02-09-2014_16-40-43 / 2013 Пакеты прикладных программ
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MeHTOB 6epyr )];Be 51qeil:KH Kpau111010 6epXHIOIO Jle6yl0 u KpaUHIOIO HUJ1CH1010 npa6y10, T.e. 3arrttcb= CYMM(Al;C2) 03HaqaeT, qTO rpe6y-
eTC51 Bb1qwcnmh CYMMY 51qeeK Al + B1+ C 1 + A2 + B2 + C2.
AHanorwqHbie 3a;::i:aqw MO)l(HO pernaTb c rrpttMeHemrnM MacTepa cPYHIGJ;HM. ,[(mI :noro Heo6xo;::i:HMO:
=> ycTaHOBHTb KYPCOp B 51qeil:KY, B KOTOpoil: rrpOH3BO)J;HTC51 BblqlfcJieHHe;
=> BhI6paTb B crpoKe Memo KOMaH.lJ:Y Bcma6Ka H B rro51BHBIIIeMc51 CIIHCKe BbI6paTb KOMaH)];y </>yHKU,Wl, B pe3yJibTaTe qero OTKpOeTC51 OKHO MaCTepa <l>YHKIIHM (pHC. 11.6);
=> BbI6paTb H3 11051BHBIIIeroc51 CIIHCKa HHTepecyio:uzyIO cPYHKIIHIO H HIDKaTb KHOIIKY [OK], B pe3yJibTaTe OTKpoeTC51 OKHO AJI5I BBO)J;a 3HaqeHHM 51qeeK, BXOMmHX B aprYMeHT cPYHKIIHH (pHC. 11.7);
=> BBeCTH B COOTBeTCTBYJOmHe IIOJ151 HMeHa 5{qeeK, IIOCJie qero II051BHTC51 pe3yJibTaT BbIIIOJIHeHHbIX BbNHCJieHHM (3HaqeHHe cPYHKIIHH);
=> HIDKaTb KHOIIKY [OK] AJI5I BBe;::i:eHAA pe3yJibTaTa B COOTBeTCTBYIO:uzyIO 5{qeMKY.
KOHTpOnbHble eonpOCbl
1. ,[(JI5I qero rrpHMeIDIIOTC51 Ta6JittqHbie rrpou;eccopbl H KaKOBhl rrpHHU:HIIhl BhlqHcJieHHM B 3THX rrporpaMMHhIX CHCTeMax?
2.,ll.ai1Te orrpe)l;eJieHH51 OCHOBHhIX 3JieMeHTOB CHCTeMhI Excel: KHHra, JIHCT, Hqei1Ka.
3.qTo 03Haqa10T B cwcTeMe Excel BhipffiKeHH51 A5=Al + B3+ B4= B3 * B4/A7
(TeKcT, cpopM)'ny,qwcno)?
4.KaKHe rpyrrrrhI BCTpoeHHhIX ct>YHKUHM co,JJ;ep:lKJfT rn6JittqHhIM rrpoueccop Excel?
5.KaKHe cymecTByIOT crroco6b1 Bh1qwcneHHH w o6pa6oTKH ,JJ;aHHhIX c rrpwMeHettweM BCTpOeHHhIX ct>YHKUHM?
6.KaK orrpe,JJ;eJIHIOTCH w 3arrwchrna10TcH apryMeHThI ct>YHKIIHM?
7.KaKoBo Ha3Haqettwe cJie)];yIOIIIHX cpopMaToB ,JJ;aHHhIX: 06w,uu, l/uc!lo6ou,
)1,eneJ1CHbllt, )1,ama, BpeMR?
8.KaKOBa IIOCJie,JJ;OBaTeJihHOCTh ,JJ;eMCTBHM rrpw BBO,JJ;e TeKCTa B Hqei1KH Ta6JIHilhI H rrpw pe,JJ;aKTHpOBaHHH ero?
