· 23. Identification: Annuity u64 10 4 40 40 0,1225 2500000 1 4 0,1225 2500000 1 1 0,1225 4 3 4...

GR T

UTO

RIA

LS

www.g

rtuto

rials.co.

za

DSC1630

MAY/JUNE 2009

SOLUTIONS

()lIESTlO'" I

S :..:::1'(1 of I'll .. ...J 500::: 4317.26(1 + 0.151) .. 1 = 103 Jays. Fmm till.' 1.lhk", 5 \la~ is IhI..' 1251h

d;t~ or III•..· .\I..';lf.: 103 + '25 ::: 22Xlll day of Ih~ y car \\ hie-h is 16 (\ugllst. 121

I·=.\'(\~d/). :.35()O='''{1-0.I3X~}- :.S= 10925.23 151

()IIESTlO'" .1

d ,. 0.1858r = --. :. d = -- = ,- D.IXD027= IX% III

1-"1 1'1+ 1 O.185Xx ~-, + 1

365

(I+~r =r""" : 1+± =r"'2.<71' :.i=12.77% HI

PV = ±..f{) 000. FV = 56000. N:::: 5. C()~1P I x 2. 1-'1

I'V=±IO(I. N=4. 1= I~. COMI'I'V. N=52. COMI'I '21114

()IIESTIO ..••7

)IV = ±140 000. \I:::: 10. I = 2X. CO\IP FV. rv after 10 Yl:ars= R 1652 82R.27

PV:::: ±1652 X2X.27. N = Q. I:::: 5. CO\W FV ISI

/

GR T

UTO

RIA

LS

www.g

rtuto

rials.co.

za

DSC1630 May/June 2009 Solutions

()I'ESTlO:\ 'J

100L~ 6 000o I :! 3 ~ :;

NO\\

13.75 .

la) P\'=±10000. ,'\!=IO.I=~. CO\IPI"V. rV=R1C)~-C!.9In n(l)

Ih) F\'=6000. N=6. 1= 13.75. CO\IPPV.PV=R ..t()26.1(,L.-nnn-(1)2

( 1) + (2) = R23 4(,9.10 151

Qn:STIO:\ III

90tlO 23-169.10

(I

Raphael P;)ys Pinky 4 yt.'ars from now

QlJESTlO:\ II

PV = ±] 64 1100. N = II. I = 9,9. CO~IP FV 14)

QlIESTlO:\ 12

~

PV = 500000(1 + 0.224 t' + 250 OOO(]+ 0,224) <, + 150 000(1 + IU24 r' + 700 OOO(]+ 0.224) ,

= R440401 ill

QIJESTIO:\ U

~20()O

(I

;!Jl!lli14 15

·1 000

II>

4w)Q

17lJlliQ

25

x = (I + i)2000(l,~11-t 4000aw1, (1 +i) 15

GR T

UTO

RIA

LS

www.g

rtuto

rials.co.

za

.DSC1630 !-'I_ay/June 2009 Solutions

()UESTION I~

-' OOQ."lirndilll: J

6J!JlP" QJl!lO

IJ

Page 3

QJlliQ

19

I he first timdillc shmys payments made at the end of each month.]1) the s",'CU!llj timclinc the first

paymcll! is Illw ..h: al the beginning oflhe 131h month and the last paymcnt is t11<Kh.'at the hcginlling

(if till' 20lh I1wllth.

The I'Y of the raIments made at the end of each month ~ 3 ooo(] + ~) 12 ~ ]U2 ~52.37.. 12

The [)V al the heginning or the 131" month or al1 the payments mauL' at the heginning of each

month = (I + ~)6 OOOal( l (J I%!P = R45 385.16. \Ve now determine the present valuc of this12 . ~

-I'

a1l1(!unt al the beginning of the term. Thus PV = R45 38S.16( (1 + 0./;6) - = R37 366.28

lIence py o!'thc loan = R32 452.37+RJ7 366.28 = R69 818.65 121

QUESTION IS

Interest rate per month = 6036.40 x 100 = 1.2% = 14.4% per annllm503 033.57

QUESTION 16

A=49) ]61.53-(]5908.46-5917.94)=R483 ]70.99

QUESTION 17

I'M f ~ ± 15'iOS.46. N ~ 2~0. ] ~ J.12. COMI'I'Y. 131]2

QUESTION IS

( ] 7(0) .1005962= x+-- ')~lIl 0.1

(LI -

QUESTION ]<J

20x] 700

0.]'. x = 6 son approximately 121

7.5"1~1 I = 90.80770 - J2.09XXX = 64.70X82

PV 64J,OS82. Pr\1T-cc±7.5, N'-'-IS.(CO:--'WJ)x2 121

GR T

UTO

RIA

LS

www.g

rtuto

rials.co.

za

DSC16JO May/June 2009 Solutions

(H TSTIO.'\ .211

PI= ~PV+~.ill\l.'s(Il1l.'~ iL' I ")...J.17.::,=195000+lnilialill\('stm~Initial inn's[lt1l.'nt ... - .• Initial inn:sllllt'1l1

Initial ill\'l.'SIIllL'111 = XOO oon I~I

()IIESTlO:\ 21

Page 4

"'9 -'larch ~OOI.) t) "'la, 21XN 29 ScrHcmbcr 2009 29 SCDtcml~r 20 15

() 12

( l'1'(29Sep~()09)= (J.Julll ~75 1100 1+ ~;~ RI1J.9JJS\tYlI.Sim.'elhcfirstl'lIlJpol1datc

and tbe sc:ltlcmcilt oale arc more than 10 days apart. we add tht: value ()f the WUptll1ltl this price.

J kIK'C prkc R 120.23381. L\lso the numhcr of days betwcen <) ~1ay 2009 and 29 Sl."ptcmhcr1-0

2(1)1) is I...J.J. I h:ncc all-in-price = 120.1338{] + .t.7S rli~ = R 115.974 7...J.%HI100

()lJESTION 22

(. = PV I (I + ~IIRR)" :. _c_ = (1 + \IIRR)". T~lkin1! thl.' natural log on hoth sides wc gel•••• PV""I ~

101-1'- = /lln( I + t\I/RR).Solving for t1 givesPVn,,!

( (' J

In

n- PV"UI 121

11l(1+~IIRR)

()IIF:STIO:\ 2J

121

()IIESTlO:\ 24

10, lx, yl. I 500. Ie,,"

15. (x, .1'). 1~(). LN"

RCIe h ISI

GR T

UTO

RIA

LS

www.g

rtuto

rials.co.

za

DSC1630 May/June 2009 Solutions

Rei r III

~

(a) 1':'-.11 ± 7.35. N:= ::!9.13.5

CO\lP I-V. PV = 92.50885------.. (I)

(h) FV -'= ] 00. N = 19. I = 1J.5 .. CO\IP PV. PV = 15.042~\9_hUU~h (2)1

:. P(24 JUIlC 2(09)=(1)+ (2):= RI07.5517..J

Sill'-'c thl.' sclth:mcnt date and the first (,.'OUP0!ldale an: more than I() days "part. add the

valuL' ol"lh(" (;'oupon to the aome price. lienee all-in-price on 24 June 2009 is R 114.90174%.

Clean Price = all-in-price - accrued interest

= 114.90174 - 4.J09J2 = R 110.59242% 151

QIIESTlO:\ 27L-

'\;0\\:~4

X

8

QIIESTlOI'O 2H

Loan = 0.&0 x I -150000 = J 160000

P\IJ=±1527·t76. 1=12.95. N=2·t CO\I!'P\'. 1'\'=130775312

IIcncl.' real cost ofloan = I J07753-1160000=RI47753 121

QII":STIO:\ 2')

FV = X50 000. N = 32. 1= 12J) .. COMP PMT 1.'14

QI'ISIIO:\ .111

't'earh cost = \Ionthl\" interest )(S + quarh:rI\' pa\ll1('Il(S )(-t.. 12 ..

