Bài tập môn toán tài chính

.
~
l\Thonl 10.
(~au 1 O~1
M~)tdJy nicn kim c6dinh, 111(1ini011Kim b5ng a Usn \~j uuqc
111\1"c
hi~nvaocac th6'ioi6111J,2, ]. , n. Tim giatt! 11m dtr,yc Cll(l (Wy llicn kinn16 nlo tl1('yi(li0m (n + k)bi2t
.
= 5%; n =
10: a: 1.0
()
0; k ==
r S{~li01] thuum:}c vaotho'i di0m 20 )[1:
+0.05)1° 1
0.05
i iX(1+0.0
5)
1
O :::: 2Q.4788,
06 USD
Cau JO.2.
M(lt day
nicllkimc6diJ)h,m&i
Ilicn kim h~ngn usn va OI1(;)'ctlwc hi~n van cae thai diem 1,
2,3, , n. Tim gia
tl'! t/mdlrgCClJa day nicn kim do vaothai diem (n + k) bitt i= 5%; n=
Io~ 1.100; k = 9.
);>
Se~ti~n thu c.1uqcvan theri <1i0n1 19/a:
(1 + 0.05)10

- 1
V20 =
1 1
00 x ;.c
. .

X
U.O:J
0.05) 9=
2.1.463,68 US!)
.Ciiu. 1.0.3.
MOCClay
nicnkim c6 c.1inh,)]]&i
nicnkim biinga USD \,(l.dln,rc
th~chi~n.vao
cactl1iJidiclp I,
2, 3, , n. Tim gia tri thu dlrqc clIn duynien kim do vim thai (li0m (n + k) bi6ti=:t 5%; n=
9; a = 1.100; k=8.
.\/ .A,ItQl)1)/'h>~-I-O,~}~v-~
~ CAT~)E
~'17.92n,38USD
~=t
~f)S-
~C.a.u
J 0.4.
M\)tdaynicll
kil11
cd (ljnh,
mOiJlicnkiJnb.1nga
USDvAdLTqL'tlnrchi~11 vap Cactb6'i .diem 1,

2,3, n Tim gia tri thu du~)'c d5Yllienkil11 dO.V[loth6'idicm (n+ik) bi0ti ~ 5%; n =
9~ a==1.300; k ==7.
';r- 20. 170,13 USD
Ciiu 10.5.


Me)tdJy nicnkim c6 (linl1, mAi nien kiln lx1ng alJSD d du\yc
tl1\rc
hi~nvfiO de thi)'i dil~1l1!,
2, 3, ,
.,ll.J'lmgiil tr! thu (/lr<,YCClllld5ynicll ki'n1
tkl do
tl1lri
di0m (n+ k) bi01 i ==
S(~():
Il~:
(} : 1.4tH):
k == 6.
r I7})f0 ,4() .lJSI)
Cau 10.6.
1\1(,[ di:iy
!lien kim cd djnh, I1lt;;nicn kim bing a USD vuduq'c th\fC hi~n vao de
theri di~m i,
~. ~, n. Tim
gi{l tri thu c!m.,c Cl'!a day ni(~n kil1l (h"lV?O.th(1';
di2111 (11 -+- k) bi&t
i = 5°/(\: n 0 "
8: 3 =1.500;
k =-5.
>

18.28lJ)3USI)
Can 10.7.
i\1()t
day llicn kim c6djnh, 1116il1ien kinl piing (lUSD v~dtr(fC tlwc hl~ll vaodc:thc)'i
di~m
2. 3,
.'
n: Tim gia tft
thudlf~)'C nia
daynienkillldo\raot!1(ri di6m (n+k}hi~t i= 5%; n ==
I: a ==1.600~ k ==4.
;> 15834,66USD
cantO.8.
M9t
daynienkinlc[Ydinh,m6.i niellikinl b5ngalJSD vii dlI9'cjlhfchi~n
v~ocacthoidj~m 1,
2, J,. '., n. Timgiatrit1u1
(ltrqcc;tladaynicnkilll
dlyyhotlu\idi&Ill .(n:+-k)lJi~t \"=5%; n ==
7~ a==1.700; k==3.
~ 16023,17
USD
eau 10.9
'.
,
_
'
," '.
".,.>,>,.' .'.
.',

c" ·
. ' ,
;
.'.
'.
' '.'
MQtdaYIlienkitl1?CQdjnh, m6i'nienkim bang 'a US9'va
du<yc
tl-hrchi~nyaodlc thaidi2ml,
2, 3, .,n.Ti\11igi~ltritlnrdll'9'Cc;l'la df1yniCi1kimd() V<'l0th(Yidi6ni(n'+"kjhi&C j.=<5°/o;n''"'
6~
a:=;. 1.80{}; k ==2.,
» 13.498,40LJSD
Call .1 O~10.
MQfdayniel1kirhct1 djl1h,1116inic\'l
k1tnhftng'~flJSD Vfldm)'c
thVcl1i~11v~ocacilliai
di2m 1,
2, 3, .",n. Timgi5trrr';"Udm)'cdbd5Y
nicn'kim d6 vacJl1(,),il:li~n1(f;+Kf,t)i8t i= 5%; !l c-=
6:
;~::':.:: 1.9C<J';k== 2.
~14.248,30 lJSD
/
,-
Nhonj 1J
(lu-11 1.
M(>t
tlnrung phi~u
COm9nhgi'l

C,
th<':rih~m JOnam. dw;rc
dcm chiGt
khfluthco lai gQP vai lai
suat i. Tim s01i6n chidtkh.1u bitt: C== 19.000; id 5%
:;" 50 titn chidt khAu :
Ciiu I1.2.
+
i)n
== 1.9.000 x
7.335}65
M(lt tlmung
phiducolll9nh gia C, thbi h?n 1Onam duve dcm
chi6tkh~11theoJ~i g(>pvai Wi
sll,h i. Tillls6ti~n chi~t kh~u bi6t:C== 19.000; i = 5,5%
}>
.s6ti~n chidt
khAu
:
E ::: C - I :::
C-C.Cl+i)1l
=19.000 x[1"'(l + 0.055)-lOr:;:::-7:876,82
Cau 11.3.