9.KaKOBa IIOCJie,JJ;OBaTeJihHOCTh ,JJ;eMCTBHM rrpw BBO,JJ;e cpopMyJI B HqeMKH Ta6JIHilhI?
rnasa 12
TEXHOnon1s:1 <l>~HAHCOBblX PAC4ETOB B CPE.QE EXCEL
12.1. MoAeint 111 MeTOAbl <1>111HaHcoeo-aK0HoM111"1ecK111x pac"leToe
PacCMOTPHM HeKOTOphie IIOIDITIDI, orrpe;::i;eJieHIDI H MeTO,ll;hl, rrpHMeIDieMbie B KJiaCCWieCKHX qmHaHCOB0-3KOHOMHqecKHX pacqeTax, KOTOphie IIOJIHOCThIO COOTBeTCTBYIOT HMeIOIIIHMCH <j:>HHaHCOBhIM <l>YHK-
U:IDIM Excel.
KoJIWiecTBeHHhIH <j:>HHaHCOBhIH aHaJIH3 rrpe;::i;rroJiaraeT rrpHMeHeHHe yHH<j:>HI.J;HpOBaHHhIX MO,ll;eJie:H H MeTO,ll;OB pacqeTa <j:>HHaHCOBhIX rroKaJareJie:H. YcJIOBHO MeTOAhI <j:>HHaHcoBoro pacqeTa rro;::i;paJ;::i;eJIHIOT Ha )];Be KaTeropHH: 6a30Bble H rrpHKJia,ll;Hble.
K 6a306blM MemoiJaM <j:>HHaHCOBhIX pacqeTOB OTHOCHTCH:
•orrpe;::i;eJieHHe rrpOCThlX H CJIO)l(HhlX rrpou:eHTOB, HBJIHIOII.J;HeCH ocHOBOH orrepaQHH, CBH3aHHhIX c HapaII.J;eHHeM HJIH ,ll;HCKOHTHpOBaHHeM IIJiarexe:H;
•pacqeT IIOCJie,ll;OBaTeJihHOCTe:H (IIOTOKOB) IIJiaTexe:H IIPHMeHH-
TeJibHO K pa3JIWIHhIM BH,ll;aM <j:>HHaHCOBhIX peHT. IIpu1<:JlaOHblMU MemoiJaMu <j:>HHaHCOBhIX pacqeTOB HBJIHIOTCH:
•IIJiaHHpoBam1e H OQeHKa 3<j:><j:>eKTHBHOCTH <j:>HHaHCOBO-Kpe,ll;HT- HhlX orrepau;H:H;
•pacqeT CTJ)aXOBhIX aHH)'HTeToB;
•IIJiaHHPOBaHHe rrorarneHIDI ,ll;OJirocpoqHOH 3a,ll;OJI)l{eHHOCTH;
•IIJiaHHpOBami:e rrorarneHIDI HIIOTeqHhIX ccy;::i; H IIOTJ)e6HTeJibCKHX Kpe,ll;HTOB;
•<j:>HHaHCOBbie pacqeTbl 110 u:eHHhIM 6YMaraM;
•JIH3HHroBhie, <j:>aKTOPHHroBbie H <j:>op<j:>e:HTHHrDBbie 6aHKOBCKHe orrepaQHH;
•IIJiaHHPOBam1e H aHaJIH3 HHBeCTHQHOHHhIX rrpoeKTOB H ;::i;p. Oco6eHHOCThIO Bcex <j:>HHaHCOBhIX pacqeToB HBJIHeTcH BpeMeHHaH
u:eHHOCTh ;::i;etter, T. e. IIPHHU:HII HepaBHOQeHHOCTH ;::i;eHer B pa3Hble
MOMeHThI BpeMeHH. Ilpe;::i;rroJiaraeTcH, qTo rronyqeHHaH cero;::i;IDI CYMMa o6Jia;::i;aeT 60Jibllle:H u:eHHOCThIO, qeM ee 3KBHBaJieHT, KOTOpbIH 6y;::i;eT rronyqeH B 6y)l;yII.J;eM, T.e. qTo IIJiaHHpyeMbie IIOCTYIIJieHHH 6y;::i;yT Mettee 1.1;eHHhIMH, qeM TeKYII.J;He. HepaBHOI.J;eHHOCTh o;::i;HHaKOBhIX no a6coJIIOTHOMY 3HaqeHHIO CYMM CBH3aHa eII.J;e H c TeM, qTo O,ll;HHaKOBbie CYMMhl HHBeCTHPOBaHHhIX B pa3Hhie rrepHO,ll;hl ;::i;eHer 6y;::i;yT rrpHHOCHTh pa3Hhii1 ;::i;oxo;::i; B 6y;::i;yII.J;eM.