~ ~ x R50000 + 15 nO.ORx 4 ~ R 188880100

GR T

UTO

RIA

LS

www.g

rtuto

rials.co.

za

GR T

UTO

RIA

LS

www.g

rtuto

rials.co.

za

MAY/JUNE 2010

1 Identification: Simple interest

Pr

29125000 0.0845

365

1684.21 (1)

SI T

R option

u u

2 Identification: Discount

5(1 )

748000(1 0.119 )12

44668 (1)

P dt

R option

�

� u

3 Identificatio: Discount

(1 ) ] (1 )

1

1

(5)

If S P rt and P s dt

dt d

r

d

rt option

d

� �

§ · � y¨ ¸© ¹§ ·�¨ ¸© ¹

4 Identification:Compounding interest

5 mar

291 days

21 Dec

GR T

UTO

RIA

LS

www.g

rtuto

rials.co.

za

9152

52

(1 )

0.296117500 1

52

29338.66 (3)

nS P i

R option

u

�

§ · �¨ ¸© ¹

5. Identification: Continuous compounding

ln 1

0.1942ln 1

12

19.24% (5)

jmC m

m

option

§ · �¨ ¸© ¹§ · �¨ ¸© ¹

6. Identification: Normal and effective interest rates

� �1 1 (5)m

jm m jeff optionª º � �¬ ¼

7. Identication: Annuities

� �

9 3

1 1

0.11321 1

32200

0.1132

66173 (1)

ni

S Ri

R option

u

ª º� � « »

« »¬ ¼ª º§ ·� �« »¨ ¸© ¹« » « »« »¬ ¼

GR T

UTO

RIA

LS

www.g

rtuto

rials.co.

za

8. Identification:Deferred annuity

5 2

: 1

0.18695000 5 20.186 2 1

2

601708.66 (3)

tmvm

PV Ranm

a

R option

�

� u

§ · �¨ ¸© ¹

§ · u y �¨ ¸© ¹

9. Identification: Differed annuity

� �4 2

1

0.186601708.66 1

2

601708.66 (3)

nPV S i

R option

�

� u

�

§ · �¨ ¸© ¹

10. Identification: Continuous compounding

(0.0847 8)53580

27 209.76 (2)

ct

ct

S Pe

P Se

e

R option

�

� u

11. Identification: Evaluation of cash flows

1 2 3 4 5 6 7 8 9

p1 p2 p3 p4 p5

GR T

UTO

RIA

LS

www.g

rtuto

rials.co.

za

330000 5

250000

26,4% (5)

Average after tax incomeAPR

Investment level

option

�

y

12. Identification: band

Settlement date of the stock is 11 August 2010 as the next coupon date of stock 538 is

28/09/2010.

Option (3)

13. Identification: Perpetuity

3500

1,112

12

375000 (4)

RP

L

R option

§ ·¨ ¸© ¹


� � � ��

3 5

7 9

25000 1 0,0864 50000 1 0,0864

75000 1 0,0864 30000 1 0,0864

19497,13 33038,57 41 988,75 14230,28

108755 (1)

PVout

R option

� �

� �

u � � u � �

u � � u �

� � �


GR T

UTO

RIA

LS

www.g

rtuto

rials.co.

za

� ��

� �

1

1

108755 1 0,18472

500024

500000 2

i

n

n

CMIRR

PVout

C PVout i

R

R option

§ · �¨ ¸© ¹

�

�

16. Identification: Sinking funds

� �

� �

Pr 350000

8486,23 20 12 0,105 12

850000

850000 350000

120000 4

iceof the house R PV of theloan

PV a

R

Total price R

R option

�

u y

�


� �

.

20 12 8486,23 850000

2036695 850000

1186695,20

1186695 3

I no of payments payments theloan

R

R

R option

u � u u � �

18. Identification: Bond

Pr

90,61202 5,31616%

85229586%

Financial calculator

BOND

Clean ice All in price Accrued Interest

R

� �

GR T

UTO

RIA

LS

www.g

rtuto

rials.co.

za

19. Identification: Amortisation

� �

intint

707,25

24522,83 8926,30

707,25

15596,53

4,5346%

4,5% 1

erest dueApplicable erest rate

accumulated amount in the fund

option

�


� �

Pr

8151,38 7444,64

1481,67 1

Interest rate incipal paid payment

R

R option

� �


� �

� �

7444,64 45000 4,5%

7 444,64 2025

5419,64 5

Valueof B additionto fund

Additionto fund

R option

o

� u

�


GR T

UTO

RIA

LS

www.g

rtuto

rials.co.

za

� ��

� � � ��

:

9,6

100

17 05 2010

14 12 2033

/ 2 2

1/ 10,4

92,

Financial calculator Clear memory and press BONDbutton

COUPON PMT ENT

REDEMPT FV ENT

Settlement date ENT

Maturity date ENT

CPN Y N always ENT

YIELD Y ENT

PRICE PV PRESS COMP BUTTON

o �

o �

� � �

� � �

o �

o �

o o

� �

� �

99634150

4,061538462

Pr

92,99634150 4,061538462

97,05788% 3

ACCU INT PRESS COMP BUTTON

All in price ice PV ACCU INT

R option

o o

? �

�

23. Identification: Annuity

� �

� �

10 4

406 4

40

0,12252500000 1

4

0,12252500000 1 1 0,1225 4 3

4

0,12252500000 1 5,06261

4

8355393,89

5,06261

1650412,32

3 4951236,95 4

Obligations

Payments

R

R option

u

u

§ ·� ¨ ¸© ¹

§ ·� u � y u u¨ ¸© ¹

§ ·� u¨ ¸© ¹

u

u

uu

now 4 10 years

p1

x 3x

p2

x

GR T

UTO

RIA

LS

www.g

rtuto

rials.co.

za

24. Identification: Simple interest Compound interest

1612

12

int

1

375000

271 0,0791

365

372818,55

int

1

0,0791372818,55 1

12

335617,209

int

1

355617

tm

Simple erest for odd periods

SP

rt

R

R

Coumpound erest for full terms

jmP S

m

R

Simple erest for odd periods

SP

rt

�

� u

�

� u

§ · �¨ ¸© ¹

§ · �¨ ¸© ¹

�

� �

, 21

1 0,0791 23 365

333952,66 1R option

� u y

25. Identification: Regression line

� �92,308 5


Slope for the angle y a bx

rcl r option

�

5 may 2009

16 months

24 Oct 2010

27 days 23 days

1 June 2009 1 Oct 2010

GR T

UTO

RIA

LS

www.g

rtuto

rials.co.

za

26. Identification: Regression line

� �0,97,15 2


rcl r option �

27. Identification: Annuity due

� �

� �

� �

52 4

1

0,134209000 1

52

122366,87

122366,87 54 2 0,134 52

758,77

758,77 1

nPV FV i

R

R

R R

weekly deposits R option

�

� u

�

§ · �¨ ¸© ¹

u y


1 2 3 4 5 6 7 8 910

P1=12,65%

c/y=2

n=7

15 500now

3

P2=35 000

C/y=12

9,5%

n=3GR T

UTO

RIA

LS

www.g

rtuto

rials.co.

za

� �

2 7

12 3

1

0,126515500 1

2

36578,61

0,0952 35000 1

12

26350,053

1 2

62928,66 5

Payment

S

R

P S

R

Total amount Frank has to pay back

P P

R option

u

� u

§ · �¨ ¸© ¹

§ · �¨ ¸© ¹

�


� �

4 5 2 4

8 20

0,109 0,10915000 1 62928,66 1

4 4

0,109 0,10962928,66 1 15000 1

4 4

52907,43 5

Payments Obligations

x

R option

u u

§ · § ·� � u �¨ ¸ ¨ ¸© ¹ © ¹

§ · § · � � �¨ ¸ ¨ ¸© ¹ © ¹

30. Identification: Annuity due and ordinary annuity

4 7

5yrs9

10

35 000now

15 000 Amount received

here

GR T

UTO

RIA

LS

www.g

rtuto

rials.co.

za

� � � �

� �

� ��

9

12

912

12

1 :

1

15 0,1641 0,164 12 4000 12

12 12

54655,23

2 :

1 1

1

0,6141 1

127000

0,614 0,6141

12 12

n

n

st set of payments annuity due

P i R a n i

a

PV R

nd set of payments ordinary annuity

iP R

i i

u

�

§ · � y u¨ ¸© ¹

§ ·� � ¨ ¸

¨ ¸�© ¹§ ·

§ ·¨ � �¨ ¸¨ © ¹ ¨¨ § ·�¨ ¸¨ © ¹© ¹

� �

58902,19

1 2

54655,23 58902,19

113557,42

113557 4

R

The amount thatVicky owes Cindy

P P

R

R option

¸¸¸¸¸

� �

GR T

UTO

RIA

LS

www.g

rtuto

rials.co.

