1. Oeiainu, eo ?ieue e ooieoeee a i?ioeanna iauanoaaiiiai
aini?iecaiaenoaa
Oeiainu i?aaenoaaeytho niaie niaieoiiinoue aeaiaaeiuo ioiioaiee,
aicieeathueo a i?ioeanna nicaeaiey oiiaeia aeaiaaeiuo n?aaenoa o
noauaeoia oicyenoaiaaiey e ainoaeainoaa e eniieueciaaiey eo ia oeaee
aini?iecaiaenoaa, noeioee?iaaiey e oaeiaeaoai?aiey nioeeaeueiuo ioaeae
iauanoaa. Auaeaeytho o?e iniiaiua noaaeee i?ioeanna iauanoaaiiiai
aini?iecaiaenoaa: i?iecaiaenoai, ?ani?aaeaeaiea e iio?aaeaiea.
Iaeanoueth aicieeiiaaiey e ooieeiie?iaaiey oeiainia yaeyaony aoi?ay
noaaeey aini?iecaiaenoaaiiiai i?ioeanna, eiaaea i?ienoiaeeo
?ani?aaeaeaiea noieiinoe i?iecaaaeaiiiai iauanoaaiiiai i?iaeoeoa. Eiaiii
ia yoie noaaeee iiyaeythony oeiainiaua ioiioaiey, naycaiiua n
oi?ie?iaaieai aeaiaaeiuo aeioiaeia e iaeiieaiee, i?eieiathueo
niaoeeoe/aneoth oi?io oeiainiauo ?ano?nia. Iioaioeeaeueii oeiainiaua
?ano?nu nicaeathony ia noaaeee i?iecaiaenoaa, eiaaea nicaeaaony iiaay
noieiinoue e inouaonaeyaony ia?aiin noa?ie. Iaeiaei ?aaeueiia
oi?ie?iaaiea oeiainiauo ?ano?nia ia/eiaaony oieueei ia noaaeee
?ani?aaeaeaiey, eiaaea noieiinoue ?aaeeciaaia. A iauae niaieoiiinoe
oeiainiauo ioiioaiee auaeaeytho o?e e?oiiua acaeiinaycaiiua noa?u:
oeiainu oicyenoaothueo noauaeoia, no?aoiaaiea, ainoaea?noaaiiua oeiainu.
A caaeneiinoe io oa?aeoa?a aeayoaeueiinoe noauaeoia eaaeaeie eo yoeo
noa? iiaeii auaeaeeoue ?acee/iua caaiuey. Eaaeaeia caaii auiieiyao naie
caaea/e, eiaao nianoaaiioth i?aaiecaoeeiiioth no?oeoo?o oeiainiaiai
aiia?aoa, iaeiaei a niaieoiiinoe iie ia?acotho oeiainiaoth nenoaio
ainoaea?noaa.
Acaeiiaeaenoaea iaaeaeo auaeaeaiiuie caaiueyie oeiainiaie nenoaiu
inouanoaeythony, eae i?aaeei, i?e iin?aaeie/anoaa o/?aaeaeaiee
aaieianeie nenoaiu, ea?athueo iniai aaaeioth ?ieue a ioiioaiee
ooieoeeiie?iaaiey anae nenoaiu (iniaaiii oeiainia i?aaei?eyoee).
Oeiainu noauaeoia oicyenoaiaaiey yaeythony iniiaiui yeaiaioii nenoaiu e
i?aaenoaaeytho niaie aeaiaaeiua ioiioaiey, naycaiiua n oi?ie?iaaieai e
?ani?aaeaeaieai oeiainiauo ?ano?nia. Oi?ie?othony oeiainiaua ?ano?nu ca
n/ao:
Nianoaaiiuo e i?e?aaiaiiuo e iei n?aaenoa (aeoeeiia?iue eaieoae, iaaaua
aciinu, i?eaueue, oeaeaaua iinooieaiey e o.ae.);
Iiaeeecoaiua ia oeiainiaii ?uiea ?ano?nu (e?aaeeou aeieain?i/iua e
e?aoein?i/iua, n?aaenoaa iinooiathuea io iia?aoeee n oeaiiuie aoiaaaie e
o.i.);
N?aaenoaa iinooiathuea a ii?yaeea ia?a?ani?aaeaeaiey (athaeaeaoiua
noaneaeee, noaaaioeee e o.i.).
Oeiainu noauaeoa oicyenoaiaaiey auiieiytho o?e iniiaiua ooieoeee:
oi?ie?iaaiea, iiaeaea?aeaiea iioeiaeueiue no?oeoo?u e ia?aueaaiee
i?iecaiaenoaaiiiai iioaioeeaea i?aaei?eyoey;
iaania/aiea oaeouae oeiainiai-oicyenoaaiiie aeayoaeueiinoe;
iaania/aiea o/anoey oicyenoaothuaai noauaeoa a inouanoaeaiee
nioeeaeueiie iieeoeee.
Cenoaia oi?aaeaiey oeiainaie ia i?aaei?eyoee
2.1. Co?oeoo?a e i?ioeann ooieoeeiie?iaaiey nenoaiu oi?aaeaiey
oeiainiauie ?ano?naie ia i?aaei?eyoee
Ethaie aecian ia/eiaaony n iinoaiiaee e ioaaoa ia neaaeothuea o?e
eeth/aaua aii?ina:
eaeiau aeieaeiu auoue aaee/eia e iioeiaeueiue ninoaa aeoeaia
i?aaei?eyoey, iicaieythuea aeinoe/ue iinoaaeaiiua ia?aae i?aaei?eyoeai
oeaee e caaea/e?
aaea iaeoe enoi/ieee oeiaine?iaaiey e eaeia aeieaeai auoue eo
iioeiaeueiue ninoaa?
eae i?aaieciaaoue oaeouaa e ia?niaeoeaiia oi?aaeaiea oeiainiaie
aeayoaeueiinoueth, iaania/eaathuaa ieaoaaeaniiniaiinoue e oeiainiaoth
onoie/eainoue i?aaei?eyoey?
?aoathony yoe aii?inu a ?aieao oeiainiaiai iaiaaeaeiaioa. yaeythuaainy
iaeiie ec eeth/aauo iiaenenoai iauae nenoaiu oi?aaeaiey i?aaei?eyoeai.
A iaeaieaa iauai aeaea iiae oeiainiaui eino?oiaioii iiieiaaony ethaie
eiio?aeo, ii eioi?iio i?ienoiaeeo iaeiia?aiaiiia oaaee/aiea oeiainiauo
aeoeaia iaeiiai i?aaei?eyoey e oeiainiauo iaycaoaeuenoa ae?oaiai
i?aaei?eyoey.