OcHOBHhIMH IIOIDITIDIMH <j:>HHaHCOBhIX pacqeToB HBJIHIOTCH:
• npou,eHm - a6coJIIOTHhii1 ;::i;oxo;::i; OT ;::i;etter, rrpe;::i;ocTaBJIHeMhIX B ;::i;oJir B JII06o:i1 ero <j:>opMe;
143
• npou,eHmHaJl cma61Ca - OTHOCHTeJibHbIM )J,OXO)J, 3a <l>HKCHpOBaHHbIM HHTepBaJI BpeMeHH, H3Mepsi:eMbIM B rrpoueHTaX, HJIH 3aIIHCbIBaeMblM B BH,LJ,e ,L1,p06H;
• nepuoa HQ"IUC/leHWl - HHTepBaJI BpeMeHH, K KOTOpoMY IIPHYPOqeHa rrpoueHTHaH crnaKa;
• 1;Canuma.t1U30U,Wl npou,enmoB - rrpHcoe,LJ,HHeHHe HaqHcJieHHbIX rrpoueHTOB K OCHOBHOM C}'MMe;
• napaw,enue - yaeJiffqeHHe rrepBoHaqaJibHOM C}'MMbIB pe3yJibTaTe KaIIHTaJIH3aUHH;
• auc1COHmUp06QHUe - rrepecqeT CTOHMOCTHOM BeJiffqHHbl, OTHOCH- I.UeMCH K 6y,LJ,yI.UeMY, Ha HeKOTOpblii:, 06bNHO 6oJiee pattHHM, MOMeHT BpeMeHH (T.e. orrepauHH, o6pamasi: HapameHHIO).
B $HHaHCOBblX pacqeTax paJJiffqaJOT cJie,LJ,yIOmHe BH,LJ,bl rrpoueHTHblX CTaBOK:
• B 3aBHCHMOCTH OT 6a3bl )J,JIH HaqHcJieHHH rrpoueHTOB - npocmble
HCllOJICHble;
•no npHHUHIIY pacqeTa - HapameHHH, T.e. ae1CypcUBHy10, H yqeT- ttyIO, T. e. anmucunamu6Hy10;
• no noCTOHHCTBY 3HaqeHHH B reqeHHe ,LJ,eMCTBHH KOHTpaKTa - rjJUIC- cupo6aHHble H Tl/IQ6010W,Ue, T. e. 3aBHCHI.UHe OT roro, <l>HKCHPYeTCH JIH
H3MeHHIOI.UaHCH BO BpeMeHH 6aJa H pa3Mep Ha,u6aBKH K Heit
6330Bble MO.Z.e.JIH cl>HHaeCOBhlX onepaD;Hii
Pa3JIHqHe crroco6oB HaqHcJieHHH rrpoueHTOB OT C}'MMbI,LJ,eHer, rrpe,LJ,ocTaBJIHeMoii: B ,LJ,OJir B JII06o:H <l>opMe, orrpe,LJ,eJIHeT H paJJiffqHe
BH,Ll,OB rrpoueHTHblX CTaBOK.
IlpoueHTbl pa3JlffqalOTCH no 6a3e HX HaqHcJieHHH. IlpH HCIIOJib30BaHHH IIOCJie,LJ,OBaTeJibHO H3MeHHIOI.UeMCH 6a3bl )J,JIH pacqeTa rrpoueHTOB Ja 6a30BYIO rrpHHHMaIOT CYMMY, rronyqeHHYIO B pe3yJibTaTe Hapa-
meHHH HJIH ,LJ,HCKOHTHPOBaHHH.
