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MHCTEPCTBO OPAOBAH POCCCO EEPA 65.9 (2) 2673 PACHOPC OCAPCTBEHH HBEPCTET Aop-cocae B.. ye .C. e B.. ye .C. e acoa aeaa: eo-eo. oec cyeo aooo oee oo. a-a/ pacop. oc. y-; Coc. B.. ye, .C. e. pacopc, 2002. - 22c.

HAHCOBA MATEMATA eo-eoec oec o ypcy Papaoao cooec c ye ao popao ypca cyeo aooo oee acoa aeaa.

ooecoo ayea peaaeo cyeo aooo oee ooecoo ayea pacopcoo ocyapceoo yepcea.

eaaec o pee peaoo-aecoo coea pacopcoo ocyapceoo yepcea.

pac, 2002 B.. ye, 2002 pacopc 2002 .C. e, 2002 2 I. OE OOEH Mey apaepa, ea ocoe acoo oepa, oeo cyecy yoae acoc. yee x acoce e ypca acoo aea ec oaee aa o papaoa a x ocoe eoo pee acox aa opeeeoo eceoo aaa acox oepa eopeecoo paecoo acca ec peeo acoo aea.

xapaepa.

yceoo ocoe ypca cye oe peapeo y acoa aeaa, a yea ca xo aae eeapy aeay, ey aepy, aaecy eoep, ocpae oee pooo apae acoo ay, oopoe aa oo aeaecoo aaa, eop epooce, poooy aece aao acox oepa oece acopoooy.

aao.

opoa ceac oac acoo aea oe oece aco aa oo cax ax aye poo aa coocx xapaepc pyx apaepo pae ooeco ay coppoac a ce ay o acax pocx cox acox oepa, ooo aee, o ce peaea. O aee a peee pooo pya aa, oco ooypx (acox pe).

px c:

- uepeue oex peymamo uacoo onepauu;

II. COEPAHE PCA - eue aucuocmu oex peymamo om ocox napaempo onepauu, uepeue auocu mux napaempo, onpeeeue ux Tea 1. peem uacoo ameamuu, aoe nomu u meponycmux paux aeu; uoou - papaoma nao noeu uacox onepau; pee, eo oe acoo aea, ee eco oec- axoeue napaempo uaemoo ueeu ycou onepauu. eo aae acox oepa. poce ece acoe Coceo, acoa aeaa pecae coo cooyoc oepa, apaep acoo oepa. aaa oxoa, pe eoo opeee ee cooc ee, pocxoeo cece pye op oa. poe, poea caa oxooc acoo x opaoo e poecce ocpooca. Co cpyypo o oepa. Cpe oxooc acox oepa.

pe o cpoa ccea aeaecx oee (aaecx opy Tea 2. Hapaeue u ucomupoaue no npocm u co cma cocoo cce). Oeo cceoa acoo aea - a c acoe oepa, a ae opeee py eoo ce- Hapaee o poco cae poeo. Pace poeo pao, eoxooc oopx oae c pa, oa ycox a- cpox oepa. Coe poe. Maeaecoe copoae coo oepa ooapac opee ae pex o apaepo, a aoc ye. epe oxooc. Opeeee cpoa acoo oeeo: pa, ee coocx apaepo oxooc. Opeeee coa a- cmouocme xapamepucmuu (oeu oa o eo ope, u- pae.

acoe oeu u peymam uacoo onepauu u m.n.); Tea 3. em oex apaeu onepau oea am, aoox - peee ae (umeocm uacoo onepauu uu am ee omuceu u uuu aaa u ooau, am namee, npooumeocm nepuoo auce- Oee ypc a aae acoo oepa o ee ooa u uu omcpou namee u m..); eee oe apae. Opeeee o coooe ypco pe- xapamepucmuu emuocmu (oxoocmu) uacoo onepauu eoo ypo oxooc oepa. Oea aoox oce ee ye (npoeme u yeme cmau). oex (opyax) apae. epe ee ye oex Ocooe ae ec opaaec a aop pee. Heoxooc apae. Heo pyo ca apae.

yea peeoo aopa eae cyoc acpoa peoa- Tea 4. uaeme ueeu ycou ompamo paaec pe epaoeoc ee, oocxc pa acoe oepa opa (ce). p acoo oea pee (time-value of money). aeoc oaec. aeoc poex yex cao. Ho3 ae ee ca. aeoc aee. Cpaee a- Taua ee x ocoa.