Oeiainiaua aeoeau aeeth/atho:
aeaiaaeiua n?aaenoaa;
eiio?aeoiia i?aai iieo/eoue io ae?oaiai i?aaei?eyoey aeaiaaeiua
n?aaenoaa eee ethaie ae?oaie aeae oeiainiauo aeoeaia;
eiio?aeoiia i?aai iaiaia oeiainiauie eino?oiaioaie n ae?oaei
i?aaei?eyoeai ia iioaioeeaeueii auaiaeiuo oneiaeyo;
aeoeee ae?oaiai i?aaei?eyoey.
E oeiainiaui iaycaoaeuenoaai ioiinyony eiio?aeoiua iaycaoaeuenoaa:
auieaoeoue aeaiaaeiua n?aaenoaa eee i?aaeinoaaeoue eaeie-oi eiie aeae
oeiainiauo aeoeaia ae?oaiio i?aaei?eyoeth;
iaiaiyoueny oeiainiauie eino?oiaioaie n ae?oaei i?aaei?eyoeai ia
iioaioeeaeueii iaauaiaeiuo oneiaeyo (a /anoiinoe, oaeay neooaoeey iiaeao
aicieeiooue i?e auioaeaeaiiie i?iaeaaea aeaaeoi?neie caaeieaeaiiinoe).
Oeiainiaua eino?oiaiou iiae?acaeaeythony ia ia?ae/iua (aeaiaaeiua
n?aaenoaa, oeaiiua aoiaae, e?aaeeoi?neay e aeaaeoi?neay caaeieaeaiiinoue
ii oaeouei iia?aoeeyi) e aoi?e/iua, eee i?iecaiaeiua (oeiainiaua
iioeeiiu, oueth/a?nu, oi?aa?aeiua eiio?aeou, i?ioeaioiua naiiu,
aaethoiua naiiu).
Nouanoaoao e aieaa oi?iuaiiia iiieiaiea nouiinoe iiiyoey «oeiainiaue
eino?oiaio». A niioaaonoaee n iei auaeaeytho o?e iniiaiua eaoaai?ee
oeiainiauo eino?oiaioia: aeaiaaeiua n?aaenoaa (n?aaenoaa a eanna e ia
?an/aoiii n/aoa, aaethoa), e?aaeeoiua eino?oiaiou (iaeeaaoeee,
oi?aa?aeiua eiio?aeou, oueth/a?nu, iioeeiiu, naiiu e ae?.) e niiniau
o/anoey a onoaaiii eaieoaea (aeoeee e iae).
Iaoiaeu oeiainiaiai oi?aaeaiey iiiaiia?aciu. Iniiaiuie ec ieo yaeythony:
i?iaiice?iaaiea, ieaie?iaaiea, iaeiaiiaeiaeaiea, no?aoiaaiea,
naiioeiaine?iaaiea, e?aaeeoiaaiea, nenoaia ?an/aoia, nenoaia oeiainiaie
iiiiue, nenoaia oeiainiauo naieoeee, nenoaia aii?oecaoeeiiiuo
io/eneaiee, nenoaia noeioee?iaaiey, i?eioeeiu oeaiiia?aciaaiey,
o?anoiaua iia?aoeee, caeiaiaua iia?aoeee, o?ainoa?oiua iia?aoeee,
oaeoi?eia, a?aiaea, eeceia.
Ninoaaiui yeaiaioii i?eaaaeaiiuo iaoiaeia yaeythony niaoeeaeueiua i?eaiu
oeiainiaiai oi?aaeaiey: e?aaeeou, caeiu, i?ioeaioiua noaaee,
aeeaeaeaiaeu, eioe?iaea aaethoiuo eo?nia, aeoeec, aeeneiio e ae?. Iniiao
eioi?iaoeeiiiiai iaania/aiey nenoaiu oeiainiaiai oi?aaeaiey ninoaaeyao
ethaay eioi?iaoeey oeiainiaiai oa?aeoa?a:
aooaaeoa?neay io/aoiinoue;
niiauaiey oeiainiauo i?aaiia;
eioi?iaoeey o/?aaeaeaiee aaieianeie nenoaiu;
eioi?iaoeey oiaa?iuo, oiiaeiauo e aaethoiuo ae?ae;
i?i/ay eioi?iaoeey.
Oaoie/aneia iaania/aiea nenoaiu oeiainiaiai oi?aaeaiey yaeyaony
naiinoiyoaeueiui e aanueia aaaeiui aa yeaiaioii. Iiiaea nia?aiaiiua
nenoaiu, iniiaaiiua ia aacaoiaaeiie oaoiieiaee (iaaeaaieianeea ?an/aou,
acaeiica/aou, ?an/aou n iiiiuueth e?aaeeoiuo ea?oi/ae e ae?.),
iaaiciiaeiu aac i?eiaiaiey naoae YAI, ia?niiaeueiuo eiiiuethoa?ia,
ooieoeeiiaeueiuo iaeaoia i?eeeaaeiuo i?ia?aii.
Ooieoeeiie?iaaiea ethaie nenoaiu oeiainiaiai oi?aaeaiey inouanoaeyaony a
?aieao aeaenoaothuaai i?aaiaiai e ii?iaoeaiiai iaania/aiey. Nthaea
ioiinyony: caeiiu, oeacu I?aceaeaioa, iinoaiiaeaiey i?aaeoaeuenoaa,
i?eeacu e ?anii?yaeaiey ieienoa?noa e aaaeiinoa, eeoeaicee, onoaaiua
aeieoiaiou, ii?iu, eino?oeoeee, iaoiaee/aneea oeacaiey e ae?.
2.2. Oeiainiaue iaiaaeaea?, caaea/e e oeaee oi?aaeaiey oeiainaie
A oneiaeyo ?uii/iie yeiiiieee oeiainiaue iaiaaeaea? noaiiaeony iaeiie ec
eeth/aauo oeao? ia i?aaei?eyoee. Ii ioaaonoaai ca iinoaiiaeo i?iaeai
oeiainiaiai oa?aeoa?a, aiaeec oeaeaniia?aciinoe eniieueciaaiey oiai eee
eiiai niiniaa eo ?aoaiey e eiiaaea ca i?eiyoea ieii/aoaeueiiai ?aoaiey
ii auai?o iaeaieaa i?eaieaiiai aa?eaioa aeaenoaee. Iaeiaei anee
iinoaaeaiiay i?iaeaia eiaao nouanoaaiiia cia/aiea aeey i?aaei?eyoey, ii
iiaeao auoue niaaoieeii aunoaai oi?aaeai/aneiai ia?niiaea. Iaeiiaoe,
oeiainiaue iaiaaeaea?, eae i?aaeei, — ioaaonoaaiiue eniieieoaeue
i?eiyoiai ?aoaiey, ii oaeaea inouanoaeyao iia?aoeaioth oeiainiaoth
aeayoaeueiinoue. Aeaaiia aa niaea?aeaiea ninoieo a eiio?iea ca
aeaiaaeiuie iioieaie. Oeiainiaue iaiaaeaea? /anoi aaiaeeo a ninoaa
aunoaai oi?aaeai/aneiai ia?niiaea oe?iu, iineieueeo i?eieiaao o/anoea a
?aoaiee anao aaaeiaeoeo aii?inia.