IlpH noCTOHHHOM 6a3e HaqHcJieHHH HCIIOJib3YIQT rrpOCTbie rrpoueH-
THbie CTaBKH, a rrpH rrepeMeHHOM - CJIO)l(Hbie.
IlpocTble npoQellTllble CTaeKH. PacCMOTPHM OCHOBHbie THIIbl MO,LJ,e-
Jieii: <l>HHaHCOBblX pacqeTOB Ha OCHOBe rrpOCTblX rrpoueHTHblX CTaBOK.
Hapaw,enue no npocmou npou,enmHou cmaBKe. IlpH BhmoJIHeHHH ,LJ,aHHoii: orrepauHH HCIIOJib3YIQTCH CJie,LJ,yIOmHe o603HaqeHHH H <l>OPMYJibI:
I - |
npoueHTbI Ja Beeb cpoK ccy,LJ,hI; |
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p - |
nepBOHaqaJibHaH C}'MMa)J,OJira; |
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S - HapameHHaH C}'MMa.aoJira B KOHUe cpoKa ccy,LJ,hI; |
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i - |
CTaBKa HapameHHH (B BH,LJ,e ,LJ,eCSJ:TffqHOM ,L1,p06H); |
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n - cpoK ccy,LJ,hI (o6biqHo ro.ahl); |
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t - |
qffCJIO ,LJ,Heii: ccy,LJ,bI; |
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K - qHcJio .aHeii: B ro.ay; |
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I =Pni; |
(12.1) |
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S= P+ I= P+ Pni= P(l + ni); |
(12.2) |
144
n=t- |
(12.3) |
x· |
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06bl'IHOK Hapa:w;emno no rrpOCThIM rrpo:u;eHTHbIM CTaBKaM rrp116era10T rrpH Bbl,ll;aqe KpaTKOCpoqHbIX ccy.n; (.n;o O,ll;HOro ro.n;a) IDIH B c.rryqaID{, Kor.n;a rrpo:u;eHThl He rrp11coe,n;11ID110TcR K CYMMe ,n;oJira, a rrepH-
o.n;~ecKH BbIIIJ1aq11aa10TCR Kpe.n;HTOPY. |
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BM6op aap11aHTa pacqeTa orrpe.n;eAAeTcR: |
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• |
6a30BOH ,ll;JIHTeJibHOCTb10 |
ro.n;a (K = 360 .n;He:U |
- |
o6blKH06eHHble |
IDIH |
KO.M.Mep11ecKue rrpo:u;eHTbl, |
H K = 365, 366 .n;He:U |
- |
mo11nble rrpo- |
:u;eHThl);
•6a30BblM ~CJIOM .n;He:U B MeCR:u;e (30 .n;He:H HJIH TOqHoe ~CJIO KaJieH,n;apHbIX .n;He:U);
•pacrrpe.n;eneHHeM Haq11cneHHR rrpo:u;eHTOB B CMeXHhIX KaJieH,n;apHbIX rrep110.n;ax (o6:w;aR CYMMa rrpo:u;eHTOB .n;eJIHTCH Me)l(Jly CMe)J(HblMH rrep110.n;aMH cornacHo <t>aKTifl!eCKHM ,n;aTaM);
•HaJIHqHeM rrepeMeHHhIX CTaBOK (B CYMMe Hapa:w;eHHR yqlITbIBaeTcH ,ll;JIHTeJibHOCTb .n;e:UCTBHH KIDK)lOH nepeMeHHOH CTaBKH);
•ycnoBHRMH peHHBecTHpOBaHHR cpe.n;cTB.