za

GR T

UTO

RIA

LS

www.g

rtuto

rials.co.

za

MAY/JUNE 2011 SOLUTION

Question 1

Identification: Simple interest

� �

� ��

7,5%

545

365

1

54525000 1 0,075

365

25000 0,075 1,4935

27799,66 1

Interest rate per year

time

S P rt

Option

? �

§ · � u¨ ¸© ¹

� u

Question 2

19.4cm

25 000

P

S545 days

GR T

UTO

RIA

LS

www.g

rtuto

rials.co.

za

� ��

� � � �

� �

� ��

� �

1

1

1 1

1 1

11

1

11

1

1 1

1

1 1

1

1

1

1

1

1

1

1 / 1

S P rt

P S dt

S S dt rt

Sdt rt

S

rtdt

rtdt

dt

dt

dt

dt

dtrt

dt

dtr

dt t

dr

dt

ddt

r

ddt

r

dt d Option

r

�

�

� �

� �

� �

��

�

� �

�

�

u�

�

�

�

§ · �¨ ¸© ¹

Question 3

19.4cm

8,15%?

PS

55 00019 Nov

21 months

Identification: Compound interest

GR T

UTO

RIA

LS

www.g

rtuto

rials.co.

za

� �

2112

12

21

1

0,081555000 1

12

0,081555000 1

12

47712,35 2

tmVm

P Sm

Option

�

� u

�

§ · �¨ ¸© ¹

§ · �¨ ¸© ¹

§ · �¨ ¸© ¹

Question 4

Identification: Compound interest

� �

4

52

1 1

0,199

4

52

0,19952 1 1

4

0,19457

19,46% 2

m

njmi n

m

with jm

m

n

i

Option

§ ·§ ·¨ ¸ � �¨ ¸¨ ¸© ¹© ¹

§ ·§ ·¨ ¸ � �¨ ¸¨ ¸© ¹© ¹

Question 5

Identification: Continuous compounding

� ��

0,175100 1

19,12% 5

J e

Option

�

GR T

UTO

RIA

LS

www.g

rtuto

rials.co.

za

Question 6

Identification: Compounding

� �

� �

� �

4 7

28

5212

12

52

1. 1

0,106510000 1

4

0,106510000 1

4

20870,43

2. 1

0,08725000 1

12

0,08725000 1

12

36398,07

36398,07 20870,43

57 268,50

n

n

S P i

S P i

Three years from now Pitso will oweClive

Optio

u

u

�

§ · �¨ ¸© ¹

§ · �¨ ¸© ¹

�

§ · �¨ ¸© ¹

§ · �¨ ¸© ¹

? �

� �3n

Question 7

Identification: Annuity due

� �

� �

1

1 0,0858 12

10 12

0,085848000 1

12

0,085848000 1 10 12 0,0858 12

12

252,18 1

S i Rs n i

with

N

S

Rs

R Option

�

y u

§ · y �¨ ¸© ¹

§ · � u y¨ ¸© ¹

GR T

UTO

RIA

LS

www.g

rtuto

rials.co.

za

Question 8

� � � �

� �

1512

12

1 1 1

28450000 1 0,0765

365

452640,82

0,0765452640,82 1

12

479970,53

14452640,82 1 0,0765

365

499371,53 4

dmS P rt rt

m

S

Option

u

§ · � � �¨ ¸© ¹§ · � u¨ ¸© ¹

§ ·�¨ ¸© ¹

§ ·� u¨ ¸© ¹

Question 9

Identification: Fractional compounding

19.4cm

7,65%04/03/2010

450 000

15 months01/04/201

01/07/201115/07/201114 days

Identification: Odd periods and compound interest

GR T

UTO

RIA

LS

www.g

rtuto

rials.co.

za

� �

15 28 14 12

12 365 1

1

0,0765450000 1

12

499368,28 4

tmdm

S Pm

S

Option

�§ ·� u¨ ¸© ¹

§ · �¨ ¸© ¹

§ · �¨ ¸© ¹

Question 10

Identification: Continuous compounding

� �

54

12

54

12

36550

25500

54

12

36550 25500

36550

25500

54 36550 54ln ln

12 25500 12

35550 54ln

25500 12

8% 2

ct

c

c

S Pe

S

P

t

e

e

c e

c

Option

§ ·¨ ¸© ¹

§ ·¨ ¸© ¹

§ · y¨ ¸

© ¹§ ·

y¨ ¸© ¹

Question 11

Identification: Bond

GR T

UTO

RIA

LS

www.g

rtuto

rials.co.

za

49

17 / 04 / 2036 17 / 04 / 2012

24

" "

24 2 1 49

45

183

9,75 0,079549 0,0795 2 100 1

2 2

104,4813372 14,80752509

119,2888622 4,875 124,163622

0,0124,163622 1

Years

Multiply with two and add oneto get n

R

H

P a

All in price

�

�

u �

§ · y � �¨ ¸© ¹

� �

�

� �

45

183795

2

122,9791 4Option

�§ ·¨ ¸© ¹

Question 12


� �

int365

183 459,75

365

3,68630% 3

H RAccrued erest C

Option

� u

� u

Question 13


GR T

UTO

RIA

LS

www.g

rtuto

rials.co.

za

� �

int

122,97940 3,68630

119,29310 5

Clean price All in price Accrued erest

Option

� �

Question 14

� �

6000

1200

9,5%

30

1200 30 12006000 30 0,095

0,095 0,095

2788914,51 378947,37

2409967 4

Q nQS R S n i

i i

R

Q

i

n

S S

Option

§ · � �¨ ¸© ¹

u§ · � �¨ ¸© ¹

�

Question 15

� �

� �

1

2

30 2930 6000 1200

2

180000 522000

702000 1

n nAmount paid nR Q

Option

�§ · � ¨ ¸

© ¹u§ · u � ¨ ¸

© ¹ �

Question 16

GR T

UTO

RIA

LS

www.g

rtuto

rials.co.

za

� �2

Q nQS R S n i

i i

QR S n i

S nQ i

S n i S n i

Q nQR S

i i

nQ nS

i nQiS n iR

iS n i

Q QS S n i n

i iR OptionS n i

§ · � �¨ ¸© ¹

§ ·�¨ ¸� © ¹

� �

� � �

� �

Question 17

� �

Pr

3081,86 1119,21

4201,07 5

Interest due at end incipal repaid of month

Option

� �

Question 18

� �

tan Pr

202152,34 199586,48

2583,85 3

Outs ding principalat beginning of month incipal at end of month

Option

� �

Question 19

GR T

UTO

RIA

LS

www.g

rtuto

rials.co.

za

� �

tan Pr tan

118191,36 3255,54 114935,82

114935,82 150 tan 2

Outs ding principal at beginning of month incipal Outs ding principal at monthend

Month outs ding principal atbeginning of month Option

� �

Question 20

Sample Option(5)

Question 21

� �1,9 22,6 1Calculator y x Option � �

Question 22

� �

2500

0,125 5

2500

0,125 12

240000 3

RP

i

R

i

Option

y

y

Question 23

GR T

UTO

RIA

LS

www.g

rtuto

rials.co.

za

� �

� �

3 10 150,118 0,118

240000 1 1 43 3

763548,1864 5,783704229

763548,1864

5,783704229

132023,38 4

528094 4

x x

x

x

x

Option

u§ · § ·� � �¨ ¸ ¨ ¸© ¹ © ¹

u

Question 24

� �

13981,97 20 12 0,064 12

1890227,99

1890227,99 1500000

390227,98 3

Tv Ra n i

a

Tr Tv P

Option

u y

? � �

Question 25

11,8%/3

now 10 yrs4x

240 000

5 yrsx

GR T

UTO

RIA

LS

www.g

rtuto

rials.co.

za

� � � � � �

� �

5 7 1070000 1 0,115 90000 1 0,115 75000 1 0,115

40618 42007 25253

107878 1

PVout

Option

� � � � � � � �

� �

Question 26

� �

� �

5150000 1 0,0870 120000

227634,97 120000

347634,97 5

C

Option

� �

�

Question 27

� ��

� �

1

8

8

1

1

291930 1 0,1081

663606,095

663600 4

n

CMIRR

PVout

C PVout i

R Option

§ ·¨ ¸© ¹§ · �¨ ¸

© ¹

�

�

Question 28

� �22,11% 5Calculator Option

Question 29

GR T

UTO

RIA

LS

www.g

rtuto

rials.co.