MQt thuO'ng phi6u co Ill~nh .gia C, thbihg.I1 JQ
115/11du9'c
(1cInchi8tklj4uthe,01frig~)p
v6'i Wi
.
sufrt.i. Tim S(1
ti~nchi~t

kll<1Uhi~t:(' ~.'lKOOO;
i d6%
AS, 0lfD
~
It
f,{)l)V ( A 1-~O£'yo

~E ==7.948,89
~ ~~)~j ,
Ciiull.4.
MOt t/mung phil~u c6 m9nh git! C, thbi IWIl 10 niimuu'.VedcH1
chiGrkIH111tIlciJJ£iig~)PV6'i liIi
sw1t
i. Tim s<1litn chi0t kh.1ubi6l:C
18.000; i=6,Y~'~ ,
.
1lO
». E ==8ALO,93
A'?/~~l~/(}OD (l+09C \) ,~
?4'W)3~
C~lu ll.5.
M~)Itlmang phi~u co l1l<;uhgia C, Ihbi h~lIl 10 nam uu~)'cdenl chiGt kluiu theo lai g9P Vlri Wi
wAn. Tim
s6titnchi6tkh~ubi6t:
C= 17.000; i ==7%
~ r~ ==8.358,06
C:IU I J.6.
M~)t tlmung phifu c6m9nh giaC, t!nxi h~lIrrO n[im dlf~),c dem chi0t kh:1u theo !iii g()P v6'i Iili
su,h i. Tim S(~ti~n
chi0t

kh,1ubi~t:C ~=17.000; 7,5%1
/;> E S.7~1,70
r-
Caull.7.
Mc')t
tlmang phi~u c6 m~nhgiaC, thiyi h:.lll IOnftmdm)'c clem chi~t kh5u then Iili g()P voi lfii
su~ti.TinlS(\ ti~ll chi~tkhAu l)i~t:C ~.16.0{)O; i.:-~:So '()
~l~ == 8.588~90
C,lull.8.
Mc')f
thu(mg J>hi2~c6111~nh giAc,. thai <h~ml 0 namdlfgc clem chi~t khau theo. Hi!g<)p
vo'i 1:'1i
su,1ti. Tinl s6ti6n Chl~tkll(1ubiEt:C= 16.000~
i ==8,S~/~
Cau.] 1.9.
Mot thuangphi~u co n1~nh gin C, thai h~lI1
]
0 nam duq'C demchi~tkhfiu thcoIaig<)p vbi Jili
,-
~
.
suat
i.
1"hlls6ti~n
chi8t'khfiu
l)i~t: C == 15.000; i == r9%
.}>'.E
=8.663,84
Call 11.10.
M9ftlllf()'ngphi&t1com~nh gia c, th(yih~m

]
0 namdlfqc dem.dliGtkhAutheo I5ig<)p vbi liii
su5t i.Tin1 s6 ti~n chiEtkh5u bi~t: C = 15.0()O; i==9,5~~
-
~~~
C;fiu 12.1.
M,)t day 20 nicn kinl dlTqc thvc hi~nvaocac,Jh(yidj~nl l~ 2, 3, , 20.Tfr thC1ik)' thunhflt
.
dEn thai k} thu k, 15isu5t I thaiky IiI 8%. Tu-'Jh(xi ky thlrk + 1 tnrdi.laisu5t
l11(>t
thai k)'
9~~LTinhgintr! cuadaynicn.kfnl.>tvi thai<.1i&nl.g6cbi&t:'a==2.000~ k ==11.
\11',' ,1-(1
+ o.osrn
"
"
,1 (1+O.09r9
"
'
\ \1A\
= l.OOOx
'
.+ 2.000x '.
.
=19.420,45
~
:'0'.,08 0.09.
:::'~.,
Cuu 12.2.
~-Ktb L{~).~,

<~~&
J
s~y
MQtday 20 nicnkinl duqc th\fChi9n VelOcac:.rl;llai.di&nl.J ,2, 3, .,20. Tirtnai k5rthu
nh~t
d6n thai
ky thu k) Iaisu5t l"tho-ikjrJil.8%. Tathai, ky thlT k + 1 tra dj, UEsuiltm(>ftha.l ky
9%. Tinh gin trj cuaday nien kinl t~lithaidienlg6c.bi~t:a ==2.000; k 12.
~
1 - (1 + 0.08)-12
. 1 - (1 + 0.09)-8
Va== 2.000x ' .+ 2.000x.'
. .
= 19.468,06
0.08. 0.09
4A.ofoO)
) b~
~ '\
O)ll";tWl/~.,,
Cau12.3.
M(>tday20nicljkirrrdl1<;rctlwc'hi~llvaocacth(yi' di6m 1 , 20. Tuthai kythuJll15t
d0n
thai k),thi'r k, lai suar
1.
thaik)'la8<)1ti.
,TiT,thNk)' thu k + I, trq di: ifti suAtmQt.thO'iiky
9%. Tinh gia tri clia day nicn kim t~li
t1iZrj
di~m g&cbi0t: a = 2.000; k ==13.
,- t-

~ V
:::
19.508,76
V ~ ~
f
A._~\O~)-4~
t
~}0lA}b~2 -I
rQ tlE " < > ,
. ,.~~
CuuJ2A. 1
~.~
'~/O)vO)"
M0fday 20nicnkirn
duQ'c th~TC
hi9n vflOcac 1h<1idi&lll.l, 2,3,. ,lQ.Tlr tho] ky thu nh51
dtn th(yik)' thu k,lai suM 1 thai ky la8%. Tirthai ky thtrk+ Itr&di,Jai sw1tmQt thaik)'
9%. Tinh gicltr!,Clladay nicn kin1 t~li th()'icli6111g6cbi6t:a==2.000: k ==14.
y
v = 19.54.3,04
Cau12.5.
M<)td5y20nicn kim
duqc
thvchi<;I1,vilO cacth(yic1i6m L,2,3, ,20. Tlr thai ky thlT nh~11
d~n th()'i k); thtf k, 15i sufrt 1 thcy) kylA8CXL1'trtllcJi k)' thtrk+ 1 trfJ(1i~ 15i 811,it lllQt th(fi k)f
9(~L"rfnh giiltr! cl'la day nicn kinlt~lith(\i di0111g(\C
bi0t:
a == 2.000:k
5.
).> V

= 19.571,~2
y',
~
\J ~
i
~
','1-
A r-~.~I~)
,
C\C]
r~.
.
A
,A.
KJ
., G\
(~.