PeHHaecTHpoaaHHe cpe.n;cTB npe.n;cnmm1eT co6o:U Heo,n;HOKPaTHoe IIOCJie,n;oBaTeJibHOe Hapa:w;eHHe no npOCTbIM npo:u;eHTHblM CTaBKaM B rrpe.n;enax 3a,n;aHHoro cpoKa. Hapa:w;eHHaR CYMMa 3a aecb cpoK ccy.n;hl
(12.4)
r.n;e n1 - rrpo,n;o.JDKHTeJibHOCTb rrep110.n;a .n;eifcTBHR ccy.n;b1; i1 - CTaBKa peHHBeCTHPOBaHHR.
EcJIH rrep110,n;b1 Haq11cJiemrn H CTaBKH He H3MeIDIIOTCR, Hapa:w;eHHaR CYMMa
(12.5)
r.n;e m - qHCJIO peHHBeCTHI.J;HH.
Hapaw,enue u BblnAama npou,enmo« « nompe6umeAbCKOM Kpeoume.
B 3TOM cnyqae HCIIOJib3yeTCR MeTo.n; pa3oaoro Haq11cJieHHR rrpo:u;eHTOB Ha BCIO cyMMY Kpe,n;HTa c rrp11coe.n;11HeHHeM HX K OCHOBHOMY ,ll;OJiry a MOMeHT OTKPbITHR Kpe.n;11Ta. Bb1IIJ1aTa Kpe.n;HTa rrpo113ao,n;HTCR c rrep110,n;11qHOCTb10 m pa3 B ro.n; B TeqeHHe n neT, T. e. rrorarneHHe ,n;oJira c rrpo:u;eHTaMH rrpOH3BO,ll;HTCR qacTRMH Ha rrpornxeHHH Bcero cpoKa Kpe.n;HTa. B 3TOM cnyqae Hapa:w;eHHaR CYMMa ,n;oJira
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S= P(l + ni), |
(12.6) |
a CYMMa paJoaoro rrorac11TeJibHoro IIJ1arexa |
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R=s- |
(12.7) |
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mn' |
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r.n;e S - |
Hapa:w;eHHaR CYMMa .n;onra; P - rrepaoHaqaJibHaR CYMMa ccy- |
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,ll;hI; n - |
cpoK Kpe.n;HTa; m - q11cJio IIJ1arexe:U B ro.n;y. |
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145
jjuc1w1tmupo6a1tue u yttem no npocmblM npou,eHmHblM cma6KOM. ,[l,11cKOHT11poBaH11e 03HaqaeT 11epecqeT CT011MOCTHOro 110Ka3aTellil, OTHOCHrn;eroCH K 6y;:t,yJJ.J:eM)',Ha HeKOTOpbIM, 6oJiee paHH11M, MOMeHT BpeMeH11. ,[l,aHHaH 3a,n:aqa HBIDleTCH o6paTHOM Haparn;eH11IO 11pou;eHTOB, T. e. 110 S 011pe,ll;eJU1eTCH P. B 3TOM cnyqae roBOPHT, qTo CYMMa S iJucKOHmupyemcR (HJI11 yq11TbIBaeTcH), caM 11pou;ecc Haq11cJieHMH 11pou;eHTOB 11 HX y,ll;ep)l(aHMH Ha3bIBaIOT yttemoM, a y,ll;ep)l(aHHbie 11pou;eHTbl - iJucKoHmOM.
CYMMa P, Haii:)l;eHHaH c 110Morn;bIO )];11CKOHT11poBaHMH, Ha3bIBaeT-
CH C06peMeHHOU Kanuma/lU3Up060HHOU cmoUMocmblO.
B 3aB11c11MocT11 OT BH)l;a 11pou;eHTHo:H cTaBKH 11p11MeHHIOT )];Ba BH)l;a )];11CKOHTIIPOBaHMH: MaTeMaTwqecKoe )];11CKOHT11POBaH11e 11 6aHKOBC-
KHM (KOMMepqecKH:H) yqeT.