A iaeaieaa iauai aeaea aeayoaeueiinoue oeiainiaiai iaiaaeaea?a iiaeao
auoue no?oeoo?e?iaaia neaaeothuei ia?acii:
iauee oeiainiaue aiaeec e ieaie?iaaiea;
iaania/aiea i?aaei?eyoey oeiainiauie ?ano?naie (oi?aaeaiea enoi/ieeaie
n?aaenoa);
?ani?aaeaeaiea oeiainiauo ?ano?nia (eiaanoeoeeiiiay iieeoeee e
oi?aaeaiea aeoeaaie).
Eiaeea auaeaeaiey oaeeo iaeanoae aeayoaeueiinoe oeiainiaiai iaiaaeaea?a
oanii naycaia ni no?oeoo?ie aaeaina, eae iniiaiie io/aoiie oi?iie,
io?aaeathuae eiouanoaaiiia e oeiainiaia ninoiyiea i?aaei?eyoey (ni.
?en.).
Oeiainiaue aiaeec e ieaie?iaaiea
AAEAIN
Oi?aaeaiea aeoeaaie Iniiaiua n?aaenoaa Nianoaaiiue eaieoae Oi?aaeaiea
eaieoaeii
Oaeouea aeoeau I?eaea/aiiue eaieoae
Auaeaeaiiua iai?aaeaiey aeayoaeueiinoe iaeiia?aiaiii ii?aaeaeytho e
iniiaiua caaea/e, noiyuea ia?aae iaiaaeaea?ii. Ninoaa yoeo caaea/ iiaeao
auoue aeaoaeece?iaai neaaeothuei ia?acii.
A ?aieao ia?aiai iai?aaeaiey inouanoaeyaony iauay ioeaiea:
aeoeaia i?aaei?eyoey e enoi/ieeia eo oeiaine?iaaiey;
aaee/eiu e ninoaaa ?ano?nia, iaiaoiaeeiuo aeey iiaeaea?aeaiey
aeinoeaiooiai yeiiiie/aneiai iioaioeeaea i?aaei?eyoey e ?anoe?aiey aai
aeayoaeueiinoe;
enoi/ieeia aeiiieieoaeueiiai oeiaine?iaaiey;
nenoaiu eiio?iey ca ninoiyieai e yooaeoeaiinoueth eniieueciaaiey
oeiainiauo ?ano?nia.
Aoi?ia iai?aaeaiea i?aaeiieaaaao aeaoaeueioth ioeaieo:
iauaia o?aaoaiuo oeiainiauo ?ano?nia;
oi?iu eo i?aaenoaaeaiey (aeieain?i/iue eee e?aoein?i/iue e?aaeeo,
aeaiaaeiay iaee/iinoue);
noaiaie aeinooiiinoe e a?aiaie i?aaenoaaeaiey (aeinooiiinoue oeiainiauo
?ano?nia iiaeao ii?aaeaeyoueny oneiaeyie aeiaiai?a; oeiainu aeieaeiu
auoue aeinooiiu a ioaeiii iauaia e a ioaeiia a?aiy);
noieiinoe iaeaaeaiey aeaiiui aeaeii ?ano?nia (i?ioeaioiua noaaee, i?i/ea
oi?iaeueiua e iaoi?iaeueiua oneiaey i?aaeinoaaeaiey aeaiiiai enoi/ieea
n?aaenoa);
?enea, annioeee?oaiiai n aeaiiui enoi/ieeii n?aaenoa (oae, eaieoae
nianoaaiieeia eae enoi/iee n?aaenoa ai?acaei iaiaa ?eneiaai, /ai n?i/iay
nnoaea aaiea).
O?aouea iai?aaeaiea i?aaeoniao?eaaao aiaeec e ioeaieo aeieain?i/iuo e
e?aoein?i/iuo ?aoaiee eiaanoeoeeiiiiai oa?aeoa?a:
iioeiaeueiinoue o?ainoi?iaoeee oeiainiauo ?ano?nia a ae?oaea aeaeu
?ano?nia (iaoa?eaeueiua, o?oaeiaua, aeaiaaeiua);
oeaeaniia?aciinoue e yooaeoeaiinoue aeiaeaiee a iniiaiua oiiaeu, eo
ninoaa e no?oeoo?a;
iioeiaeueiinoue iai?ioiuo n?aaenoa;
yooaeoeaiinoue oeiainiauo aeiaeaiee.
I?eiyoea ?aoaiee n eniieueciaaieai i?eaaaeaiiuo ioeaiie auiieiyaony a
?acoeueoaoa aiaeeca aeueoa?iaoeaiuo ?aoaiee, o/eouaathueo eiii?iienn
iaaeaeo o?aaiaaieyie eeeaeaeiinoe, oeiainiaie onoie/eainoe e
?aioaaaeueiinoe.
Eiaeea auaeaeaiey iniiaiuo caaea/ oeiainiaiai iaiaaeaeiaioa oaeaea a
cia/eoaeueiie noaiaie ii?aaeaeyaony niaea?aeaieai aooaaeoa?neie
io/aoiinoe e i?aaenoaaeaia ia ?en. 3.
2.3. Oeaee oeiainiaiai iaiaaeaeiaioa
*oi yaeyaony i?eciaeii oniaoiiai oeiainiaiai oi?aaeaiey? Iao?oaeii
noi?ioee?iaaoue oeaeoth nenoaio oeaeae:
auaeeaaiea oe?iu a oneiaeyo eiieo?aioiie ai?ueau;
ecaaaeaiea aaie?ionoaa e e?oiiuo oeiainiauo iaoaea/;
eeaea?noai a ai?ueaa n eiieo?aioaie;
iaeneiecaoeey ?uii/iie noieiinoe oe?iu;
i?eaieaiua oaiiu ?inoa yeiiiie/aneiai iioaioeeaea oe?iu;
?ino iauaiia i?iecaiaenoaa e ?aaeecaoeee;
iaeneiecaoeey i?eauee;
ieieiecaoeey ?anoiaeia;
iaania/aiea ?aioaaaeueiie aeayoaeueiinoe e o. ae.
I?ei?eoaoiinoue oie eee eiie oeaee ii-?aciiio iauyniyaony a ?aieao
nouanoaothueo oai?ee i?aaiecaoeee aeciana.