,
·
1\0 ) J 0' J
(")"
- S-
_{
~ 1'-
A ~10~)
OjJ~
~
K
())1)~)

CfiuJ2.6.
r lot
day 20
nicI1'kimdU'O'tthUchienv;'\()cdC
thai .diem .1,2,3, , 2Ct 111 thai h' thll' nh,81
.
.
-
.
,. . .
.
. . . . . . . .
.'0
.
den thai k)' thLI'
k,15iSll~tlthai k)'
138%.liu'th6'ik)'
thLr k + Itra,di,laisu8t ll1QtthO'1k~'
,. ~
'
90;;l. T1nhgi.1 tricua claynicn kimtc;li thcridienl g6cbiet: a = 3.000;K
-,c11.'
:J
,

_ , '7
.
A'3<Ct,I&'):1J
A U)l)~)
r V

' '-'-
29.130,67
:>rY6\)
1
',~ <\
~'tV5\)
1
'r
~
(h CJ R
. @;tJf!)
A::t
0~S)~
~
Cau 12.7.
M(1tdTiy
20rtl~rtkimalT<.Jct1wchi~f1
vao CilCthbi dieFl1.I, 2, 3, .,. 20. Tirtl1t)'iky th{1'nhflt
a~n thb'iky thit !c, Hiisu5tl thai ky la8%.ilXt thai kythuk-t-1 lro ai, Hiisu5tn19t thai k)'
9%. Tinhgia HjelIa day nien kim t~li
th&idi~mg6chi~t:.a""3.0.00;k=
12.
:YV=:29.2;02,09
Call 12.8.
M{)tday 20nien kim am!cthvchi~n vaocac
thaidi~111
1,2,3, .;.,20. Tirthaik)'thirllll:lt
d~n thai. k)Lthlrk, 15i su5t 1 thai ky 1ft8%.1\1' thai k),thlf k + 1 trodi, luisu5t
1I10t
thai K)'

9%. Tirihgia trjcti:)
day hi
enkitlif{litllo-i.'difrl1'i;g6icbf~b)(i,=;3i.ooOr
k.7 j3.
>:"V,':::: 29.263,15
Cuu14.9.
M<}tday 2bnicnkil11duqc tlwc hi~n vaodcthiJi c1i~m I, 2, 3, , 20. Tll' th0'ik)'
thtrnhAt
"
. .
'
denthO'iky thu. k, laisuat.l thtyi kylfl 8%.Tlrthbik)' thlrk +1 tr& dkU.lisqat m()t.th('I'iky
9%. Tinh.giatrj cuadaynicil kim't~i thaidi8mg6cbiGt: a= 3.000;1\:;:=14.
> V =29,314.,55
Call 12.10.
Mc)tday20nicn kimdll'(Jcth~fchi~11 v;'lodic tht)'i diem \, 2, 3" ,20.Tirthai ky tl1lrtlhtlt
d~n thai ky .th(r k,lai'su:1t Ith(1i k)'lli 8%. Tir th(1i ky,thLf k 1Jr<y:cli,15isuJtm()! tho'i k.5:
9(~,~.Tinh gin tricua day l1icnkimt<.1i tho-idi~m g6cbi~t:a= 3.000;1<==15.
>v ==19.3S6,9E3
I
I
I
I
I
I
I
I
I'
I
I

I
I
Nhonl 130
Cau 13.1.
M(ll nguoi mua mOl 10
hAngco
3 phuung (lil tnl tifi1
> l)huo'ng
anA:
tr(i<ngays6ti~n S.
> Phuang an B: tfa b~ngn1(.)fdiTy.I1 nienkim cadjliH.M6ihienYimb
VSD.Kicn kil11
dAuticn dugc
th\1"c
hi~nsau khimua IthaikS', LaisUfrtm6itha) k)rlaS%.
» Phuang an C: tn! b5nglnOtduYlll pien kln"lc6djrIh, m6i nicn ki11lc l.JSD.N ien kll11
dAu tien dugc
th\1"chi911sau klli nllla r thaikji. Llis1l5t m6i thaikjrJa 5%
S:1px0p 3 pJnrang c.lntrentheo tll([ t~rtang;dallbi0t:
S == 10.000;
11
b=900;
~,
If,} thcophuang 5n.2:
1-(1+ 0.05)-16
Vo = 900 x
.
,
== 9.754-
'0.05

> l'rii tlleo phlrang an 3:
~ S;}px&P:~.1\, C
.CauI3.2.
M(>tnglrai muam(>tI6 hang cc.'>3 plnrang ,Ill tl"<1ti~n
,. I)hlrangan
A: trt1
ngay 56 tj~n S.
);> Phuang an 13: tni bAng Il1Qtdily n nien killl el1<linh.Moi nien limb USD. Nicll kim
clAnticndugc thlJc hi911 saukhi mua 1th(YI k)'. UiI su[1t m6i tht')'i ky hi 5%.
Y Phmyng an C: tnlbAngm<.')td5ynl /lien kim cl1 dinh,.m0i nien kinlCUSD.Nien kil1l
dAu tien duge thlJc hi~1l sau khiJllU3
1
thai k)'. Lui su;1t m6i th()'i k)! In 5%
S5p x~p 3 plllwng ,In tren thcoth(r lIJtnngdan bi~t:
5==1
O.OOO~
n == 16; b == 900; In==22;c>==800.
~ r]'r~i theo ph U(Jl1g' ~ln2:
l-i(1+0.0SJS16
Vu=<JOOx
.0.05
9.751.
~' 1'r~1 then phuo'ng~in3
:" StlP xcp:
13, /\,(~
.
Cau 1303.
M<)tngnai
mun
111<)t 16hang cb 3 phuang{\l1 tn\ ti~11

, Phuang an A: tn\ ngay
~;()
ti2n S.
}> Phuang (111B: tra hllng m()t day n nien kim of>djnh. M6i nien kimb usn. Nicn
kil11
dAuticnduqc tlwc hi~n SilUkhimUH1 thai ky. Uii suit m6i thiYik5,la 5%.
» Phuong an C: trab5ng mOtday mnict1kim
C(~djnh, m6i nien killlcUSD. Nicn kim
d5u tien duqc t1wchi~n
saukhimual therik)'. Uli
su5tm6ithalkyl~'5%
sAp x~p 3 phlTangan trentheo thi'l t\rtang dlin bi~t:
S = 10;000; n = 17; b= 900; m= 20; c=800.