za

� �3 12

1

0,079532978,19 1

12

674993,989 1

60000

1/ 7,9%

/ 12

3

/ 12

2444456,79 2

674993,989 2444456,79 3119450,78

nS p i

PMT

Y

C Y

N

P Y

FV

u

�

§ · �¨ ¸© ¹

�

Question 21

� �

5 12 2 40,104 0,098

20000 1 35000 112 4

33565,27 28838,48

62403,75 5R Option

u � u§ · § ·� � �¨ ¸ ¨ ¸© ¹ © ¹

�

2 5 6 7

5 yrs -2

GR T

UTO

RIA

LS

www.g

rtuto

rials.co.

za

GR T

UTO

RIA

LS

www.g

rtuto

rials.co.

za

OCTOBER/NOVEMNER 2011

1. Identification: Simple interest

� �1

3217800 1 0,062

365

8252,30 (1)

S P rt

R Option

�

§ · � u¨ ¸© ¹

2.

� �

1

0,0961

0,12

0,096

25

4

d

rtd

time months

Option

�

�

3. Identification: Nominal and effective interest rates

� �

52

1 1

0,131 1

52

13,01%

3

mjm

jeffm

Option

ª º§ · � �« »¨ ¸© ¹« »¬ ¼ª º§ · � �« »¨ ¸© ¹« »¬ ¼

321 days

4 Jan2011

21 Nov2011

GR T

UTO

RIA

LS

www.g

rtuto

rials.co.

za

4.

� �

� �

1

3035000 1 0,0998

12

26267,50

5

P S dt

R

Option

�

§ · � u¨ ¸© ¹

5.

0,1056

4

1

4 1

10,7%

c

mjm m e

e

§ · �¨ ¸

© ¹§ ·

�¨ ¸© ¹

6. Identification: Simple interest

� �

1

35000

27 141 0,102

12

31517,33

4

SP

rt

R

Option

�

�

� u

7. Identification

� � � �> @

� �

10 11150000 1,12 1,05

796808 3

3

R

Option

u u

GR T

UTO

RIA

LS

www.g

rtuto

rials.co.

za

8. Identification: Fractional Compounding

� �

� �

13 20 912

365 12

1

0,0693560000 1

12

59348,69 3

nS P i

R Option

�§ ·§ ·� u¨ ¸¨ ¸© ¹© ¹

�

§ · �¨ ¸© ¹

10. Identification: Compounding interest

� �

� �

4 4

1

0,084568000 1

4

95010,47

4

nS P i

R

Option

u

�

§ · �¨ ¸© ¹

11. Bond: Identification

9 months

13 days 20 days

1 Mar16 Feb

1 Dec 21 Dec

GR T

UTO

RIA

LS

www.g

rtuto

rials.co.

za

� �

38

119

183

19 12 38

183

119

9, 4

2

4,7

9, 4 0,06938 0,069 2 100 1

2 2

98,68966 27,55759

126, 24725 4,7

130,94725

0,069130,94725 1

2

128,09903%

4

H

R

PMT

a

R

Option

�

§ ·�¨ ¸© ¹

u

§ ·y � �¨ ¸© ¹

� �

§ · �¨ ¸© ¹


� �

.

128,09903 1500 192149

4

All in price no of Bonds Amount tobe received

R R

Option

u u

PreviousCoupondate

Settlementdate Next coupon

dateMaturitydate

16/10/2011 19/12/2011 16/04/2012 16/04/2031

119days

183 days

GR T

UTO

RIA

LS

www.g

rtuto

rials.co.

za

13. Identification: Deferred annuity

� �

3 4

1

0,0915000 4 4 0,09 4 1

4

199689,47

2

tmjm

PV Ran im

a

R

Option

�

� u

§ · �¨ ¸© ¹

§ · u y �¨ ¸© ¹

14. Identification: Deferred annuity

� �

4 3

1

0,09199689,47 1

4

152895,73

4

n dy

cPV S

dy

R

Option

� u

� u

§ · �¨ ¸

© ¹

§ · �¨ ¸© ¹

15. Identification:

� �

� �

12 5

12 2

1

0,104300000 1

12

505479,04

1

0,10470002 12 1

12

185858,32

503479,04 185858,32

689337

3

n

m n

PV P i

R

jmS Rsn i

m

R

Total value

R

Option

u

u

u

�

§ · �¨ ¸© ¹

§ · �¨ ¸© ¹

§ · u �¨ ¸© ¹

�

GR T

UTO

RIA

LS

www.g

rtuto

rials.co.

za

16. Identification: Perpetuity

� �

18000

0,114 4

631579

3

RP

L

R

Option

y

17. Identification:

� �

12 4 12 5 12 40,1095 0,1095 0,1095

1 2 3 1 631579 112 12 12

1,546529981 2 1,739495563 976755,86

5,286025544 976755,86

5,286025544 5,286025544

184780,77

2 2 184780,

Payments Obligations

x x

x x R

x

x

x x

u � u u

§ · § · § ·u � � � � �¨ ¸ ¨ ¸ ¨ ¸© ¹ © ¹ © ¹

� �

u

� �77 369600

2

R

Option

u


� �

� �

12 10

1

0,1662543,42 1

12

306521,61

2

nFV P i

R

Option

u

�

§ · �¨ ¸© ¹

19. Identification: Slope of regression

GR T

UTO

RIA

LS

www.g

rtuto

rials.co.

za

� �, 0,129

2


rcl b

b slope

Option

20. Identification: Correlation coefficient

� �0,948

3


rcl r

r

Option


� �

int

tan

8690,0412

948004

0,00916667 12

0,11 100

11%

2

erest dueInterest rate compounding periods

outs ding principle

R

R

Option

u

u

u u


� �

int

8690,04 17114,67

25804,71

4

payment ersest due principal repaid

R

R

Option

� �


GR T

UTO

RIA

LS

www.g

rtuto

rials.co.

za

� �

20 12

1

0,1125804,71 20 12 0,11 12 1

4

2500000

2

tmjm

PV Ran im

a

PV R

Option

�

� u

§ · �¨ ¸© ¹

§ · u y �¨ ¸© ¹


� �

870000

870000

58 12 0,092 12

6166,12

3

S Rsn i

s

R

R

Option

? u y


� �

1 Pr

3870000 0,134

12

29145

cos 4 29145 12 1166,12

190573

190600

5

S t

R

Total yearly t

R to the nearest hundred

R

Option

u u

u � u


GR T

UTO

RIA

LS

www.g

rtuto

rials.co.

za

44

10,45,2

12

0,0875Pr 100 1

2

/ 2, / 2, 5,2,1/ 8,75, 22

100,7945625

Pr

115,9914448

115,8565584

51 10,4 0,14246753

365

in

PMT

ice

PV p y c y PMT y n

R

Current price PV ice

All in price

A

Clean price All in price Acrued

�

§ · �¨ ¸© ¹

�

�

u �

�

� �

t

115,99903%

2

erest

Option

27. Identification; MIRR (Evaluation of cash flows)

� � � ��

� �

2 6

8

400000 1 0,076 800000 1 0,076

750000 1 0,076

1278385,60

2

PVout

R

Option

� �

�

� � �

�

28. Identification: Profitability index

� �

11

1

381991,2122

1,2122 38199

1,2122 38199

0,2122 38199

0,2122 0,2122

180014,14

180000

4

NPVP

x

x

x x

x x

x

x

R

Option

�

�

�

GR T

UTO

RIA

LS

www.g

rtuto

rials.co.

za

29.

20 12

20 12

1

0,047517505,96 12 20 0,0475 12 1

12

2708963,159

0,047517505,96 12 20 0,0475 12 1

12

1600000

cos

270

tmjm

PV Ra n im

a

Total value R

Original value a

R

Total real t Total value original value

�

� u

� u

§ · �¨ ¸© ¹

§ · u y �¨ ¸© ¹

§ · u y �¨ ¸© ¹

�

� �

8963,159 1600000

1108963

1

R

Option

�

30.