Iaeaieaa ?ani?ino?aiaiiui yaeyaony ooaa?aeaeaiea, /oi oe?ia aeieaeia
?aaioaoue oaeei ia?acii, /oiau iaania/eoue iaeneiaeueiue aeioiae aa
aeaaeaeueoeai. Iau/ii yoi annioeee?oaony n ?aioaaaeueiie ?aaioie, ?inoii
i?eauee e nieaeaieai ?anoiaeia. Iaeiicia/ai ee oaeie auaiae?
A ?aieao o?aaeeoeeiiiie iaieeanne/aneie yeiiiie/aneie iiaeaee
i?aaeiieaaaaony, /oi ethaay oe?ia nouanoaoao aeey oiai, /oiau
iaeneiece?iaaoue i?eaueue (iau/ii iiae?acoiaaaaony, /oi ?a/ue eaeao i
i?eauee n iiceoeee ia ?aciaiai, ii aeieain?i/iiai aa iieo/aiey). A
eaeaaea, eiaaea i?aaeiieaaathony ?aaiiaeinooiiinoue eioi?iaoeee, iaee/ea
iiuoiiai ?oeiaiaenoaa e ae?oaeo aniaeoia, aeinoe/ue oaeiai iaeneioia
iaaiciiaeii; i?e yoii noiia?iue ia?aeeiaeueiue aeioiae ?aaai ioeth.
Eiaiii iiyoiio i?eiaiyaony iiiyoea «ii?iaeueiie» i?eauee, o. a. i?eauee,
ono?aeaathuae aeaaeaeueoeaa aeaiiiai aeciana. Aeaenoaeoaeueii,
i?eaueueiinoue ?acee/iuo aeaeia i?iecaiaenoa iiaeao nouanoaaiii
?acee/aoueny, /oi ia aucuaaao oai ia iaiaa no?aieaiey anao aecianiaiia
iaeiia?aiaiii niaieoue naie aecian ia aieaa i?eaueueiue. A iniiaa oaeiai
iiaeoiaea eaaeeo e aanueia ?ani?ino?aiaiiay nenoaia oeaiiia?aciaaiey ia
i?iecaiaeeioth i?iaeoeoeeth — «naaanoieiinoue iethn iaeay ono?aeaathuay
i?iecaiaeeoaey iaaeaaaea».
Ae?oaea enneaaeiaaoaee auaeaeaatho i?aaeiieiaeaiea, /oi a iniiaa
aeayoaeueiinoe oe?i e eo ?oeiaiaenoaa eaaeeo no?aieaiea e ia?aueaaieth
iauaiia i?iecaiaenoaa ecauoa. Yooaeoeaiinoue ioeaieaaaony iai?eia?
iieacaoaeai «aeioiae ia aeoeeth».
O?aouey a?oiia enneaaeiaaoaeae i?aaeeaaaao oai?eth «caeioa?aniaaiiuo
eeoe» i?aaeiieaaathuay, /oi oeaeue ooieoeeiie?iaaiey ethaie oe?iu –
caeeth/aaony a ai?iiiecaoeee eiioeeeoothueo oeaeae ?acee/iuo a?oii
th?eaee/aneeo e oece/aneeo eeoe, eiathueo iaiin?aaenoaaiiia eee
einaaiiia ioiioaiea e aeaiiie oe?ia, – aeoeeiia?ia, iaaiiiai
oi?aaeythuaai, ?aaioieeia, eiio?aaaioia, ainoaea?noaaiiuo i?aaiia.
2.4. No?oeoo?a enoi/ieeia oeiaine?iaaiey i?aaei?eyoey
A oeiainiaii iaiaaeaeiaioa iiae aioo?aiieie e aiaoieie enoi/ieeaie
oeiaine?iaaiey iiieiatho niioaaonoaaiii nianoaaiiua e i?eaea/aiiua
(caaiiua) n?aaenoaa. Ecaanoiu ?acee/iua eeanneoeeaoeee enoi/ieeia
n?aaenoa. Iaeia ec aiciiaeiuo e iaeaieaa iaueo a?oiie?iaie i?aaenoaaeaia
ia ?enoiea.
Enoi/ieee n?aaenoa i?aaei?eyoey
Enoi/ieee n?aaenoa e?aoein?i/iiai iacai/aiey
Aaaine?iaaiiue (aeieain?i/iue) eaieoae
caaiiue eaieoae
nianoaaiiue eaieoae
Iniiaiui yeaiaioii i?eaaaeaiiie noaiu yaeyaony nianoaaiiue eaieoae.
Nianoaaiiue eaieoae i?aaei?eyoey
Eaieoae, i?aaeinoaaeaiiue nianoaaiieeii
I?i/ea aciinu th?eaee/aneeo e oece/aneeo eeoe
?aca?au, iaeiieaiiua i?aaei?eyoeai
Onoaaiue eaieoae
Yienneiiiue aeioiae
?aca?aiue eaieoae
Aeiaaai/iue eaieoae
Iaeiieaiiay i?eaueue
Oeaeaaia oeiane?iaaiea
Iiaea?oaiaaiey, aciinu
Ia?ani?aaeaeaiiay i?eaueue
Oiiaeu iaeiieaiey
E iniiaiui enoi/ieeai i?eaea/aiiuo n?aaenoa ioiinyony:
nnoaeu aaieia;
caaiiua n?aaenoaa;
n?aaenoaa io i?iaeaaee iaeeaaoeee e ae?oaeo oeaiiuo aoiaa;
e?aaeeoi?neay caaeieaeaiiinoue.
I?eioeeieaeueiia ?acee/ea iaaeaeo enoi/ieeaie nianoaaiiuo e caaiiuo
n?aaenoa e?iaony a th?eaee/aneie i?e/eia — a neo/aa eeeaeaeaoeee
i?aaei?eyoey aai aeaaeaeueoeu eiatho i?aai ia oo /anoue eiouanoaa
i?aaei?eyoey, eioi?ay inoaiaony iinea ?an/aoia n o?aoueeie eeoeaie.
I?e nicaeaiee i?aaei?eyoey aeeaaeaie a aai onoaaiue eaieoae iiaoo auoue
aeaiaaeiua n?aaenoaa, iaoa?eaeueiua e iaiaoa?eaeueiua aeoeau. A iiiaio
ia?aaea/e aeoeaia a aeaea aeeaaea a onoaaiue eaieoae i?aai nianoaaiiinoe
ia ieo ia?aoiaeeo e oicyenoaothuaio noauaeoo, o. a. eiaanoi?u oa?ytho
aauiua i?aaa ia yoe iauaeou. Oaeei ia?acii, a neo/aa eeeaeaeaoeee
i?aaei?eyoey eee auoiaea o/anoieea ec ninoaaa iauanoaa eee oiaa?euanoaa
ii eiaao i?aai eeoue ia eiiiainaoeeth naiae aeiee a ?aieao inoaoi/iiai
eiouanoaa, ii ia ia aica?ao iauaeoia, ia?aaeaiiuo ei a naia a?aiy a
aeaea aeeaaea a onoaaiue eaieoae. Onoaaiue eaieoae, neaaeiaaoaeueii,
io?aaeaao noiio iaycaoaeuenoa i?aaei?eyoey ia?aae eiaanoi?aie.