» S~p x~p: C(9.969,77),A,
B(10.146,6)
Ciiu13.4.
MOtnguaj l11uamOt16hang co 3 p1urong{mtril ti~n
» Phuong an A:tra ngay 56 tiEnS.
);> Phuang an B: tra b5ng mOt day n nien kirn c6 djnh. M6i nienkim b USD. Nien kim
.
d~ufienduqe tln)'chi~nsau khilTIpa.lthai
ky,Uiisu5t m6i thai ky 1a S%.
);> PhuonganC:trab5ngmOt
Q5Ylnnien kim c6dinh,m6i
~ienkimcUSD.
Nicn kim
dfru tien duqc thl)'ehi~n sau khi. mual tho-ily. Uii.5U5t m6i thaikylit 5%
~
-
,

':.
;-
_~'.~'i
.
'
.,.'. ,-
:
, ,.
.
' '
Sup xep 3phuanga.11 trcll then thu. t\r.tang dan biet:
s == 1 O.OOO~
. n == 17~
~
Sftp
x€p:A, B,.C
Cuu13.5.
MQt ngubimuarnOt 16hang c()3 phtr<mgim trati2n
» Phuong all A: trii llgay s6ti~llS,
> Phuangan B:triibiing
tnOtdaynnicllkim
cAdjl:h. MGiI1icn kin1hUSD. Nicll kim
d5u tienduQ'c tlwc hi~n sau khi 1l1ua 1thai k)'. Uiisuatmoithbi
kyJa
5%.
>-
Phumig ane: trab5ngmQt<.H'iy
mnienkirilc{ldinh, 111QLnienkimcUSD. !'lien kim
dAutiendu(1c thue hien sau khi tl1UaJthal kv. Uii su5t n10i thaik\I la 5%

. ."
. '
01
sflp x0r 3 phmmg an tren theo thlthr tnngdlln hiet:
S = 10.000: n = 17: h =
9()()< 111= 22: c= gOO.
; Sap r"~\):;\~ l1C"
, 1
,
Cfiu 13.6.
\1 dt n JlfCyi ll1Ua!1111i ':(. J-
-111a c/~ '{ Ptft"yq 0 UP tra ti
;~>-
. b. ~.
-
.;;.
-

-b '-,
J
__'
-
~
'LJ'-
b! . -J
_ _
? Phuo~ng ~inA: tra ngayso ti~n S.
r PI1lfaHg {ill13: tta b5qg.l;lQl dilyn nien kim c6 dinh. MoiinienkirtlbUSD. Nicn kim
d5u ticn dw,Yethl!ehi~nBaU khimua
I

thO-ikjf,
Lilisu5tmOitho-ikyla 5%.
>- PhuO'ng [laC: tra bftngm9tdaym nicIIkime6.djnlI,moi nien Ki.~leI.JSp.iNicn kim
d.1uticn dlf~Yethl!chiMsaukhinIUal thai k5'.)Laisu.1tmoi tbfiik)' hY5%
SJp xfp 3 phlfO'ngantrcntI1C()lhlrt~f.tang d5nbi6t
S == 20.000; 11 == 16; b==] .800: 111 == 20~ c=1.600.
~S5pxEp: B,C, A
enu J3.7.
MOtnglrai 1l1UanlQt16hang c6 3 phlfangan
{ra ti0n
r Ilhu()'ng {illA: tra ngay S(~tien S.
);>
PlmO'llg an B: tr<ibEing11191daYOJlicnkinlc6djnh.Moi nicnkimb USD.Niienkim
dfiut ieu quqcth\tc. hi~n.saukllimu a ItlltJi
k
Y.?4aisf)5tm9gti!I!iJi~)ri~a5%.
> PhuO'nganC: tnihiing.ul<)l.daym nicnkim c64inl1,moinienkim cUSP. Nien Kim
dJuticndlrqc th1!ehi~n sau khi muaj thai ky. Uii SUi,1tlU6ithaikyla 5%
S;1px~p 3 phuO'ng an trcnthco thu t\f tang d&nbi&t:
S == 20.000; n == 16; b == I.800;ul==21;
~'sjp- x~p: B, l\,C
C,lU 13.8.
MOt nglf('yi mUll l11<)t 16 h£mge()3plmO'llg {\11tn1 1i0n
~ I>haollg (lnA: trtlngays(1 tj~nS.
» Phuung~nB: tni bUng !1l0tday nnicnkimc6 dinh.M6inicnkim b USD. Nicn kirn
d;1u ticn duqc th~fe hi911 sau khi HIlla I thb-i k51. Lili sufit n1(~ith(yi k)! hI 5%.
),> Pilliong unC: Ini biing 111\)1day Innicllkilllc0 diuh,rlloi fIicn kim c USD.NiCn 1im
d;1u licn dlfqC tlwe hi~n sall khi mua I th(yi kSt.tili su;h n1(~ithl'rj
"'5"
L:I Y~1)

sfip
x0p
]
plul'Ung (Ill trcn then
tht'1'
t~l't?ingd;1n hijL
s ~= :2().
000: 11 == 17~ b ==- 1.~00 ~ III , = 20: c IX)OO.
", sjp xcp: C, f\, 13

Cau 13 9.
tl.lt)tngu()'imuc! m(>t10
hiU1gC[)3.phtn.),l1g[tntrati~n
> PhuO'ng an A: trangay s6ti~n
So.
> PhuO'nganB: tftl p~ng ll1QLduynnienkH'l1 c6 din11.Mainie! l'~rnbUSD. Nicn kin
d~lI lien dugc thgchignsau khil11ualt!1&iky. Lai suAtm6itho-IJ.;.yh'r51%.
>- P11ll'O'ngan C: tra biing m(>tduy<m nien.~in1c6dil1h, moi nien khl1 cl.JSD.
14;(}nkim
dau tiendmJc Owe hi~11saukhi ll1l.HlI t!1(riky. Uiisu,1t m6i thaik)' laS/i)
S5p x2p 3 phmmg tl11tren th00 thtr tv tang drln bi0t:c
S
~ 20.000; n
~ 17; b = LlWO; m= 21; c = 1.600.
» Sfillx2p:A,
B,C
CaD
13.10.
Mgtllgl.ro-lnlbail11QtJohang co 3plwO'ng all.trirti~n
> Pl1Hang{in A:tra ngaYs6ti~nS.