Ilp11 MaTeMaT11qecKOM )];11CKOHT11pOBaH1111 paccqHTblBaIOTCH )];11CKOHTHbIM MHO)l(HTeJib 11 )l;HCKOHT (D) co BCe:H CYMMbl )l;OJira (S):
s |
(12.8) |
P= -- · |
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1+ni' |
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D=S-P· |
(12.9) |
TaKHM o6pa3oM pernaeTCH 3a,n:aqa, o6parnaH 3a,n:aqe HapameHMH 11epBOHaqaJibHOM CYMMbl CCY)l;bl, T. e. 011pe,ll;eJU1eTCH, KaKYIO 11epBOHaqaJibttyIO CYMMY Ha,n:o )l;aTh B )l;OJir, qT06b1 110Jiyq11Tb B KoHu;e cpoKa CYMMY S 11p11 ycJioB1111, qTo Ha ;::i:oJir Haq11cJU1IOTCH 11poueHTbI 110 cTaBKe i. Ilp11 3TOM )];11CKOHTHblM MHO)l(HTeJib, paBHblM 1/(1 +ni), 110Ka3blBaeT, KaKYIO .ll:OJIIO COCTaBJIHeT 11epBOHaqaJibHaH CYMMa )l;OJira B OKOHqaTeJibHOM CYMMe.
Ilp11 6aHKOBCKOM (KOMMepqecKOM) yqeTe 11pou;eHTbl Haq11cJU1IOT-
CH Ha CYMMY, 110.ll:Jle)l(amyIO yrrJiaTe B KOHUe cpoKa, cornacHo yqeTHo:H CTaBKe d:
P= S- Snd= S(l - nd); |
(12.10) |
D=Snd, |
(12.11) |
T. e . .n:11cKOHTHb1:H MHO)l(HTeJih P= (1 - nd).
IlpOCTaH yqeTHaH CTaBKa 11p11MeHHeTCH 11Hor.n:a 11p11 pacqeTe HapameHHOM CYMMbI. EcJI11 113BeCTHa TeKYrn:aH CYMMa ;::i:oJira 11 Tpe6yeTcH 011pe;::i:eJI11Tb ero 6y.n:ymyIO CT011MOCTb, TO 11p11 11Cl10Jib30BaH1111 yqeT-
HOM cTaBKH
p |
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S= -- |
(12.12) |
1-nd' |
|
1
r.n:e 1_ nd - MHO)l(HTeJib Haparn;eHMH.
CJIOlKHLie npou,eemwe cTaBKH. Ilp11cpe;::i:HecpoqHbIX11 ;::i:oJirocpoqHbIX <t>11HaHCOBO-Kpe,ll;11THbIX 011epauMHx, eCJI11 11poueHTbl He BbII1Jia-
146
'll1BaIOTCHCpa3y xe IIOCJie MX Haq11cJieHMH, a IIpMCOe)J,MHHIOTCH K CYMMe .u.o.rrra, )1)UI HapameHMH npMMeHHIOTcH cJIO)Kllbie npou:eHTHhie cTaBKM. oa3a .ll;JIH HaqMcJieHMH CJIO)K:HblX IIPOU:eHTHbIX CTaBOK yseJIMqMBaeTCH c K~blM nepMO)J,OM BbIIIJiaT.
IIp11coe.u.11HeH11e Haq11cneHHhIX npou:eHTOB K CYMMe .u.onra, KOTOpaH CJIY)K:MT 6a3o:H AJIH MX Haq11cneHMH, Ha3b1Ba10T Kanuma.tlU3at1iueu npot1ieHmo6.
<l>opMyna AJIH pacqern HapameHHOH CYMMhI B KOHU:e n-ro ro.u.a np11 ycnoBMM, qTo npou:eHThI Haq11cJ1H10TcH O.U.MH pa3 B ro.u.y, MMeeT
BM,!l;
(12.13)
r.u.e P - nepBoHaqaJihHhlH pa3Mep .u.onra; i - cTaBKa HapameHIDI no
CJIO)K:HhlM npou:emaM; n - |
q11cno neT HapameHMH. |
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IIpou:eHThl 3a 3TOT xe nep110.u. (n neT) HaxO.u.HT no cPOPMYJie |
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l = S - P= P(l + i)n - P= P[(l + l)n - 1]. |
(12.14) |
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Benwq11Ha q = ( 1 + i)n |
Ha3brnaeTcH MHOXMTeJieM HapameHIDI no |
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CJIO)K:HblM npou:eHTaM, a cPOPMYJia (12.13) HBJIHeTCH OCHOBHOH cl>opMYJIOH AJIH MX pacqern.