Onoaaiue eaieoae oi?ie?oaony i?e ia?aiia/aeueiii eiaanoe?iaaiee
n?aaenoa. Aai aaee/eia iauyaeyaony i?e ?aaeno?aoeee i?aaei?eyoey, a
ethaua ei??aeoe?iaee ?acia?a onoaaiiai eaieoaea (aeiiieieoaeueiay
yienney aeoeee, nieaeaiea iiieiaeueiie noieiinoe aeoeee, aianaiea
aeiiieieoaeueiuo aeeaaeia, i?eai iiaiai o/anoieea, i?eniaaeeiaiea /anoe
i?eauee e ae?.) aeiioneathony eeoue a neo/ayo e ii?yaeea,
i?aaeoniio?aiiuo aeaenoaothuei caeiiiaeaoaeuenoaii e o/?aaeeoaeueiuie
aeieoiaioaie.
Oi?ie?iaaiea onoaaiiai eaieoaea iiaeao nii?iaiaeaeaoueny ia?aciaaieai
aeiiieieoaeueiiai enoi/ieea n?aaenoa — yienneiiiiai aeioiaea. Yoio
enoi/iee aicieeaao a neo/aa, eiaaea a oiaea ia?ae/iie yiennee aeoeee
i?iaeathony ii oeaia auoa iiieiaea. I?e iieo/aiee yoeo noii iie
ca/eneythony a aeiaaai/iue eaieoae.
I?eaueue yaeyaony iniiaiui enoi/ieeii n?aaenoa aeeiaie/ii
?acaeaathuaainy i?aaei?eyoey. A aaeaina iia i?enoonoaoao a yaiii aeaea
eae ia?ani?aaeaeaiiay i?eaueue, a oaeaea a caaoaee?iaaiiii aeaea — eae
nicaeaiiua ca n/ao i?eauee oiiaeu e ?aca?au. A oneiaeyo ?uii/iie
yeiiiieee aaee/eia i?eauee caaeneo io iiiaeo oaeoi?ia, iniiaiui ec
eioi?uo yaeyaony niioiioaiea aeioiaeia e ?anoiaeia. Aianoa n oai a
aeaenoaothueo ii?iaoeaiuo aeieoiaioao caeiaeaia aiciiaeiinoue
ii?aaeaeaiiiai ?aaoee?iaaiey i?eauee ?oeiaiaenoaii i?aaei?eyoey. E /eneo
oaeeo ?aaoee?othueo i?ioeaaeo? ioiinyony:
aa?uee?iaaiea a?aieoeae ioianaiey aeoeaia e iniiaiui n?aaenoaai;
onei?aiiay aii?oecaoeey iniiaiuo n?aaenoa;
i?eiaiyaiay iaoiaeeea aii?oecaoeee iaeioeaiiuo e auno?ieciaoeaathueony
i?aaeiaoia;
ii?yaeie ioeaiee e aii?oecaoeee iaiaoa?eaeueiuo aeoeaia;
ii?yaeie ioeaiee aeeaaeia o/anoieeia a onoaaiue eaieoae;
auai? iaoiaea ioeaiee i?iecaiaenoaaiiuo caiania;
ii?yaeie o/aoa i?ioeaioia ii e?aaeeoai aaieia, eniieuecoaiuo ia
oeiaine?iaaiea eaieoaeueiuo aeiaeaiee;
ii?yaeie nicaeaiey ?aca?aa ii niiieoaeueiui aeieaai;
ii?yaeie ioianaiey ia naaanoieiinoue ?aaeeciaaiiie i?iaeoeoeee
ioaeaeueiuo aeaeia ?anoiaeia;
ninoaa iaeeaaeiuo ?anoiaeia e niinia eo ?ani?aaeaeaiey.
I?eaueue — iniiaiie enoi/iee oi?ie?iaaiey ?aca?aiiai eaieoaea (oiiaea).
Yoio eaieoae i?aaeiacia/ai aeey aiciauaiey iai?aaeaeaeaiiuo iioa?ue e
aiciiaeiuo oauoeia io oicyenoaaiiie Aeayoaeueiinoe, o. a. yaeyaony
no?aoiaui ii naiae i?e?iaea. Ii?yaeie oi?ie?iaaiey ?aca?aiiai eaieoaea
ii?aaeaeyaony ii?iaoeaiuie aeieoiaioaie, ?aaoee?othueie aeayoaeueiinoue
i?aaei?eyoey aeaiiiai oeia, a oaeaea aai onoaaiuie aeieoiaioaie.
Aeiaaai/iue eaieoae eae enoi/iee n?aaenoa i?aaei?eyoey ia?acoaony, eae
i?aaeei, a ?acoeueoaoa ia?aioeaiee iniiaiuo n?aaenoa E ae?oaeo
iaoa?eaeueiuo oeaiiinoae. Ii?iaoeaiuie aeieoiaioaie cai?auaaony
eniieueciaaiea aai ia oeaee iio?aaeaiey.
Niaoeeoe/aneei enoi/ieeii n?aaenoa yaeythony oiiaeu niaoeeaeueiiai
iacia/aiey e oeaeaaiai oeiaine?iaaiey: aacaiciacaeii iieo/aiiua
oeaiiinoe, a oaeaea aacaica?aoiua e aica?aoiua ainoaea?noaaiiua
anneaiiaaiey ia oeiaine?iaaiea iai?iecaiaenoaaiiie aeayoaeueiinoe,
naycaiiie n niaea?aeaieai iauaeoia nioeeaeueii-eoeueoo?iiai e
eiiioiaeueii-auoiaiai iacia/aiey, ia oeiaine?iaaiea ecaea?aeae ii
ainnoaiiaeaieth ieaoaaeaniiniaiinoe i?aaei?eyoee, iaoiaeyueony ia iieiii
athaeaeaoiii oeiaine?iaaiee, e ae?.
3. Eiaeea oeiainiauo iia?aoeee a ?uii/iie yeiiiieea
Oeiainiaua au/eneaiey, aace?othueany ia iiiyoee a?aiaiiie noieiinoe
aeaiaa, yaeythony e?aaoaieueiui yeaiaioii oeiainiaiai iaiaaeaeiaioa e
eniieuecothony a ?acee/iuo aai ?acaeaeao. Iaeaieaa eioaineaii iie
i?eiaiythony aeey ioeaiee eiaanoeoeeiiiuo i?iaeoia, a iia?aoeeyo ia
?uiea oeaiiuo aoiaa, a nnoaei-caaiiuo iia?aoeeyo, a ioeaiea aeciana e
ae?.
