Toán tài chính (tiếng Anh: mathematical finance) là một ngành toán học ứng dụng nghiên cứu thị trường tài chính. Nói chung, tài chính toán học sẽ thừa kế và mở rộng các mô hình toán học hay con số mà không cần phải thiết lập một liên kết đến lý thuyết tài chính, bằng cách lấy giá cả thị trường quan sát như đầu vào. Tính thống nhất toán học là cần thiết, chứ không phải là tính phù hợp với lý thuyết kinh tế.
. ~ 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, [...]... ,:khi vhyi J thbik5' T'it1hkhoah tharlh toa'n nc 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 h i~Il suu k hi vayl ~~i(~: i) =c~~:().OOO~ ,,/ n~-: ): i l)d'~)~k thili k)' T mh kIh)illl t hanh ;1 (1;\ ~.~1 to,~).t1 ') t... kinlthlr2.13i~t n == f.' 2.720 5: i== 9(~'~) khn nangthanI1t(){U1Ut r g(k C(~ Can 16.6 c{)kh,l nang 1hanh to:n1 n 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 . 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. 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. ' O)ll";tWl/~.,, Cau12.3. M(>tday20nicljkirrrdl1<;rctlwc'hi~llvaocacth(yi' di6m 1 , 20. Tuthai kythuJll15t d0n thai k) ,thi& apos;r k, lai suar 1. thaik)'la8<)1ti. ,TiT,thNk)' thu k + I, trq di: ifti suAtmQt.thO'iiky 9%.