dilu lien (hrQ'Gt1Wcl1ign SIltlkhi mua 1.thaik)' Uii suat moi thai k)'h15%.
S5p x~p3 phlfO'ngimtren th~QJl1tr t1Jtang dAn bi~t:
s == 20.000~
n
==16; b==1.800;
> sfipx~p:-B,A,
Nhorn 14:
Call 14.10
M()l nh6m tf1lf<Jl1gphi6u c6 m~nh giaC, th<'rib?nJil n n,5m du<,1'cdClnchi~t kh;1u theo Jili g<)p
v('11laisu~lt 1£1i. Tinls6 ti0n
chi0t khilu bi0t:
C ==1.000; i ==0,08;n== 4
);> S6 ti~n chi~t kh5u:
E = 1OOOx[l ~Cl + 0.08)-4J = 264} 97
Call 14.2.
M(lt nh6m thtr,.tmgphifuc6 m~nhgiaC, th(rih$nJan.nam dugc dem chi8tklu1u theo.lui g(>p
vai lal su5t lai.:Yinl s6 ti~nchi6t kh{1ubi~t:
c == 1.000~
j
== 0,08; n == 5
~ S(1ti~n chi~t kh,iu:
E = 1000xll- (1 + 0.08)-5] = 319}42
Ciiu 14.3.
M(ll l1h6nltJnmng phiJu cO 1119nhgiil c, Ihaih~1I1JaWnanJdJrqc c1eIll.qllji0t:~11A\.1tl]colaig()p
v6'i JilisuJtla i. Tin1
s6 tiEn
chi~t kh5u biEt:
c == 1.000~ i ==0,08;n ==6
>- E == 369,83
.

-')J
/{Cfo'O.'f-(t~ (A -r~
Or )
.
~
Cau 14.4.
M<)t nh6mtlnmng
phifu c6 11191111
gi<i C, thai h?I1Ja
n D3rn dmlCiu0!WcIh6t
V(1i
Hii sLn1t
J(l i. l'ln1 s(1tifnclli6tkh5u bi0t:
g()P
c == 1.()OO~ j.:=
0,08; n == 7
J;>E
== 4 I6,5 I
Cau .14.5 M<:'>tnh6mtlllfullg phi0u>c(lm~nhgi;lC, til<'ri 11\1111;'111n;Ul1
dm.yc
dCIll chij( kh:1u
thcol5i g<)p v&i Wi sw1t la i. '~illl s(1ti2n chi2tkh5u bi0t
c
~
1.000:
i == O,OR;
n == t\
'r 459,73
Can 14.0.
M()tnh6m thmmg phi~u (t') m~nh gia C, thaih,.nll{ll1nam dm)'cckm

chi~t khfm
thel)!fii gl)P
\,l)-i mi S1Ji1tJa i. Tim sb ti~nchi~tkhffu 'hih:
c== 1.000: i == O~09; n~-=4
y 291,57
Cau 14.7.
Mo.t
nh6111tlmangphi&uc6 m~nh giuc'
thaih~ll1 1:.111nam duqc
dcm,chh?t
khAn (!leolai g()P
Vtli'Hii'sufrt la i. Tim s6ti~n chiMkh5tlbiH:
c == 1.000~ i == O,09~ n == 5
>
350,07
Cau 14.8.
Mo.t'
nh6nlthU'crng'phi~uc6l11~nhgiil
C, thlYi"h~ll1Tit 11,nal11'dmJc
.demchi~t.,khfillJheO lai g(?P
v6i liiisuatJa i.11111s6 ti~nchi~tkl1Aubi~t
c ==
T.OOO;i==O,09~
y 403,73
Can 14.9.
Mo.t
nh6mlhtrangphi2ucOn1qnllgia
C, tl1()'ih~1I1.1a,llnan1
dugcdcll1Chi&tkhl1uthetilfiig{)p
vai hIi suAt lai. Tlms6ti~Jlchi~fkhALlbi~t:

C ==1.000;
i ==
0,09; n ==7
>452,97
Call 14.10.
Mo.t
nh6m thuang phi6L1cdn1~1111gi4(:,
tl1&ilwn'IWn ntnn dtrc:cdenlchi~t khAuthco Inigo.P
vd'i lilisu5t !ili. Tim s6ti~nclliet kh,lilbiet:
c~=:-:: 1.000: i
:~: 0,09: n
> .lq~. i J
.
~hbnt IS~
Cau 15.r~ .
Jv1()t khq61!~fll<.,Ddrrgc thanlrtoanb5ng n nien kinl co d!nh vO'ilaisuAti. Nicn kinld5uticn
dlr~YC
th~rchi~n sau khivayl thai k)i. Tinh khO(lll thanh<toan l1<l goc thtl' k.
I3ict:
D== 10.000; n ==4;i==5~:~y~k ==2 (lan1 tron 2s(~Jc sau (h1u
phAy)
r (Ji[l tri khoan 119'g0e dau tien IiI:
I 0.05
M1
:;::
DXC1+i)n
1:;:: lO.OOOx
(1+0.05)4-1:;::
2.320)2
-~

.
Gin trj khoanngg5c tht'r k:
M2 = M1x(1.+
i)k-l
=2.320,12x(1 + O.05)2~1= 2.436,42
CauI5.2.
-'-
M9tklloann~)' D duqc thanl1 toan b~ng nnicn kiInC{~dinhv(Jilaisu~ti.Nicnkinld~u tien
UlfgC th\fC hi~n sau khi vay 1 thaiky.Tinllkhocin thanhtoan nqg6c thtF -k
Bi0t: 0 = 10.000; n = 4; i= 6%; k =.J(liUl1 tt(l!1
2 s6 Ie sandau
pI1<1y)
> Gia. trj khoan ngg{~cd,luticn:
Ciill 15.3.
M0tkho£nll1Q'IJdtrgc thanhtoitl1 bfll1g nnicn kimc(1djllh v(1i15isu.1fi. Ni6i'lkiul d5u tien
<.1lr~)'cth~fC hi9I1 saukhi va)' 1 tbcJi k5'.1~illh khoillllllanhtoan B<l g6c thtrk.
Bi~t:
D:::: 10.000; n == 5; 1== k== 2 {Iaul tr()112
sBilc
s3uuAu phAy)
~
M2 = 1.860,63 )D20~'\) m~pq-£~ - A:Y~r)3
,~ .
