNVVP P\ 0DWKHPDWLFV )
([SORULQJ(UD&KDSWHU SGI

WORD B A N K

‡ RULJLQDO ‡ DVDO

‡ JHRPHWULFDO VKDSH ‡ EHQWXN JHRPHWUL

‡ GHJUHH ‡ GDUMDK

‡ JULG ‡ JULG

‡ VNHWFK ‡ ODNDU

‡ REMHFW ‡ REMHN

‡ VL]H ‡ VDL]

‡ VFDOH ‡ VNDOD

87

4.1 Scale Drawings

What is the relationship between the actual measurements LEARNING
and the measurements of various sizes of drawings of an object? STANDARD

'R \RX NQRZ WKDW WKH PDSV IRXQG LQ QDYLJDWLRQ VRIWZDUH DUH GUDZQ WR Investigate and explain
a certain scale? the relationship between
the actual measurements
The distance between two towns shown in the software is and the measurements of
proportional to the actual distance. various sizes of drawings
of an object, and hence
explain the meaning of
scale drawing.

CHAPTER 4 PL
NP

)RU H[DPSOH LQ WKH SLFWXUH DERYH WKH GLVWDQFH EHWZHHQ -RKRU %DKUX DQG .XDOD /XPSXU LV
VKRZQ XVLQJ D VFDOH RI FP NP

Example 1

7KH GLDJUDP EHORZ VKRZV WKH GUDZLQJV UHSUHVHQWLQJ REMHFW PQRST GUDZQ WR GL൵HUHQW VL]HV

Q S ƒ ƒ
ƒ R ƒ

P 2EMHFW T 'LDJUDP 'LDJUDP

'LDJUDP

:KDW FDQ \RX VD\ DERXW WKH VL]H RI 'LDJUDP 'LDJUDP DQG 'LDJUDP FRPSDUHG WR REMHFW
PQRST?

Solution:
'LDJUDP /HQJWKV RI DOO VLGHV DQG VL]HV RI DOO DQJOHV DUH WKH VDPH DV REMHFW
'LDJUDP /HQJWKV RI DOO VLGHV UHGXFHG E\ D FHUWDLQ SURSRUWLRQ FRPSDUHG WR REMHFW EXW VL]HV RI

all angles unchanged.
'LDJUDP /HQJWKV RI DOO VLGHV LQFUHDVHG E\ D FHUWDLQ SURSRUWLRQ FRPSDUHG WR REMHFW EXW VL]HV RI

all angles unchanged.

,Q FRQFOXVLRQ DOO VLGHV RI 'LDJUDP 'LDJUDP DQG 'LDJUDP IROORZ D FHUWDLQ VFDOH WKDW LV
SURSRUWLRQDO WR WKH REMHFW ZKHUHDV DQJOH VL]H UHPDLQV XQFKDQJHG 7KHUHIRUH 'LDJUDP 'LDJUDP
DQG 'LDJUDP DUH VFDOH GUDZLQJV RI REMHFW PQRST.

88

Chapter 4 Scale Drawings

Scale drawing LV WKH GUDZLQJ RI DQ REMHFW ZLWK DOO PHDVXUHPHQWV LQ WKH GUDZLQJ SURSRUWLRQDO
WR WKH PHDVXUHPHQWV RI WKH REMHFW

MIND TEST 4.1a
1. 7KH GLDJUDP EHORZ VKRZV GUDZLQJV UHSUHVHQWLQJ REMHFW ABCDE GUDZQ WR GL൵HUHQW VL]HV

D E 'LDJUDP
BC

A

'LDJUDP

'LDJUDP

'LDJUDP 'LDJUDP Diagram 6 CHAPTER 4

6WDWH WKH GLDJUDP ZKLFK LV WKH VFDOH GUDZLQJ RI REMHFW ABCDE.

8VLQJ JULG SDSHU GUDZ DOO WKH VKDSHV EHORZ XVLQJ

(a) the same size (b) a smaller size (c) a bigger size

(i) (ii) (iii) (iv)

How do you interpret the scale of a scale drawing? LEARNING
STANDARD
The scale used to draw a scale drawing depends on the ratio of
PHDVXUHPHQW RI VFDOH GUDZLQJ WR PHDVXUHPHQW RI REMHFW ZKLFK LV Interpret the scale of a
scale drawing.

6FDOH Measurement of scale drawing
0HDVXUHPHQW RI REMHFW

This ratio can also be written in the form;

0HDVXUHPHQW RI VFDOH GUDZLQJ 0HDVXUHPHQW RI REMHFW

8VXDOO\ IRU VFDOH GUDZLQJV ZH XVH VFDOH LQ WKH IRUP RI UDWLR

Q
where Q is a positive integer or fraction

Q means one unit on the scale drawing will represent Q XQLWV RQ WKH REMHFW

89

Brainstorming 1 In pairs

Aim: ,QWHUSUHW WKH VFDOH RI D VFDOH GUDZLQJ

Steps:

1. 6WXG\ WKH GLDJUDPV EHORZ

R R' R' R'

P 2EMHFW Q P' Q'
'LDJUDP
CHAPTER 4
R'

P' Q'
'LDJUDP

R'
P' 'LDJUDP Q'

P' 'LDJUDP Q' P''LDJUDP Q'

2. &RPSOHWH WKH WDEOH EHORZ EDVHG RQ WKH GLDJUDPV DERYH

Diagram Scale drawing Object Scale 1:n
Side Length (unit) Side Length (unit) Ratio
—
P'Q' PQ —
'LDJUDP

P'R' PR

'LDJUDP P'Q' PQ
'LDJUDP P'R' PR
'LDJUDP P'Q' PQ
'LDJUDP P'R' PR
P'Q' PQ
P'R' PR
P'Q' PQ
P'R' PR

Discussion:
Discuss the results based on the table above.

90