GR T

UTO

RIA

LS

www.g

rtuto

rials.co.

za

� �

� �

� �

� �

� �

� ��

� ��

11

1

1

11

1 1

ln 1ln 1

ln 1 ln 1

ln 1

ln 1

2

n

n i

n i

n

n

If S Rs n i n

is R

i

iR

is

R R

i SR

i R

i S

i R

Si i

R

Si

i n R

i i

Si

Rn

i

Option

�

�

�

?

ª º� « »

« »¬ ¼ª º�« »« »¬ ¼

ª º� « »

« »¬ ¼

� �

§ ·� �¨ ¸© ¹

§ ·�¨ ¸� © ¹ � �

§ ·�¨ ¸© ¹

�

GR T

UTO

RIA

LS

www.g

rtuto

rials.co.

za

GR T

UTO

RIA

LS

www.g

rtuto

rials.co.

za

MAY/JUNE 2012 SOLUTION

Question 1

Identification: Simple interest

� �

1

Pr

460 400 60

400 0,08 400 0,08

460 11

400 0,08

1

t

or

t

option

�

u u

§ · � u¨ ¸© ¹

Question 2

� �

12

100

300

10,5%

/ 12

0,105300 100 1

12

10,5 " "

2

n

Take as PV

Take as FV

Interest

C Y

n years Calculator

Option

u

§ · �¨ ¸© ¹

Question 3

� �

� �

1

12620000 1 0,12

12

45200

2

S P rt

Option

�

§ · � u¨ ¸© ¹

GR T

UTO

RIA

LS

www.g

rtuto

rials.co.

za

Question 4

� �

� �

� �

18

518 0,15

1 1/

1 0,15 175,83638

0,15

75,83638

5

n

xR

Sn i

iSn is equivalent the same as

i

R

Option

§ ·� �¨ ¸¨ ¸© ¹

§ ·� �? ¨ ¸¨ ¸© ¹

Question 5

� �

� �

� �

2 12

2 6

1 1

0,1251 1

121500

0,125

12

40660,72

1

0,1540660,72 1

6

54684,15

5

n

n

S Rsn i

iR

i

S P i

Option

u

u

§ ·� � ¨ ¸

¨ ¸© ¹§ ·§ ·� �¨ ¸¨ ¸© ¹¨ ¸

¨ ¸¨ ¸© ¹

? �

§ · �¨ ¸© ¹

Question 6

GR T

UTO

RIA

LS

www.g

rtuto

rials.co.

za

� �

� �

� �

4 10

1

1

430 451

0,0841

4

187 454

3

n

n

S P i

SP

i

Option

u

�

�

§ ·�¨ ¸© ¹

Question 7

� �

712

12

25300000 1 0,0925 301900,68

365

0,0925301900,68 1 318572,32

12

16318572,32 1 0,0925 319864,07

365

319864,07

4Option

u

§ ·� u ¨ ¸© ¹

§ ·� ¨ ¸© ¹§ ·� u ¨ ¸© ¹

Question 8

17/07/20121/07/20126 Nov 2011

1Dec 2011

25 days 7 months16 days

GR T

UTO

RIA

LS

www.g

rtuto

rials.co.

za

� �

0,0925 17 25 16 12300000 1

12 12 365 1

319860,34

3

S

Option

�§ ·§ ·� � u¨ ¸¨ ¸© ¹© ¹

Question 9

� �

2200516 0,154 12

39297,56

45200 2200516 0,154 12

2

S Rsn i

Option

y

?u � y

Question 10

Previous

Coupon

Date

09/04/2012

Settlements

Date

16/07/2012

Next

Coupon date

09/10/2012

Maturity

Date

09/10/2038

183 R

H

85GR T

UTO

RIA

LS

www.g

rtuto

rials.co.

za

� �

� �

09 /10 / 2012 09 /10 / 2038

26

2

52 26 2

int

85

Years

Multiply by to get the number of half

yearly coupons thus

The number of days fromthe settlement dateuntil next coupon

erest rate is R

Thus R

Number of days in half year whichthe settlement d

�

� u

� �

� �52

09 / 04 / 2012 09 /10 / 2012

183

09 /10 / 2012 :

100 1 3

9,4 0,10652 0,106 2 100 1

2 2

82,63215 6,8190629

89,45121 4,7

94,15121%

n

ate falls

is H

Thus H

The present valueof theband on is

P dan z

a

We nowdiscount this present valu

�

�

�

� �

§ ·y � �¨ ¸© ¹

� �

� �

85

1830,10694,15121 1

2

91,91965

4

eof thebond back to the settlement

bond back to the settlement dateto obtain the all in price

All in price

Option

§ ·�¨ ¸© ¹§ · �¨ ¸

© ¹

Question 11

� �

int365

183 859,4

365

2,52384

3

H RAccrued erest C

Option

� u

� u

GR T

UTO

RIA

LS

www.g

rtuto

rials.co.

za

Question 12

� �

int

91,91965 2,52384

89,39581%

4

Clean price All in price accrued erest

Option

� �

Question 13

� �

� �

1

1

10

10

1

32,7%

20514

10

0,327 120514

1,327 20514

347344

2

nCMIRR

PVout

with M

P

N

C

C

Option

§ · �¨ ¸© ¹

§ ·? �¨ ¸

© ¹

u

Question 14

� �

� �

45000 50000 60000 55000 60000 5

200000

52000100

200000

26%

4

ARR

Option

� � � � y

u

Question 15

GR T

UTO

RIA

LS

www.g

rtuto

rials.co.

za

� �192

5

Variance

Page Study guide

Option

�

Question 16

� �

� �

18556,84

/ 12

/ 12

/ 12,05

20

1679999,97

1680000 84%

100

2000000

5

PMT

P Y

C Y

I Y

n

PV tothe nearest rand

more

whole amount R

Option

Question 17

� �

2000000 1680000

320000

4

Down PMT

R

Option

�

Question 18

GR T

UTO

RIA

LS

www.g

rtuto

rials.co.

za

� �

950000

10833,54

int 13,5%

6,8%

10833,54 20 12 0,068 12

1419 230 950000

469 200

1

Homeloan

R

Fixed erest

Inflation

Tv Ran r

Option

u y�

Question 19

� �

19000

0,095%

19000

0,0158333

1200000

2Option

Question 20

x

3 3 yrs

2x

-4

4x

6 10

Amount

Received

here

GR T

UTO

RIA

LS

www.g

rtuto

rials.co.

za

� �

4 6 4 40,086 0,086

1200000 1 14 4

1999411,332 1,29080 2 2,846073

1999411,332 6,136873

1999411,332

325803

6 2 325803 2

651606

3

PMT Obligation

yrs from nowis x

Option

u � u

§ · § ·� u �¨ ¸ ¨ ¸© ¹ © ¹

u� u� u

u

u

Question 21

� �

5 12 2 40,104 0,098

20000 1 35000 112 4

33565,27 28838,48

62403,75

5

R

Option

u � u§ · § ·� � �¨ ¸ ¨ ¸© ¹ © ¹

�

S

now

-2

S 7

Amount

Received

here

20 000

N=5

C/Y=12

I/Y=10,4

35 000

I/Y=9,8

N=-2

C/Y=4

GR T

UTO

RIA

LS

www.g

rtuto

rials.co.

za

Question 22

� �

1

0,122 3

4 3

35000 4 3 0,122 3

327 210,63

5

P Ran i

i

n

R a

Option

y u

u y

Question 23

� �

5 3

1

0,122

3

327 10,63

5

0,122327 210,63 1

3

179950,37

1

tmdm

S Pm

dm

m

S

t

Po

Option

� u

§ · �¨ ¸© ¹

§ · �¨ ¸© ¹

2

Question 24

� �

570,08

12

0,08 4,75

45946

45964

31420,70

ct

ct

S Pe

P Se

e

P

�

§ ·� u¨ ¸© ¹

� u

Question 25

GR T

UTO

RIA

LS

www.g

rtuto

rials.co.

za

� �

10000 8,5% 12000 8,75% 15000 9% 20000 11%

25000 11,50% 30000 11,75% 100000 12%

10000 12000 15000 20000 25000 30000 100000

23850100

212000

11,25%

4

Weighted average

Option

u � u � u � u �

u � u � u� � � � � �

u

Questions 26

� �0,019 12,33

2

calculator y x

Option

� �

Question 27

� �

7665,2556 12 0,119 12

800000

5

S Rsn i

Option

u y

Question 28

� �

cos 4 12

34 800000 0,156 12 7665,25

12

124800 91983

216783

3

Total yearly t Interest PMT

R

Option

u � u

§ · u u u � u¨ ¸© ¹

�

Question 29

GR T

UTO

RIA

LS

www.g

rtuto

rials.co.

za

� �

182

20

119,47116 6,2

113,27116

Pr 113,27116 10,41966

102,8515

12,40,108 2 102,8515

2

7884

12 2034

3

H days

R days

Current price Coupon rate

esent value

an

Calculator n days

Maturity date December

Option

� �

? y

?