coe ooae cooece apao ooae aox o, oaaee acoo aea Tea 5. omou namee u ux napaemp Hepeype peype oo aee. acca acoHaeoae oaae pye oox pe. apaep pe. ocoa pea ocyepao. Meo pacea e apa ooex apaepo ooo. Opeeee apaepo pe.

ooae Tea 6. Bauocae noceoamee nomou namee Caacpoaoc ooo aee. oepc ooo. apaep Cmouocme napaemp (xapamepucmuu) uacox onepau oocpoo aoeoc apoae ee oae. oace cxoa cya (copeea cooc apaeo cy) P PV o. oaee ac aea. Ayap eo, pao opoCopeea cooc ooa aee A S(0); PVf a, oaee pa ac ocooo oa oe aoeoc.

c pee oxo (cooc) N NPV Tea 7. Ocoe xapamepucmuu oocpox npoemo cxoa cya pyo ae P Oea co copeeo cooc, eca peaeoc, ycxoa cya pyx Pr pee op oxooc.

Hapaea cya S FV; F; Fn Hapaea cooc pe S Sn; S(T); Pn; FVf Taua Hapaea cya pyo ae S Pacpeeee e o a a Hapaea cya pyx Sr Te a e Hapaea cya c yeo C FVI (aco) Hapaea cya oce ya aoa S S 1. pee acoo aea, aoe o epoo Acoa ea acex poeo I In; Id,r 2. Hapaee copoae o poc co caa Acoa ea coa D Dr,d 3. e oex apae oepa oea a, aoox oce- Acoa ea aoa G Bea aea (ea ooa) ooa aee R 4. aee ee yco opao oaameu omoeu cmouocmx napaempo uacox onepau 5. oo aee x apaep poca poea caa apae is i; i 6. Baocae oceoaee oo poca yea poea caa ds d; d 7. Ocoe xapaepc oocpox poeo Coa ea (peaa) poea caa apae i i ; r; ref; rt; f oo aco Coa oaa poea caa apae j I Coa ea (peaa) yea poea caa d dc; dt Coa oaa yea poea caa f III. METOECE AAH EH PCA ocoa ca poca p ye oo peea opao oo cea cy pepeea ca poca t a a a epoo ccea ooae o. coae, acoo oco ppoc (e poca) c poca oeceo aae ooe acoo aeae acoc e cyHepep ppoc (e poca) c poca ecye eo ycoec cce ooae o epo. opoea caa apae CB i j oy pa oa peex cce aece ocoo, apyc a ooea caa poea (p yee ) i* coax, yaax cce ocoo epayp. Oao yo o pyo-caa (p yee ) r r o o, o pao epaype ooo peee pyx oeco Caa aoa a poe g R; q ooae epo o (a. 2) 5 poe ooaee Ocoee peea cyea aooo oee eoxoo pooMoe (oe) apae o poc poea q ; Bt a opao o epayp coa, opac p o a ypc Moe (oe) apae o co poea q ; M(n,i); fni; Bt e. Cco ocoo epayp o ypcy acoa aeaa co oe o poc poea 1; t ae ce co, e ye oopx ae peea e oe co oe o co poea n 2; Dis(n,d); fnd; t ocao. Cco ooeo epayp peaae pacoe apae pe sn ff pe pyoopa oac oeceoo acooo aaa. Taoe oe pee pe an fp pacpee popeae ocoy aoc p ye ceyx a Bea ocooo acooo ppoca aea pe a acoo aeao yex ypco.

Bea ocooo ooceoo ppoca aea pe Pacpeeee yaex opoco o ea pecaeo a. 1.

Bea ea poca e aea pe q Ocoe acoc cxe pacea ye e Hapaee ec oyaeo cocooc ee(p yee ) Jc I copoae o poc co caa pee a. 3 4.

ec opeecx e (p yee ) Jp I ; Ip Te H Inf Taua Cpeeooo e poca e ip Ip Cxe pacea cpoa paocpoo acoo oepa Cpeeooo e h ; ht pocx poeo ypc oea a aae oepa (oe) 0 Haeoae cxe (eoa) pacea poeo co e oe- co e ypc oea a oe oepa (oe) 1 pa (T) oy () ec ypco a k Toe poe c o co e oepa Tooe 365(366) op (poe , oco ee) D (365/365) oaameu peex napaempo uacox onepau Ooee poe c o co e Tooe co epoo (cpo) acoo oepa oax n T; N; l oepa (365/360) co e oepa T ; t Ooee poe c pe co peoe co e oy (peea aa) K Y e oepa (360/360) co ace poeo oy m co aee oy ( acoo pe) p Ocoe acoc ye e aee ee yco opao pee a. 5.