<
(0+01Dt) ;{
Call 15.4.
> At\1?}~'tt l
"f
0lCJ:f)
~

1\1,)t kho:ln n,1 D dU\lC
thanh~&fLb{lI1g Ilnicnkim c(1 dinh \,(1i lai su.1ti. Nicl1kiilld,1u ticll
du\yc th~rc
lli~n sau khl vay thtyj k51 "finh kho~lll
thanh
to {ll1 IH) gtJC thtl' k.
l3i0t: l)=-=IO.(}(JO: 4:
j ) (J~lnltrl)n 2 st11csau lhiu ph,ly)
,~
Mz'~2.SgR,5
~
C~iu 15 5.
,.
,
"
!'v1(hkhoan no D dtwC thanh tU<'lIlbiln!!, 11niel1 kim Ct) dinh \'ai 15i SUflli. Ni~n kim d£iu
ticl!
. . .
.

'-
.
.
Jlrr rc tht.rc hi9n
sau kIJi,
vayl
t!1(yi
k~. Tinh kho~111 thanh toim lH! gClC tht[ k.
Biet: 0= 10.000; n = 5~
.

{==9~'o; 4 (Hmtf'0I12 56 Ie Still
dAu phAy)
» 2.163~90
Call 15.6~
M0t khoanng.OdLrgc Ibaol1toan hilng nnicukilll ct\dinh V(~iEii suAt i.NiGI1 kim dAtilien
dm.rc th\fc hi~n sau khi val'
1 th(yi k)'.
,',
Tinhkhoan thanh loan nq g6c thtr k.
Bi~t: 0 = 20.000; n =4,; i = Y%; k = 2(Hull tn,)n
2'
s6 lc sau dAuph5y)
> 4.8,72~25
Cau-15.7.
M0t khmlnnqp qlCqCtl1anh t()un biing nnicnkim c(1dll1h vtYilaisu5t i. N'icllkilll d~u tien
dugc th\rchi~n sau khivay 1 thai ky. tinhkhoim thanh toah 11(!gtlcthtc,k.
Bi2t: D=20.000; n= 4; i=6%;
k=3(Ultntr()I12s6Jesaud~uph5y)
y 5.136,90
fvl()t khoanm:t Ddlcqcthanh toan hilng nnicllkii1) c6 dinhv6'ilaisu5ti.Nicfl kiln dt1u liSo
duQ'c thvchi~n sau klli yay 1 thaik5'. T}nl1 kh6im tl1anh toahl1Q g6c thlrk
Bi~t: D == 20.000; n == 5; i ==7,5%; k=' 2 (him
tron2
561c saud5u,plH1y)
Cau 15.8.
> 3.701,54
Call 15.9.
MOt kho(ln 11<,YDd(l'qcthahhto{Hlb~ng
n:I1icn,kim cA dinh v6iHli suAt i.Nien kim dIlu tien
duqc thvc, hi~n sau ,:khi vhyi J thbik5'. T'it1hkhoah

tharlh
toa'n n<.t gt>c thilFk.
Bi0t: 0='20.000;, n = 5;i=$%; k= 3(hirn tron 2 $(\ lesauLi5uph.1y)
>3.976,4()
(~au 15.10.
t\10t kho,'lJl 11(.r\) dut.)'c thanhto:\11 hflng n niell kim ell djnh v(yi lili su,~t i. Nien kim d:1u til'Ill
dlrl.re th~rc hi~Il suu khi vayl thili k)'. T mh kIh)illl t hanh to[m 11()' go(' thiI' k.
~~i(~:
i) =c~~:().OOO~ n~-: ): i
l)d'~)~k
;1
(1;\
~.~1
t
to
,~)
.t1
')
t ,1
\."
1~ s n II d~1 u p 11 ~~y )
,,/
~-
Nhoh-n
]
6.
etA == ~ l~~)
~k
~\:\)~ );;
Cflu j6.1.

(11./0
ivl(H khoanlJ<} I) dlf</C thanh toanb5ng nicnkin1 cc\ (1jnhc6.khil nang thanh to{lIl l1q'g{)C
co
dinh
vcri lfli su,1t i. 1~inh l1icn kinl thlr
2.Bi~t
D
=::: 10.000:
n== 5: i==5~/~
';> 2.400
Cau 16.2.
M(Hkhol'll1nq.D cilrQ'cthanh toan bc1ngn nicnkil11c6 djnh
'co kiln nang thanhto{mng g(~cc6
dinh Vlyilaisu5t i.Tinh nicnkinl thtr 2 Bi~t
.
-
,' ,'- '. -
,
- '-" -
,'
- -
-:
-
.
D == IO.O()O~
n == 5; i==6%
~2.480
Cau16.3.
M0t kho:inlH)' D du<)'cthanh to{mb5ng nnicnkim C(~dinh c6khanflng thanh to{m
11<l

g(lcc6
J~nh v(1i li'ii suiit i. Tinh nicnkinl thu 2. Bifl
D.
=-=.1
(}.OO{)~ n == 5;

.
i=7(/~)
).> 2.560
Cfiu16.4.
M()tkhminnq 0 duqe thanh toanb5ngnnicnkinI cAdinhc6 khiI !lung thanh toann(f g(1cc6
djnh vcyi
IJisu5t i.Tinh nicn kinl thll' 2. 13i~t
D == IO.OOO~
n.==.
5;i==80/0
);.>
2.640
Call 16.5.
M0t.khoan 11(/D duqe thanhtoa(lbflngn niel1kimc6djnhc{) khn nangthanI1t(){U1Ut r g(k C(~
dinh v('ri IJisut1t i.~l~inh nien kinlthlr2.13i~t
D ==
10.000: n == 5: i== 9(~'~)
f.' 2.720
Can 16.6.
MQtkhoan n<1D chrQ'c t11anh
to<111
h5ng1) nictikim co dinh
c{)kh,l nang 1hanh to:n1
djnh v{ri Eii suat 1. Tfnh nicl1kiJrtthir2.

D
~ 30.000:
11:::: 6; i== 5~/o
>-
6.250
Can 16.7.