Question 30

� � � �

� �

4 9100000 1 0,0799 900000 1 0,0799

73530,21 450599,43

524130

2Option

� ��

�

SettlementDate23/05/2013

Next couponDate12/06/2013

MaturityDate?

PreviousCouponsDate12/12/2012

H

182 R

20

GR T

UTO

RIA

LS

www.g

rtuto

rials.co.

za

GR T

UTO

RIA

LS

www.g

rtuto

rials.co.

za

BASIC SOLUTIONS FOR DSC1630 EXAMINATION QUES-

TION PAPER OCT/NOV 2012

1. Identification: Simple interest rate

2 months 10 months now

11,5%

R9 000 R10 000

Savings worth at month 10 – move R9 000 from 2 month’s ago to 10 month’s in future:

S = P (1 + rt)

= 9 000

!

1 + 0,115×12

12

"

= 9 000(1,115 . . .)

= R10 035,00.

Money Short:

R10 035,00− R10 500 = −465,00

She shorts R465,00.

Option [3]

2. Identification: Simple discount rate

31 Aug

R5 000

2 Nov

0,18 d =

t = day number 306 - day number 243 = 63 days

P = S(1− dt)

5 000 = S

!

1− 0,18×63

365

"

5 000#

1− 0,18× 63365

$ = S

S = R5 160,32.

Option [2]

1

GR T

UTO

RIA

LS

www.g

rtuto

rials.co.

za

3. Identification: Compound interest

jm = 12%

m = 12

P = P

S = 2P

t = ?

S = P

!

1 +jmm

"tm

2P = P (1 +0,12

12)t12

2P

P=

!

1 +0,12

12

"12t

ln 2 = 12t ln

!

1 +0,12

12

"

ln 2

ln#

1 + 0,1212

$ = 12t

t =

%

ln 2ln(1+ 0,12

12)

&

12t = 5,80506 years

t ≈ 5,81.

Option [1]

4. Identification: Odd periodes – method given

R375 000

7 March 1 April 1 May 1 June 1 July 1 Aug 1 Sept 1 Oct 1 Nov 28 Nov

25 days odd

10,45%/12 Full=7 months 27 days odd

S = P (1 + rt)(1 + r)t(1 + rt)

= 375 000

!

1 + 0,1045×25

365

"!

1 +0,1045

12

"7

12×

12

1

!

1 +27

365× 0,1045

"

= 404 419,5870 . . .

≈ R404 419,59.

Option [4]

2

GR T

UTO

RIA

LS

www.g

rtuto

rials.co.

za

5. Identification: Fractional compounding

S = P

!

1 +jmm

"tm

= 375 000

!

1 +0,1045

12

"( 7

12+ 25

365+ 27

365)× 12

1

= R404 415,85.

Option [4]

6. Identification: Compound interest

5 years

R50 000 ? 0,1388/52

S = P (1 + jm/m)tm

50 000 = P

!

1 +0,1388

52

"5×52

P = R25 001,79.

Option [2]

7. Identification: Continuous compounding rate

?

57 weeks

R32 412,87

10,15% c =

S = Pect

P = S/ect

=32 412,87

e(0,1015×57

52)

= R29 000,00.

Option [1]

3

GR T

UTO

RIA

LS

www.g

rtuto

rials.co.

za

8. Identification: Equivalent compound interest rate

jn = n

'

!

1 +jmm

"m

n

− 1

(

j52 = 52

'

!

1 +0,149

4

"4

52

− 1

(

= 0,14650

≈ 14,65%.

Option [1]

9. Identification: Effective interest rate

jeff = 100

!!

1 +jmm

"m

− 1

"

= 100

'

!

1 +0,165

6

"6

− 1

(

= 17,67684

≈ 17,677%.

Option [4]

10. Identification: Re-scheduling of debt – equation of value.

now 4 years

10 years

X 3X

2 500 000 0,1225/4

2 500 000

!

1 +0,1225

4

"10×4

= X

!

1 +0,1225

4

"6×4

+ 3X

2 500 000

!

1 +0,1225

4

"10×4

= X

)

!

1 +0,1225

4

"24

+ 3

*

2 500 000

!

1 +0,1225

4

"10×4

= 5,06261X

2 500 000

!

1 +0,1225

4

"+

5,06261 = X

X = R1 650 412,32

3X = R4 951 236,95.

4

GR T

UTO

RIA

LS

www.g

rtuto

rials.co.

za

Option [4]

11. Identification: Re-scheduling of debt – time value of money.

150 000

6 years - now 3 years

X

6 years 9 years

R250 000

0,155

12

0,164

2

X = 150 000

!

1 +0,155

12

"9×12

+ 250 000

!

1 +0,164

2

"

−(2×3)

= 599 863,8759 + 155 803,23

= R755 667,10.

Option [4]

12. Identification: Payments paid indefinitely – Perpetuity

PMT = 3 500 i = 0,112/12

P = R/i

= 3 500

+

(0,112/12)

= R375 000.

Option [4]

13. Identification: Equal payments in equal time intervals plus compound interest rate – annuity

but time intervals of payments not equal to compounding periods thus change compound

interest rate from quarterly to monthly.

5

GR T

UTO

RIA

LS

www.g

rtuto

rials.co.

za

jn = n

'

!

1 +jmm

"m

n

− 1

(

= 12

'

!

1 +0,0775

4

"4

12

− 1

(

= 0,07700.

Thus

S = Rs n i

= 1 200s 10×12 0,077

12

= R215 899,01.

Option [2]

14. Identification: Maths manipulation of equation.

S = Pect

S ÷ P = ect

ln(S ÷ P ) = ln ect

ln(S ÷ P ) = ct ln e

ln(S ÷ P )

t= c

Option [5]

15. Identification: Payments that are made on equal time periods but payments increase each

time period with a constant amount – increasing annuity.

S =

!

R +Q

i

"

s n i −nQ

i

=

!

3 600 +360

0,10

"

s 20 0,10 −20(360)

0,1

= R340 379,99

≈ R340 380.

Option [2]

16. Identification: Payment being postponed – deffered annuity.

R25 000 R25 000

5 years 6 years

0,169/6

R25 000

A now

6

GR T

UTO

RIA

LS

www.g

rtuto

rials.co.

za

A = Ra n i

= 25 000a 6×6 0,169/6

= R561 047,91.

Option [4]

17. Identification: Moving money back in time – time value of money and compound interest.

P = S/(1 + jm/m)tm

=R561 047,91

(1 + 0,1696

)5×6

= R243 834,05.

Option [4]

18. Identification: Equal amount’s deposited in equal time periods + payments made immedi-

ately − annuity due.

R350 000 5 000 5 000

0,124/12 now 4 years

S = (1 + i)Rs n i

= (1 +0,124

12)5 000s 4×12 0,124

12

= R311 882,75.

Amount needed still:

= 350 000− 311 882,75

= R38 117,25.

Option [1]

19. Identification: Sinking fund.

5 years

R275 000

0,16/4

sinking fund 0,14

2

7

GR T

UTO

RIA

LS

www.g

rtuto

rials.co.

za

S = Rs n i

275 000 = Rs 5×2 0,14

2

R = R19 903,81

R ≈ R19 904.

Option [3]

20. Identification: Amortisation schedule.

A = payment

Interest + principal repaid = 3081,86 + 1119,21

= R4 201,07.

Option [5]

21. Identification: Internal rate of return.

Using your calculator:

IRR = 15,23893%

≈ 15,24%.

Option [5]

22. Identification: Equal payments in equal time intervals – annuity or armotisation

A = Ra n i

= 5 311,69a 20×12 0,0975

12

= 559 999,54

≈ R560 000.