Bec oec opoco acoo aea oo ycoo paeOcoe acoc ye e e oex apae a e ocox ac. B epy ac e oe acox oepa oea a, aoox oce pee a.

oepa: apae copoa, ye oex apae oepa 6.

oea a oepa, aoox oce ox poecco, acca ooo aee acox pe ye e ocoe o, cae c ae eee yco opaoo aee x apaep peea a pc. 1.

o, eo cpae oee oex aee, a ae opoc x Ocoe acoc ye e oo aee x apapaecoo pee. Bo opo ac paccapac oe ooo ep Ocoe xapaepc oocpox poeo pee aee, acoc ocox pe, eo oae oocpox aa. 7.

oeoce oye ocox oeo oocpox poeo.

yee c acoa aeaa pooc cooec c popao ypca a ocoe opaoaex caapo cooecyx yex ao ceaoce, apae o ooe ypae. Cye ocea e, o yae pacee aa ae ca ae.

7 Taua Ocoe acoc apaep pocx cox acox oepa p ace poeo B oepa o ace poeo Coe poe poecc poce poe o eo cae o oao cae j S = P(1+ nis ) S = P1+ S = P(1+ i)n m ln(S ) S - P P ln(S P) n = n = Hapaee n = j Pis m ln1+ ln(1+ i) m S - P S n j = m mn S P -is = i = -P Pn S S S P = P = P = j n 1+ 1+ nis (1+ i) m Maeaecoe ln(S ) S - P ln(S P) P n = copoae n = n = j Pis m ln1+ ln(1+ i) m S - P S n is = i = -1 j = m mn S P - P Pn f P = S(1- nds ) P = S(1- d ) P = S1 m ( ) S - P ln(P ) = S n = aoc ye n = - Sds ln(1- d) S - P P P f = m1- ds = d = 1- S S Sn Taua aee acoc ey pa a poex cao poce poe Coe poe B cao is ds j f i d is 1 n mn is ds = d = 1- n f = m1- mn --- i = 1+ nis -1 j = m( 1+ nis -1) 1+ nis 1+ nis 1+ nis ds 1 n mn ds is = n -1 j = m f = m(1- 1- nds ) --- i = d =1- 1- nds mn 1- nds - 1- nds 1- nds n (1+ i)n -1 i (1+ i) -m m ds = f = m1- --- d = i is = j = m( 1+ i -1) n 1+ i n(1+ i) n 1+ i mn m mn j j 1+ 1+ m - -1 j j 1+ j m m j f = 1+ ds = d = m -1 mn --i = m j is = m -j j 1+ 1+ n1+ n m m m 1- (1- d)n d 1- (1- d)n m is = j = mm -f = m(1- 1- d ) d ds = i = --n 1- d n(1- d) n 1- d m mn 1- f 1- f mn 1- f 1- 1- f m m m 1- j = 1- f is = m i = f d = 1- --mn m f ds = m f 1- f 1n1 n m m m copoae poce poe Coe poe * K n Taua s + i ) mr r P P K K r r K K * * oepc a n + i ) + ni ) ( pHepeype s CB Py Py CB Py CB CB Py S = P K * ( S = * ( * K S = P K * ( S = * + ni ) n n n n s n h h h n n + i ) + ni ( h + h h h ( + ) + ) ( + nr ( + r s B ceao acoo oepa + ) ( + oo aee oo aee i = s + ni ) C = P ( ) i = C = P acoe pe acoe pe r = i + + i r = s n n s g ) + i ) ( + n ( i ] g ) Peype G = Pni g Hao a poe G = P [ (+ i ) ] g S = P [ S = P [ ( + g ] Pc. 1. oo aee acoe pe, x ocoe apaep acca Ocoe acoc ceax acox oepa, cax c acee poeo poeo B oepa o ace ) e a c o e o ( poe poce poe Coe IV.

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