M§t.khoan nq Ddtrqt.thanhtoanbftngn
nicnkirnc6dynh co khunang1hanh toao.l10'
g&CCl\
dinh Val T5isu5ti. 'Troll nien kim th(f 2. ni&t
D == 30.000~ n== 6:
i:;::6~~
» 6.500
Cau 16.8.
dinh vai Iai su~t. i.Tfnh nien kim tl1(r2. 131&t
D == 30.000; n == 6~i==
7%
»6.750
Call 16.9.
Ni<)l
kho~\n nt.YDdlrqcthanh toanb~ng.n
nicnkim c6 dinh .c6 khanang thanh to{1l1l1lrg5C;&Cl
din 11v6ilar sLIM
i.
1'inl1ni
enkin1thtr2.Bi&t
D
= ::
30.000-;
" }1== 6~ i==8°/o

}
7.000
Call 16.10.
Mt)t khoii.n.n<.y.l)
dlf<.rc.thanhlq{lrlbf1ngnnicnkim
Cl\
dinhv6iHiis.uAti. Tfnh ni611kiI11Jll«(:Z.Bi~t
D == 30.000~.
Il.:=:: 6;i==
gOlD
> 7.250
/~ ,,~
-~
~
-fl~
-lI(
'L-
LA .y- (A + t) -I ~
-,C A+t )
C; ~l)-
~4


r\hOilli 17.
Cau 17.1.
\'\
.
r'"
Thay the 2 khm1n
J](l, khoiin nq thlr

nhat j
a.ODo, tn1 sat!
I nam, khoan thu hai 20.000 tr{isau
'" 'L-
3 !lam bAng
I11Qt
kh03I1 IH)'
duy nh<1t
S tra S3Un nam. Lili
su;}t
1<1i%
rrinll S v(yi 11== 1; i ==6%
fr> l)htrang .trinh t?i th(yi diCnlO:
Sx(l +
0.06)~1= 10.000x(1 + 0.06)-1 +ZO.OOOx(l + 0.06Y3
).> V ~y S ==27.799,93
Cau 17.2.
Thay
th6'p~hoannq, khoan
119'tllu nhat JO.OOO,-trasau-l<11fim khotlnthfrl1ai20.QOOH'as.au
3 l1am b~llg
mot khoan
119'duynh5t S tn1SaUHl1an1.Lal sudtlai%
rrinh S v&i n =1,5; i;= 6%
').> Phtfc)'ng tfinh t~i thCri{1i~nl0:
$x(1 + O.06)'c-1.5=10.000x(1+ 0.06)-1 +ZO.OOOx(1 +0.06r3
~ V~y S ==28.621~78
Call '17.3.
Thay th~
2kho.111

119',khO<ll1nq thir. nilAt 10.000, JUl.san 1 nanl. khoill1thtrhai 20.000
tra- sau
3 nam b5Ilgm~)t
khoall nq duy nhc1tS tnl sau nam. till suAlla i(~'o
Tfnh S v(ri n == 2; i ==
6<X)
.,. s
- 2<).46
7~92
M.JrtrDi'f (_
-~
-1-
qDb J~ 2,»
/ nTVi(1)i)'
C~lU17.4.
Tbay
th0 2 khoim
119", khm1ll.
/19'thtr11h[1t1O.OOO,triisan 1 11anI, khoulltIllrhai 20.000Jrii
sau
3
nal11b~ng
mot khO<lll
nvduynh,kS tI'.1saun L5isu5t1il i%
rrinh S V(yill
=-= 2,5; i == 6<10
~ S== 30.339,09
'finh Sv()'i n ~ ~ i ==6(>~)
r~
S

]
J2J6,OO
-
C,lu 17.6.
Thay th~ 2 khexll1 11(1,kilO.ln lltfth11' nh5t i o.non, tnl sat! 1 l1am, khoiln tl11rhai 20.000 rd. Silt!
3 nam h~l1g m0t khoilnnQ'dnynhAt
Stra::;aull naln.t,ITisuat 1a1%
T i1111S v
l.(,.i
n == 3,5'
.
::= 6
o/~)
}> S==32.159,43'
Cau 17.7.
Thay th~ :2khoclnnq, khoan IH!thlr nhfrt JO.OOO,tni san 1 nam, khoatl tht.'rhai 2:0.000 tra sat!
3 l1am biing m0t khO<lnI1gtillY nhAt S tn'1sau n nam. Lai su.1t 13i%
Tinh S v6-i n==4;'j ==6%
rS ==33.110,16
Cuu 17.8.
Thay th~:2 khoimnq, khoun n(}thlT nh5t 10.000, trasau.lnIil11,khofmthfThai20.000 td SllU
3 nam bilngm0tkhmil1 n~ftluy nhAtS triisaul1nITm.Lili su5tl~ i%
Tinh S Vt1i.n== 4,5;i
==.6°ib
» s ==34.088,00
Thay th~ :2khoannq, khpj\n n(1
tl11T
nl~ftt 10.000, trasau 1.nam,khoan thlT hai 20.000tnlshU
3 iIamb5ng,m0t.khoan.tlqduy nilAcS Ira SFIU'1
nam U'ii su5t 1ft i%

.
l"'inhSv(yill == 5;i== 6~)
>S ==05.096,77
Call 17.10.
Thay th~ 2 khoun n(1, khoan n~)'th(rl)hfitl 0.000, tra sat! 1 nam,kho.untl1uhai20.000 td S~lU
3 nan1 b~ngmQtkhoan n()'du:ynl.}flrStrit~atrnnam Lai su5tlili%.
l~inh SVl~i n.==:.5,5; i ==.6lX>
>S ==36.134,34
-
Nhon~ J8
(',lu 18.JQ
~ia (rihi~n tZljelm s6 ti0n C thu(iln.YCs<UIIlH[llll t~rh:ln hoali6n t~ICla v.
Tim laisu5t i. Bi~t c= 10.000; V'='9Cl48,374.; n = :2
,.:> Do hi<;n t?i houlicn t~lCIlcn:V. C.
e-in
r. rra'c6 9.048,374 == 10.00'0 xe-2i
> i ==0,05 5%
Ciiu 18.2.
Gia trj hi9H t~licIJas6 ti~1lCthodugc S3Un nam (trbdnhoa licntl,lcJaY.
(,~ 3
A
0 ~~()l)V ~ ~
'Ii)
, ,
~) -{ ::
.