Option [3]

23. Identification: Percentage calculation.

560 000 = 80%

? = 100%560 000

1×

100

80= R700 000.

Option [4]

8

GR T

UTO

RIA

LS

www.g

rtuto

rials.co.

za

24. Identification: Total real cost

Total real cost = PV of annuity using inflation rate − PV of annuity

PV = 5 311,69a 20×12 0,0467

12

= 827 543,12.

Real cost = 827 543,12− 560 000

= R267 543,13.

Option [2]

25. Identification: Correlation coefficient.


r = −0,98185.

Option [2]

26. Identification: Slope of regression line.


intercept a = 1 021,13

slope = b = −207,59

Option [1]


7 Aug 12 15 Nov 12 7 Feb 13 7 Aug 13 7 Feb 14 7 Aug 14 7 Feb 35 7 Aug 2035

11,25% YTM

2 = 9,75% c =

n = 22,5 years

= 22× 2 + 1

= 44 + 1 = 45

9

GR T

UTO

RIA

LS

www.g

rtuto

rials.co.

za

P = da n z + 100(1 + z)−n

=9,75

2a 45 0,1125/2 + 100

!

1 +0,1125

2

"

−45

= 87,80282

Add coupon as number of days > 10 days between settlement date and next coupon date.

87,80282 + 4,8785

= 92,67782%.

Option [5]


107,55174 = da 29 0,135 + 100

!

1 +0,135

2

"

−2

107,55174− 100

!

1 +0,135

2

"

−29

= da 29 0,135

92,50885 = da 29 0,135

This looks like an annuity formule. Thus use your calculator’s financial mode with

92,50885 = PV ; N = 29; P/Y = 2; I/Y = 13,5 and solve for your payment which is d.

c/2 = d = 7,35%.

Option [2]

29. Identification: Profitability index

Typing error in answers – Question ignored in October/November 2012 exams.

PI =NPV + initial

initial

1,0514 =25 700 + x

x1,0514x = 25 700 + x

0,0514x = 25 700

x = 500 000.

30. Identification: NPV ; PI and IRR

Investment A Investment B

NPV < 0 reject NPV > 0 accept

PI < 1 reject PI > 1 accept

IRR < K reject IRR > K accept

Accept Invest B Option [2]

10

GR T

UTO

RIA

LS

www.g

rtuto

rials.co.

za

DSC 1630: MAY/JUNE 2013

QUESTION 1

� �

int

1

129000 1 0.115

12

10035

10500 10035 465

3

simple erest

S P rt

option

�

§ · � u¨ ¸© ¹

? �

QUESTION 2

� �int

1

9000

1 8%

4

?

5.12

2

n

compound erest

FV PV i

FV

Y

C Y

N

N yrs calculator

option

�

?

QUESTION 3

� �1

830000 1 0.165

12

26700

1

simple discount

P S dt

option

�

§ · � u¨ ¸© ¹

QUESTION 4

� �38

612

int

1

0.113513300 1

6

18988.31

5

n

compound erest

S P i

option

u

�

§ · �¨ ¸© ¹

QUESTION 5

25000

1 7.5%

6

6

721181.68

3

PMT R

Y

P Y

N

PV

option

QUESTION 6

sin

870000 8 120.092 12

870000

8 120.092 12

6166.12

2

king funds

S Rs ni

Rs

RS

option

u y

u u

QUESTION 7

40000

/ 2

/ 2

1/ 9.56

7

?

401574.30

4

PMT

C Y

P Y

Y

N years

PV

PV

option

?

QUESTION 8

19cm

7 years

513

1

PMT

40 000

01 2 3 4 5

5 years

401 574.30

401574.30

1/ 9.56

/ 2

5

?

251757.24

4

FV

Y

C Y

N

PV

PV

option

?

QUESTION 9

189002279396

0.0995

12

2

Q

i

option

QUESTION 10

6.6 tan

3

calculator s dard deviation

option

QUESTION 11

5;500

15;900

19;1500

7;2000

0.16428

2

correlation coefficient

DATA

DATA

DATA

DATA

RCL r

r

option

QUESTION 12

5500

1/ 8.9%

/ 12

/ 10

10

?

173000

4

PMT

Y

C Y

P Y

N

FV

FV

option

?

QUESTION 13

� ��

6

3

45000 1 0.1159 86.876

90000 1 0.1159 125059.97

115000

326950

5

TOTAL

option

�

�

�

QUESTION 14

1

1

9

1

3269501

95000

14.72%

1

n

out

CMIRR

PV

option

§ · �¨ ¸© ¹

§ · �¨ ¸© ¹

QUESTION 15

2

5000

/ 4

1/ 9.5

/ 4

10

?

131242.59

4

calcultor nd F FV BGN

PMT

P Y

Y

C Y

N yrs

PV

PV

option

o

�

?

QUESTION 16

Pr

3081.86 1119.21

4201.07

2

payment Interest due incipal repaid

option

� �

QUESTION 17

Pr

4201.07 1617.22

2583.85

3

incipal repaid Payment Interest due

option

� �

QUESTION 18

sin

1200 20 12007500 0.12

0.12 0.12

160917.74 200000

1060917.74

4

Increa g annuity

Q nQS ni R

i i

S n

option

§ ·� �¨ ¸© ¹

u§ · � �¨ ¸© ¹

�

QUESTION 19

3 4

100000 1/ 9.71% / 4

4 ?

146779.42

0.971146779.42 1 195732.99

4

12000

/ 4

/ 4

1/ 9.71

3

164869.85

360602.85

3

PV Y C Y

N FV

FV

PMT

P Y

C Y

Y

N

FV

option

u

?

§ ·? � ¨ ¸© ¹

?

QUESTION 20

� � � �

312

12

1 1 1

28450000 1 0.0765 452640.82

365

0.0765452640.82 1 461352.88

12

14461352.88 1 0.0765 462706.60

365

5

tmvm

S P rt rtm

option

u

§ · � � �¨ ¸© ¹

§ ·� u ¨ ¸© ¹

§ ·� ¨ ¸© ¹§ ·� u ¨ ¸© ¹

QUESTION 21

3 28 1412

12 3650.0765450000 1

12

462703.60

5option

�§ ·� u¨ ¸© ¹§ ·�¨ ¸

© ¹

3cm11.5cm

4.5cm

4 March 1 April 1 May 1 June 1 July 15 July

14 days3 months28 days

QUESTION 22

17505.96 20 120.119 12

1600000

17505.96 20 120.0475 12

2708963.16

2708963.16 1600000

1108963

1

P Rani

a

Tv Ra ni

a

optuion

u y

u y

? �

QUESTION 23

6 4

2.5 12

0.1265120000 1 253341.21

4

0.15265000 1 94821.93

12

348163.14

4option

u

u

§ ·� ¨ ¸© ¹

§ ·� ¨ ¸© ¹

0 1 64

65 000 2.5 years

6 years

12 000

Now

QUESTION 24

3 2

5 2

0.137348163.14 1 518119.51

2

0.13785000 1 164878.56

2

518119.51 164878.56 353240.95

3option

u

u

§ ·� ¨ ¸© ¹

§ ·� ¨ ¸© ¹

? �

QUESTION 25

� �

� �

� �

1

1

1

1 1

1 1

1 1

1 1

1

m

m

m

m

vmJeff

m

vmjeff

m

vmjeff

m

vm m jeff

option

§ ·� �¨ ¸© ¹

� �

� �

½ � �® ¾¯ ¿

QUESTION 26

� �0.165 512000

27383.57

3

ctS Pe

e

option

u

QUESTION 27

68

132

183

10.5 0.07955680.07955 2 100 1

2 2

122.68844110 7.048922876

129.7373339

129.7373339 5.25 134.9873339

0.7955134.9873339 1

2

131.24248%

4

a

All in price

option

�

§ ·�¨ ¸© ¹

§ ·y � �¨ ¸© ¹

� ? �

§ · �¨ ¸© ¹

QUESTION 28

34 x 2 = 68 Maturity date

8/10/2047

183 days

132 days

Next coupon date

29/05/20138/04/2013

Prev coupo Settlement

8/10/2013

H

( )

( )

14983 ( )1.034

( )