3.1. A?aiaiiay oeaiiinoue aeaiaa
Ia?aoiae e ?uii/iie yeiiiieea nii?iaiaeaeaaony iiyaeaieai iaeioi?uo
aeaeia aeayoaeueiinoe, eiathueo aeey oeiainiaiai iaiaaeaea?a
i?aaei?eyoey i?eioeeieaeueii iiaue oa?aeoa?. E eo /eneo ioiineony
caaea/a yooaeoeaiiai aeiaeaiey aeaiaaeiuo n?aaenoa. A oneiaeyo
oeaio?aeeciaaiii ieaie?oaiie yeiiiieee ia o?iaia i?aaei?eyoey oaeie
caaea/e i?aeoe/anee ia nouanoaiaaei.
Iuia aeaiueae i?eia?aoatho aua iaeio oa?aeoa?enoeeo, aeinaea iaaaaeiioth
oe?ieiio e?oao ethaeae, ii iauaeoeaii nouanoaothuoth, a eiaiii —
a?aiaiioth oeaiiinoue. Yoio ia?aiao? iiaeii ?anniao?eaaoue a aeaoo
aniaeoao: ia?aue aniaeo naycai n iaanoeaiaieai aeaiaaeiie iaee/iinoe n
oa/aieai a?aiaie, aoi?ie aniaeo naycai n ia?auaieai eaieoaea (aeaiaaeiuo
n?aaenoa). I?iaeaia «aeaiueae — a?aiy» ia iiaa, iiyoiio oaea ?ac?aaioaiu
oaeiaiua iiaeaee e aeai?eoiu, iicaieythuea i?eaioe?iaaoueny a enoeiiie
oeaia aoaeoueo aeeaeaeaiaeia n iiceoeee oaeouaai iiiaioa. Ei?ioei
ioa?aeoa?ecoai eo a oai?aoe/aneii e i?aeoe/aneii aniaeoao.
3.2 Iia?aoeee ia?auaiey e aeeneiioe?iaaiey
Eiaeea iino?iaiey iniiaiuo aeai?eoiia aeinoaoi/ii i?inoa e iniiaaia ia
neaaeothuae eaeaa. I?inoaeoei aeaeii oeiainiaie naeaeee yaeyaony
iaeiie?aoiia i?aaeinoaaeaiea a aeiea iaeioi?ie noiiu PV n oneiaeai, /oi
/a?ac eaeia-oi a?aiy t aoaeao aica?auaia aieueoay noiia FV. Eae
ecaanoii, ?acoeueoaoeaiinoue iiaeiaiie naeaeee iiaeao auoue
ioa?aeoa?eciaaia aeaiyei: eeai n iiiiuueth aaniethoiiai iieacaoaey —
i?e?inoa (FV — PV), eeai iooai ?an/aoa iaeioi?iai ioiineoaeueiiai
iieacaoaey. Aaniethoiua iieacaoaee /aua anaai ia iiaeoiaeyo aeey
iiaeiaiie ioeaiee aaeaeo eo ianiiinoaaeiinoe a i?ino?ainoaaiii-a?aiaiiii
aniaeoa. Iiyoiio iieuecothony niaoeeaeueiui eiyooeoeeaioii — noaaeie.
Yoio iieacaoaeue ?ann/eouaaaony ioiioaieai i?e?auaiey enoiaeiie. noiiu e
aaciaie aaee/eia, a ea/anoaa eioi?ie iiaeii a?aoue eeai PV, eeai FV.
Oaeei ia?acii, noaaea ?ann/eouaaaony ii iaeiie ec aeaoo oi?ioe:
oaii i?e?inoa rt = (FV- PV)/PV
oaii nieaeaiey dt = (FV- PV)/FV
A oeiainiauo au/eneaieyo ia?aue iieacaoaeue eiaao aua iacaaiey
«i?ioeaioiay noaaea», «i?ioeaio», «?ino», «noaaea i?ioeaioa», «ii?ia
i?eauee», «aeioiaeiinoue», a aoi?ie — «o/aoiay noaaea», «aeeneiio».
I/aaeaeii, /oi iaa noaaee acaeiinaycaiu, o.a. ciay iaeei iieacaoaeue,
iiaeii ?ann/eoaoue ae?oaie:
rt = dt/(1-dt) dt = rt/(1+rt)
Iaa iieacaoaey iiaoo au?aaeaoueny eeai a aeieyo aaeeieoeu, eeai a
i?ioeaioao.
I?ioeann, a eioi?ii caaeaiu enoiaeiay noiia e i?ioeaioiay noaaea, a
oeiainiauo au/eneaieyo iacuaaaony i?ioeannii ia?auaiey. I?ioeann, a
eioi?ii caaeaiu iaeeaeaaiay a aoaeouai e iieo/aieth (aica?auaaiay) noiia
e eiyooeoeeaio aeeneiioe?iaaiey, iacuaaaony i?ioeannii aeeneiioe?iaaiey.
A ia?aii neo/aa ?a/ue eaeao i aeaeaeaiee aeaiaaeiiai iioiea io
ianoiyuaai e aoaeouaio, ai aoi?ii — i aeaeaeaiee io aoaeouaai e
ianoiyuaio.
Iaiaoiaeeii ioiaoeoue, /oi a ea/anoaa eiyooeoeeaioa aeeneiioe?iaaiey
iiaeao eniieueciaaoueny eeai i?ioeaioiay noaaea (iaoaiaoe/aneia
aeeneiioe?iaaiea), eeai o/aoiay noaaea (aaieianeia aeeneiioe?iaaiea).
Yeiiiie/aneee niune oeiainiaie iia?aoeee ia?aueaaiey ninoieo a
ii?aaeaeaiee aaee/eiu oie noiiu, eioi?ie aoaeao eee aeaeaao ?aniieaaaoue
eiaanoi? ii ieii/aiee yoie iia?aoeee.
FV = PV + PV* rt
Ia i?aeoeea aeioiaeiinoue yaeyaony aaee/eiie iaiinoiyiiie, caaenyuae,
aeaaiui ia?acii, io noaiaie ?enea, annioeee?oaiiai n aeaiiui aeaeii
aeciana, a eioi?ue naeaeaii eiaanoe?iaaiea eaieoaea. Naycue caeanue
i?yii i?iii?oeeiiaeueiay — /ai ?eneiaaiiaa aecian, oai auoa cia/aiea
aeioiaeiinoe. Iaeiaiaa ?eneiaaiiu aeiaeaiey a ainoaea?noaaiiua oeaiiua
aoiaae eee a ainoaea?noaaiiue aaie, iaeiaei aeioiaeiinoue iia?aoeee a
yoii neo/aa ioiineoaeueii iaauniea.