Gia trihi~Jl tZlicl'laso tienClhuUlfQ'C saUIlllanltlf baJ1I10tllien
Tim l5is1l4t i. Blft C= ]0.000; V = 8.478,937041; n~ 3
\
V ~ C

-'
L IIV)
~
l) {it ~')a-olf
4 -
'y.i== 5,5%
Cau 18.3.
rri.Ill15i su5ti. Bi6tC==1 O.OOO~V ==7.866,278611 ;n =='4
~ i ==6%
Cau18.4.
Giu trj. hi9n t{li.'cllas6li611>(~ tllUdlf<}C. saUIln[Ul11tf l-HlnlH.)(}lien t~Jc.'l(l \1.
rrinl J5isUi1t i.BialC==10.()OO~ V::::
7.225,273536 ;
» i ==6,5(~~)
Cau 18.5.
Gin trihi~n t~li cuas6 tifnC thi.Jdtfqcsau n llanl(ll'hiiJlIlO;'rlicn (~ICI{lV,
Tinl 15i suRt i. Bi6tC== 10.000; V
.,. i ~7%
Call 18.6.
Gi,ltrj hi~rl t~li CLI3S(\ ti~n(~ thu dl[\JC salllllli1Intlf b~irll1o('llicnl~lc Ia\/
rriI11 I5i SLI~1ti.
13i6t
C~ :10.000; \.I~. J.7,~2J4,I
~,
i

7
,5{~/~)
-
Ciiu 18.7.

Gifl tri hi~n U,tictws0 ti~n Cthu dtr()'c saun
T111113isuat i. l3ier c~ 20.000~
t Lf h 3n 110 a 11en Ivel i1 V.
)~
i ==
g(~<1
Cau 18.8.
Gia tri hi~n t~lici'1as[lti0n Cll1u dUt.1'c
saLll1113111ttrban hoa lien t~ICi3 V.
Tim 15isu5t.i. Bi0rC== 20.000; V "",14.235,40665
;n:::o:4
>
.i==8,5~~
Call 18.9.
Ghl trj hi~n t?i cuas6ti~11 C thudttqc
Tl1111aisu5t i.Bi~tC==20.000~
»
i. =.:::<)°/0
Call 18.10.
Gin ft-j l1i9n .t~ll.Cl1aSS ti&n Cfhudlr{l'c.sR1IH
num.{l.rbilnhoalien t~ICla\!.
Tinl 15i sufiti.Bi~tC=:: 20.000~ \l
» i==9,5%
f\horr: Jge
- ~f{)
~
"
~-l-_ ~-~
-\- 0~lA
-+ 1) +G~~(A-+t)~~(t\~l)

,'-~
~
Gfl\
~ AA ~) ·
;'=iiu 19. J
iv10td~f.In dilu Ill'COlu6ng ti0nIJi c6 dfnhnhlfsau: CFo=
]
00.000
CFJ==cIO.OOO CF20;=30.000 CF3= 50.000CF4=jO.000
l'i1111NP\' v(yi
laisu5ti.=== 11%
NPV= 100.000+10.000x(1+O,11}-1+30.000x(1
+ 0.11)-2
+ SO.OOOx(l+O,11}-3 + 70.000x(1 +O.11r-4 := 16.028,42
Call J9.2
M{>t(I~fan <h1utu c61u6ngti6n Jaj c6dinhnhusan: 'CFo='100.000
CFj7= 10.000 CF2=30.000 CF3= 50.000 CF4=,=70.000
l~inhNPV v{ri J5i su~t i
=== 12%
NP~~~: 100.000 + 10.000x(1 + O,12r1+30.000x(1 + 0.12)-2
+SO.OOOx(l +0,12)-3 + 70;OOOx(1+ 0.12)-4 = 12.919,67
Ciill 19.3
M\'Hd~ran ({,hi tu c61U(1ng ti<3nJaic6'dinh nhustlu:
C
Fo=loo.ooer
CF1== 10.000
CFz==30A100
CF3==50.000 C/~=='70.000
rf'i 1111N
f)Y

vlli
J5i sur1t
i == 13{!/~)'
:~ NPY ==9.928,78
Cuu 19.4
M()t d~rAn dflll tu colu6ng ti0nli'iic6>dinh nhifsau:CFo:'=<lOO.OOO
CFI= 10.000 CF2= 30.000 CFs=50.000 Cf~= 70.000
l"inh NPV Vl)'j 15i su,lti
== 14(!iQ
'yNPV== 7.050,15
Call J9.5
M(Hd~j'an (J,111ltrctl 11I(~ng th~n liIi c<}(lfnhnlllf snll:CF(l= ]
oO.non
C~~Fl=~10.000
ClS~ JO.OOOC I;]~
50.nOO
C'l~~l-=70.000
rrinhNP\! Vtyi IJi su~it i == I5
(},()
~NI)\! ::::
4.:27:-LSO
t
-
(~all 19.6
~.1(}t d~l{m dllU Itr t.:c\ Ill(~lllgti~nEli u1dj n11 n!n rsau: CTu
;O;J. Od()
CF1= 10.('()O CF2=
30.0()() CF3= )0.000 CF4~70.000
l~il1h Nr~v vo'ilai suAti==
16(~/~1

Ciiu 19.7
M91dV andliu tHca luc\ng.ti~nlaicc~ dinhnhlY sau:
CFo=:
LOO.OOO
CF1=lO.000CF2= 30J)(20 CF3=
5Q.OOO
CF4= 70.000
I
' } .N.P.
V '
1 .
17-01
~- ~-~~-~-t~~ l~J __~~CJ'l
HI suat 1 == /0
.;-
>Nl~_Y == =-963.,55
M91(hran.d~u tl~£6JlIc\ng
ti0nlili.c6dinhnlnrsall:
C Fo=1
00.000
CF1=
10.000
CF2=30~00()CF3= 50.000 CF4= 70.000
l"'inh
NPVvailaisu5ti '71
S(~1>
>NI)Vd==.~ 3.443~13'
Cllu 19.9
M9tdv ano<1u tlrc61q(1ngti~11Wi C(~dinh nlnfsau:
CFo=

100.000
'TinhNPVv6i.15i
su§t;je:: l~}~/o
y
N PV===~5 ~.834,OC)
I
Cau19.JOc~c
C F1 =
10.000 CF2=
JO.OOOC
F3"'"
50.aOD
CF4=<'170.000
'1 inhN P\/ v(yi 1~ i su~1t i
='=
2(V~/~)
~> t~ r'
\1 ~-= ~ 14 O :L'