1.034 14983

1.034 14983

0.034 14983

14983

0.034

440676.47

5

NPV initial investment xPI

initial investment x



x x

x x

x

x

x

option

�

�

��

QUESTION 29

444391.83

2 444391.83 2

888783.67

4

x

x

option

? u

QUESTION 30

� �

29

74

181

0.1357.35 290.135 2 100 1

2

95.50885 15.04289

107.55174

int 74

24 / 06 / 2013 10755174 7.35

114.90174

0.135114.90174 1 111.87288

2

111.873

a

This is a cum erest case dueto the fact that R

P

P

clean price

�

�

§ ·y � �¨ ¸© ¹

�

�

�

§ · � ¨ ¸© ¹

88 7.30932

107.56456%

1option

�

DSC 1630 OCT/NOV 2013

QUESTION 1

� �

int

18000

2011 0.0847

12

15773.33

3

simple erest

SP

rt

option

� § ·� u¨ ¸

© ¹

QUESTION 2

0.1429

811 0.1429

12

15.79%

5

simplediscount

dr

dt

option

� � u

QUESTION 3

� �38

612

int

1

0.113513300 1

6

18988.31

5

n

compound erest

FV PV i

option

u

�

§ · �¨ ¸© ¹

QUESTION 4

570.105

52

32412.87

29000

ct

ct

continous compounding

S Pe

SP

ee

u

QUESTION 5

7 2

2 4

0.11335000 1 75551.82

2

0.10150000 1 40957.34

4

116508.49

4

S

option

u

� u

§ · � ¨ ¸© ¹

§ · � ¨ ¸© ¹

QUESTION 6

252032

2

calculation

option

35 00050 000Nov2 3

QUESTION 7

52

100 1 1

29.61 100 1 152

26%

1

mvm

jeffm

vm

vm

option

§ ·§ · � �¨ ¸¨ ¸¨ ¸© ¹© ¹§ ·§ · � �¨ ¸¨ ¸¨ ¸© ¹© ¹

QUESTION 8

200000 12 60.084 12

2145.84

S Rs ni

Rs

R

u y

QUESTION 9

1 Pr

4200000 0.156

12

10400

cos 4 10400 12 2145.84

67350

5

t

Total yearly t

option

u u

u � u

QUESTION 10

0.07911250000

4

24718.75

1

Pertuity

R iP

option

u

QUESTION 11

� �

� �

� �

61212

261 75000 1 0.0837

36

75447.16

0.08371 75447.16 1

12

78660.20

201 78660.20 1 0.0837

365

79020.96

5

n

S P rt

S P i

S P rt

option

u

§ · � � u¨ ¸© ¹

§ · � �¨ ¸© ¹

§ · � � u¨ ¸© ¹

5 April21 NovSeptJuly 1 Nov

4.8cm

5.3cm

26 days 6 months20 days

QUESTION 12

6 26 20 12

12 365 10.083775000 1

12

79020.29

3

1

tm

P

option

vmS P

m

�§ ·� u¨ ¸© ¹§ ·�¨ ¸

© ¹

§ · �¨ ¸© ¹

QUESTION 13

4

4

1

0.089000 6000 1

4

9000 0.081

6000 4

9000 0.08ln 4 ln 16000 4

9000ln6000

40.08

ln 14

4 20.48

5.12

2

tm

t

t

vmS P

m

t

t

t

t years

option

§ · �¨ ¸© ¹

§ · �¨ ¸© ¹

§ · �¨ ¸© ¹

§ · § · �¨ ¸ ¨ ¸© ¹© ¹

§ ·¨ ¸© ¹ § ·�¨ ¸© ¹

QUESTION 14

95000 2 5 0.186 2

601708.66

3

P Rani

a

optionj

u y

QUESTION 15

� �2 4

1 601708.66

0.186601708.66 1

2

295410

4

nP S i

option

�

� u

�

§ · �¨ ¸© ¹

4 yrs 5 6 78 9

0 1 2 34 5

601 708.66

QUESTION 16

35000

500

1/ 11.32

/ 12

?

35000 500 0.1132 12

54 ( )

FV

PMT

Y

C Y

N

S Rs n i n

n months calculator

��

��

�

y

QUESTION 17

790 000 20 12 0.1375 12

9680.70

9680.70 20 12 0.092 12 1060.749

1060.749 790000 270749

3

P Ran i

Ra

R

TV Ranr

Tr

option

u y

y y �

QUESTION 18

Maturity date

14/12/2036

182 days

28 days

Next coupon date

17/05/201314/12/2012

Prev coupo Settlement

8/10/2013

H

14 /12 / 2036 14 / 06 / 2013

23

Years �

We must multiply by two to get the number of half coupons and add one to get “n”

� �47

28

182

23 2 1 47

2 100 1 2

9.2 0.10447 0.104 2 100 1

2 2

83.78654 9.23124

93.01778

93.01778 4.8 97.81778

0.10497.81778 1

2

97.05788

2

nP da n

a

P

option

�

�

�

u �

� �

§ ·y � �¨ ¸© ¹

� ? �

§ · �¨ ¸© ¹

QUESTION 19

96.80770 32.09888

64.708820

7.5

64.70882

15

1/ 7.87

1

PMT

PV

N

Y calculator

option

�

QUESTION 20

sin

3600

360

0.10

20

360 20 3603600 0.10

0.10 0.10

412380 72000

340380

2

Increa g annuity

Q nQS R S n i

i i

R

Q

i

n

S S n

option

§ · � �¨ ¸© ¹

u§ · � �¨ ¸© ¹

QUESTION 21

ln ln

ln

5

ct

ct

ct

S Pe

Se

P

Se

P

S

Pt

c

option

§ · ¨ ¸© ¹§ ·¨ ¸© ¹

QUESTION 22

4

12

1 1

12

4

0.0775

0.077512 1 1

4

7.7%

1200 10 12 0.77 12

215900

2

m

n

General annuity

vmvm n

m

n

m

vm

vm

S Rs n i

S

option

§ ·§ ·¨ ¸ � �¨ ¸¨ ¸© ¹© ¹

½° °§ ·? � �® ¾¨ ¸© ¹° °¯ ¿

u y

QUESTION 23

/ 500000

75000

190000

40000

150000

180000

2

2

7.78%

1

Calculator DATA

DATA

DATA

DATA

DATA

DATA

nd F cash

nd F CA COMP

option

o � �

QUESTION 24

ln 1

0.19412ln 1

12

19.245%

5

continous compounding

vmC m

m

option

§ · �¨ ¸© ¹§ · �¨ ¸© ¹

QUESTION 25

int

2080.54 2014.27

66.27

3

Monthly payment principal repaid

erest dueat monthend

option

� �

QUESTION 26

Nov

End of May Aug 15000 Oct 15 000 Dec 15 0002 months

4 months

415000 1 0.10 15500

12

215000 1 0.10 15250

12

15000

45750

1OPTION

§ ·� u ¨ ¸© ¹§ ·� u ¨ ¸© ¹

�

QUESTION 27

0.90828

4

calculator r

option

o

QUESTION 28

Nov 10 months 28 months 32 months

3 000 18 months 4 months25 000

28 18 46 6 6

12 12 12

14 9 2

9 2

14

0.1475 0.1475 0.14751 3000 1 25000 1

6 6 6

0.1475 0.1475 0.14751 3000 1 25000 1

6 6 6

0.1475 0.14753000 1 25000 1

6 6

0.14751

6

X

X

X

u u � u

�

�

§ · § · § ·� � � �¨ ¸ ¨ ¸ ¨ ¸© ¹ © ¹ © ¹

§ · § · § ·� � � �¨ ¸ ¨ ¸ ¨ ¸© ¹ © ¹ © ¹

§ · § ·� � �¨ ¸ ¨ ¸© ¹ © ¹

§ ·�¨ ¸© ¹

19607.4519607.48

5

Approximately

option

QUESTION 29

1

1

8.04

Positive NPV

OPTION

PI greater than

IRR greater than

QUESTION 30

17287.42 2310.26

40497.68

3option

�

· 23. Identification: Annuity u64 10 4 40 40 0,1225 2500000 1 4 0,1225 2500000 1 1 0,1225 4 3 4...

Documents

Transcript of · 23. Identification: Annuity u64 10 4 40 40 0,1225 2500000 1 4 0,1225 2500000 1 1 0,1225 4 3 4...