Aaee/eia FV iieacuaaao eae au aoaeouoth noieiinoue «naaiaeiyoiae»
aaee/eiu PV i?e caaeaiiii o?iaia aeioiaeiinoe.
Yeiiiie/aneee niune aeeneiioe?iaaiey caeeth/aaony ai a?aiaiiii
oii?yaei/aiee aeaiaaeiuo iioieia ?acee/iuo a?aiaiiuo ia?eiaeia.
Eiyooeoeeaio aeeneiioe?iaaiey iieacuaaao, eaeie aaeaaiaeiue i?ioeaio
aica?aoa oi/ao (eee iiaeao) eiaoue eiaanoi? ia eiaanoe?oaiue ei eaieoae.
A yoii neo/aa eneiiay aaee/eia PV iieacuaaao eae au oaeouoth,
«naaiaeiyoithth» noieiinoue aoaeouae aaee/eiu FV.
I?eia?: I?aaei?eyoea iieo/eei e?aaeeo ia iaeei aiae a ?acia?a 5 iei.?oa.
n oneiaeai aica?aoa 10 iei.?oa. A yoii neo/aa i?ioeaioiay noaaea ?aaia
100%, a aeeneiio — 50%.
3.3. I?ioeaioiua noaaee e iaoiaeu eo ia/eneaiey
I?aaeinoaaeyy naie aeaiaaeiua n?aaenoaa a aeiea, eo aeaaeaeaoe iieo/aao
ii?aaeaeaiiue aeioiae a aeaea i?ioeaioia, ia/eneyaiuo ii iaeioi?iio
aeai?eoio a oa/aiea ii?aaeaeaiiiai i?iiaaeooea a?aiaie. Iineieueeo
noaiaea?oiui a?aiaiiui eioa?aaeii a oeiainiauo iia?aoeeyo yaeyaony 1
aiae, iaeaieaa ?ani?ino?aiai aa?eaio, eiaaea i?ioeaioiay noaaea
onoaiaaeeaaaony a aeaea aiaeiaie noaaee, iiae?acoiaaathuae iaeiie?aoiia
ia/eneaiea i?ioeaioia ii enoa/aiee aiaea iinea iieo/aiey nnoaeu.
Ecaanoiu aeaa iniiaiua noaiu aeene?aoiiai ia/eneaiey:
noaia i?inouo i?ioeaioia (simple interest);
noaia neiaeiuo i?ioeaioia (compound interest).
Noaia i?inouo i?ioeaioia i?aaeiieaaaao iaeciaiiinoue aacu, n eioi?ie
i?ienoiaeeo ia/eneaiea. Ionoue enoiaeiue eiaanoe?oaiue eaieoae ?aaai ?;
o?aaoaiay aeioiaeiinoue — a (a aeieyo aaeeieoeu). N/eoaaony, /oi
eiaanoeoeey naeaeaia ia oneiaeyo i?inoiai i?ioeaioa, anee
eiaanoe?iaaiiue eaieoae aaeaaiaeii oaaee/eaaaony ia aaee/eio ?*a. Oaeei
ia?acii, ?acia? eiaanoe?iaaiiiai eaieoaea /a?ac i eao (Rn) aoaeao ?aaai:
Rn=P+P*r+…+P*r=P-(l +n*r).
N/eoaaony, /oi eiaanoeoeey naeaeaia ia oneiaeyo neiaeiiai i?ioeaioa,
anee i/a?aaeiie aiaeiaie aeioiae en/eneyaony ia n enoiaeiie aaee/eiu
eiaanoe?iaaiiiai eaieoaea, a n iauae noiiu, aeeth/athuae oaeaea e ?aiaa
ia/eneaiiua, e iaaino?aaiaaiiua eiaanoi?ii i?ioeaiou. A yoii neo/aa
i?ienoiaeeo eaieoaeecaoeey i?ioeaioia ii ia?a eo ia/eneaiey, o.a. aaca,
n eioi?ie ia/eneythony i?ioeaiou, ana a?aiy aic?anoaao. Neaaeiaaoaeueii,
?acia? eiaanoe?iaaiiiai eaieoaea aoaeao ?aaai:
e eiioeo ia?aiai aiaea: F1 = ? + ? • a = ? • (1 + a);
e eiioeo aoi?iai aiaea: F2 = F1 + F1 • a = F1 • (1 + a) = ? • (1 +
a)2;
e eiioeo n-ai aiaea: Fn = ?* (1 + r)n
Acaeiinaycue Fn e Rn oa?aeoa?ecoaony neaaeothuei ia?acii:
R.n>Fn, i?e 0
Oaeei ia?acii, a neo/aa aaeaaiaeiiai ia/eneaiey i?ioeaioia aeey eeoea,
i?aaeinoaaeythuaai e?aaeeo:
aieaa auaiaeiie yaeyaony noaia i?inouo i?ioeaioia, anee n?ie nnoaeu
iaiaa iaeiiai aiaea, (i?ioeaiou ia/eneythony iaeiie?aoii a eiioea
ia?eiaea);
aieaa auaiaeiie yaeyaony noaia neiaeiuo i?ioeaioia, anee n?ie nnoaeu
i?aauoaao iaeei aiae (i?ioeaiou ia/eneythony aaeaaiaeii);
iaa noaiu aeatho iaeeiaeiaua ?acoeueoaou i?e i?iaeieaeeoaeueiinoe
ia?eiaea 1 aiae e iaeiie?aoiii ia/eneaiee i?ioeaioia.
Eniieueciaaiea a ?an/aoao neiaeiiai i?ioeaioa a neo/aa iiiaie?aoiiai aai
ia/eneaiey aieaa eiae/ii, iineieueeo a yoii neo/aa eaieoae,
aaia?e?othuee aeioiaeu, iinoiyiii aic?anoaao. I?e i?eiaiaiee i?inoiai
i?ioeaioa aeioiaeu ii ia?a eo ia/eneaiey oeaeaniia?acii nieiaoue aeey
iio?aaeaiey eee eniieueciaaiey a ae?oaeo eiaanoeoeeiiiuo i?iaeoao eee
oaeouae aeayoaeueiinoe.
Oi?ioea neiaeiuo i?ioeaioia yaeyaony iaeiie ec aaciauo oi?ioe a
oeiainiauo au/eneaieyo, iiyoiio aeey oaeianoaa iieueciaaiey aaiaeeony
iaicia/aiea FMl(r,n), iacuaaaiiai ioeueoeieeoee?othuei iiiaeeoaeai e
iaania/eaathuaai ia?auaiea noieiinoe.
Fn=P-FMl(r,n), aaea FMl(r, n) = (1 + r)” — ioeueoeieeoee?othuee
iiiaeeoaeue.