IIpou:eHThI 3a K~hIH nocne.u.yiom11:H ro.u. ysen11q11BaIOTCH. M AJIH
HeKOTOporo npoMexyTOqHoro ro.u.a t paccq11Tb1Ba10TCH IIO cPOPMYJie
(12.15)
r.u.e t= 1, 2, ... , n.
IIp11 MCIIOJib30BaHMM CJIO)K:HbIX npou:eHTHhIX CTaBoK B03HMKaIOT Te xe npo6JieMbI, qTo M IIPM MCIIOJlb30BaHMM IIPOCTblX npou:eHTHblX CTa-
BOK.
IIp11 Haq11cneHMM npou:eHTOB B cMe)K:HhIX KaJieH)J.apHbIX nep110.u.ax 06m11:H cpoK ccy.u.h1 .u.enMTCH Ha .U.Ba nep110.u.a n1 11 n 2. Tor.u.a 3a Beeb cpoK n
|
(12.16) |
a 3a nepMO)J,bl n, M n2 COOTBeTCTBeHHO |
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11 = p [ (1 + it -1]; |
(12.17) |
12 = p [ (1 + ir - (1 +if' J. |
(12.18) |
Heo6XO)J,MMO OTMeTMTb, qTo OCHOBHaH cPOPMYJia )1)UI pacqeTa CJIOXHbIX npou:eHTOB (12.13) npe.u.nonaraeT IIOCTOHHttyIO npou:eHTttyIO CTaB-
KY Ha npoTHXeHMM Bcero cpoKa .u.e:HcTBMH ccy.u.h1. 0.u.HaKo qacTo 11cIIOJih3yIOT IIJiaBa10m11e MJIM nepeMeHHbie npou:eHTHbie cTaBKM. Tor.u.a HapameHHaH CYMMa
147
(12.19)
r.ue ii>, i2, ... , ik, - nocJie.llOBaTeJibHbie BO BpeMeHH 3HaqeHIDI npou;eHTHbIX CTaBoK; n" n2, ..., nk> - MHTeJibHOCTH nepHO.llOB, B TeqeHHe KOTOpblX HCnOJib3YJOTCH COOTBeTCTBYJOW:He CTaBKH.
.l(JISI HaqHcJieHIDI npou;eHToB npH .upo6HoM cpoKe ccy.llhl n Hcnonb3YJOTCH )lBa MeTO.lla pacqeTa: o6w,uu, 3aKJIIOqa10rn;HHCH B npHMOM pacqeTe no <l>OPMYJie ( 12.13), H CMeUlaHHblu, npe)lnonaraIOrn;HU: HaqHcneHHe npou;eHToB Ja u;enoe qHcno neT a no <l>OPMYJie CJIO)l(HbIX npou;eHTOB H Ja .upo6Hyio qacTb nepHO.lla b no <t>oPMYJie npocTbIX npou;eHToB:
a+b=n;
S= P(l + i)0 (1 +bi). |
(12.20) |
3aMeTHM, ~ npH pacqere no CMeIIIaHHOMY MeTOJlY CYMMa HaqHcJieHHH OKa3b1BaeTCH 6onhrne, a npH b =1/2 otta MaKCHMaJibHa.
Hapaw,eHue u oucKoHmupoBaHue no CJIOJICHblM npou.eHmHblM cmaB-
KOM. ConOCTilBHB pe3yJibTilT Haparn;eHIDI CYMMbI npH pacqere no CJIOIHhIM npou;eHTHhlM CTilBKaM c pe3yJibTaTOM npH pacqere no rrpocThIM npou;eHTHhlM CTaBKaM, YBHJlHM, ~ MH cpoKa ccy.llhl MeHbrne ro)la CYMMa npocThlX npou;eHTOB, KaK npaBHJIO, 6onbrne CYMMhl CJIO:xcHblX npou;eHTOB, a MH cpoKa ccy.llhl 6oJibIIIe ro)la nonyqHM o6paTHhlH pe3YJibTaT.
Ilpou;eHThl KanHTaJIH3HPYJOTCH o6wqHo HeCKOJibKO pa3 B ro)l. EcnH fO.llOBaH HOMHHaJibHaH CTaBKa j, qHCJIO nepHO.llOB KanHTaJIH3all;HH B fOJlY m, a o6rn;ee qttcno nepHOJlOB HaqttcneHIDI N = nm, TO KlUKJlbIH pa3 npou;eHTbI HaqHcAAIOTCH no cTaBKej/m. Tor)la Haparn;eHHaH CYMMa
.llOJira
S= P(l +j/m)N. |
(12.21) |
3<P<PeKmU6HaJl cma6Ka - 3TO fO.llOBaH CTaBKa CJIO)l{HbIX npou;eHTOB, o6ycJiaBJIHBaIOrn;aH TOT xe pe3yJibTaT, qTo H npH m-pa30BOM HaqffCJiemrn npou;eHTOB no CTilBKe j/m.
0603HaqHB 3<l><l>eKTHBHYJO CTaBKY qepe3 i, 3anHIIIeM
i = (1 +j/m)m - 1. |
(12.22) |
.ll:HCKOHTHpoBaHHe no CTaBKe CJIO)l(HblX npou;eHTOB, eCJIH npou;eHTbl HaqHCAAIOTCH m pa3 B fOJlY, ocyrn;eCTBAAeTCH no <l>OPMYJiaM
s
(12.23)
(1 +if'
D=S- P. |
(12.24) |
BenHqHHa P B 3TOM cnyqae Ha3bIBaeTCH co6peMeHHou cmoUMocmbJO S.
148
Ilp11 pacqeTe no C/lOJICHoii y11emHoii cmaBKe d npou,ecc AHCKOHTHposaHIDI npOHCXOAHT c 3aMe.arreHHeM, TaK KaK yqeTHa.sl CTaBKa npHMeIDieTCH K CYMMe, yxe AHCKOHTHpOBaHHOH Ha npe.nhl,Dyll.l,eM :nane:
(12.25)
Ec;rn AHCKOHTHposaHHe no yqeTHOH CTaBKe npoH3BOAHTCH m pa3 B ro;:zy, HCnOJib3YJOTCH noIDITHH HOMUHOJlbHOUfH 3<jJ<jJeKmU6HOU gyqeTHbIX CTaBOK:
(12.26)
3ct>ct>eKTHBHa.sl yqeTHa.sI CTaBKa xapaKTepH3yeT pe3yJibTaT AHCKOHTHPOBaHIDI 3a ro.n.
Hapall.l,eHHe CYMMhl npH pacqeTe no CJIO)KHOH yqeTHo:H CTaBKe:
S= p
(1-dr
p
S= (1- ~)mn .
OnpeoeAeHue cpoKa MameJtCa u npou,eHmHblX cmaBoK.
n paccqHThIBaeTCH AJIH HOMHHaJibHOH j H 3cl>cl>eKTHBHOH i
HOH CTaBOK COOTBeTCTBeHHO no cPOPMYJiaM
n = log(S/P) . mlog(l + ~)'
log(S/P) n - --'-----'-
- log(l + i) ·
IlpH AHCKOHTHPOBaHHH no CJIO)KHOH fOAOBOH yqeTHOH CTaBKe d H HOMHHaJibHOH yqeTHOH CTaBKe f cpoK IIJiaTeJKa onpe.neJIHeTCH COOTBeTCTBeHHO no cPOPMYJiaM
n- log(S/P) . |
(12.31) |
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- |
log(l-d)' |
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log(S/P) |
(12.32) |
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n = |
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|
( |
f ). |
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mlog |
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1- m |
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149