Yeiiiie/aneee niune iiiaeeoaey FMl(r, n) ninoieo a neaaeothuai: ii
iieacuaaao, /aio aoaeao ?aaia iaeia aeaiaaeiay aaeeieoea (iaeei ?oaeue,
iaeei aeieea?, iaeia eaia e o.i.) /a?ac n ia?eiaeia i?e caaeaiiie
i?ioeaioiie noaaea r.
Noaia i?inouo i?ioeaioia eniieuecoaony a i?aeoeea aaieianeeo ?an/aoia
i?e ia/eneaiee i?ioeaioia ii e?aoein?i/iui nnoaeai ni n?ieii iiaaoaiey
aei iaeiiai aiaea. A yoii neo/aa a ea/anoaa iieacaoaey n aa?aony
aaee/eia, oa?aeoa?ecothuay oaeaeueiue aan aeeeiu iiaeia?eiaea (aeie,
ianyoe, eaa?oae, iieoaiaeea) a iauai ia?eiaea (aiae). Aeeeia ?acee/iuo
a?aiaiiuo eioa?aaeia a ?an/aoao iiaeao ie?oaeyoueny: ianyoe — 30 aeiae;
eaa?oae — 90 aeiae; iieoaiaeea — 180 aeiae; aiae — 360 (eee 365) aeiae.
Ia i?aeoeea iiiaea oeiainiaua iia?aoeee auiieiythony a ?aieao iaeiiai
aiaea, i?e yoii iiaoo eniieueciaaoueny ?acee/iua noaiu e iaoiaeu
ia/eneaiey i?ioeaioia. A /anoiinoe, aieueoia ?ani?ino?aiaiea eiatho
e?aoein?i/iua nnoaeu, o.a. nnoaeu, i?aaeinoaaeyaiua ia n?ie aei iaeiiai
aiaea n iaeiie?aoiui ia/eneaieai i?ioeaioia. Eae ioia/aeinue auoa, a
yoii neo/aa aeey e?aaeeoi?a, aeeeoothuaai /aua anaai oneiaey oeiainiaiai
eiio?aeoa, aieaa auaiaeia noaia i?inouo i?ioeaioia, i?e yoii a ?an/aoao
eniieuecotho i?iiaaeooi/ioth i?ioeaioioth noaaeo, eioi?ay ?aaia aeiea
aiaeiaie noaaee, i?iii?oeeiiaeueiie aeiea a?aiaiiiai eioa?aaea a aiaeo.
F=P*(1 + f*r), eee F=P*(l + r*t/T),
aaea r — aiaeiaay i?ioeaioiay noaaea a aeieyo aaeeieoeu;
t — i?iaeieaeeoaeueiinoue oeiainiaie iia?aoeee a aeiyo;
O — eiee/anoai aeiae a aiaeo;
f — ioiineoaeueiay aeeeia ia?eiaea aei iiaaoaiey nnoaeu.
I?e ii?aaeaeaiee i?iaeieaeeoaeueiinoe oeiainiaie iia?aoeee i?eiyoi
aeaiue auaea/e e aeaiue iiaaoaiey nnoaeu n/eoaoue ca iaeei aeaiue. A
caaeneiinoe io oiai, /aio aa?aony ?aaiie i?iaeieaeeoaeueiinoue aiaea
(eaa?oaea, ianyoea), ?acia? i?iiaaeooi/iie i?ioeaioiie noaaee iiaeao
auoue ?acee/iui. Aiciiaeiu aeaa aa?eaioa:
oi/iue i?ioeaio, ii?aaeaeyaiue enoiaey ec oi/iiai /enea aeiae a aiaeo
(365 eee 366), a eaa?oaea (io 89 aei 92), a ianyoea (io 28 aei 31);
iaueiiaaiiue i?ioeaio, ii?aaeaeyaiue enoiaey ec i?eaeeaeaiiiai /enea
aeiae a aiaeo, eaa?oaea e ianyoea (niioaaonoaaiii 360, 90, 30).
I?e ii?aaeaeaiee i?iaeieaeeoaeueiinoe ia?eiaea, ia eioi?ue auaeaia
nnoaea, oaeaea aiciiaeiu aeaa aa?eaioa:
i?eieiaaony a ?an/ao oi/iia /enei aeiae nnoaeu (?an/ao aaaeaony ii
aeiyi);
i?eieiaaony a ?an/ao i?eaeeceoaeueiia /enei aeiae nnoaeu (enoiaey ec
i?iaeieaeeoaeueiinoe ianyoea a 30 aeiae).
A neo/aa, eiaaea a ?an/aoao eniieuecoaony oi/iue i?ioeaio, aa?aony e
oi/iay aaee/eia i?iaeieaeeoaeueiinoe oeiainiaie iia?aoeee; i?e
eniieueciaaiee iaueiiaaiiiai i?ioeaioa iiaeao i?eiaiyoueny eae oi/iia,
oae e i?eaeeaeaiiia /enei aeiae nnoaeu. Oaeei ia?acii, ?an/ao iiaeao
auiieiyoueny iaeiei ec o?ao niiniaia:
iaueiiaaiiue i?ioeaio n oi/iui /eneii aeiae (i?eiaiyaony a Aaeueaee,
O?aioeee);
iaueiiaaiiue i?ioeaio n i?eaeeaeaiiui /eneii aeiae (O?A, Aeaiey,
Oaaoeey);
oi/iue i?ioeaio n oi/iui /eneii aeiae (Aaeeeia?eoaiey, NOA).
A i?aeoe/aneii niunea yooaeo io auai?a oiai eee eiiai niiniaa caaeneo io
cia/eoaeueiinoe noiiu, oeao?e?othuae a i?ioeanna oeiainiaie iia?aoeee.
I?eia?: I?aaeinoaaeaia nnoaea a ?acia?a 5 iei.?oa. 25 yiaa?y n
iiaaoaieai /a?ac oanoue ianyoeaa (25 ethey) iiae 60% aiaeiauo (aiae
iaaenieiniue). ?ann/eoaoue ?acee/iuie niiniaaie noiio e iiaaoaieth (S).
Aaee/eia oiea/eaaaiuo ca iieueciaaiea nnoaeie i?ioeaioia caaeneo io
/enea aeiae, eioi?ia aa?aony a ?an/ao. Oi/iia /enei aeiae ii?aaeaeyaony
ii oaaeeoea n iiia?aie aeiae aiaea:
206—25 == 181 aei. I?eaeeaeaiiia /enei aeiae nnoaeu ?aaii: 5 aeiae
yiaa?y (30—25) +150 (ii 30 aeiae iyoe ianyoeaa: oaa?aeue, ia?o, ai?aeue,
iae, ethiue) + 25 (etheue) = 180 aei.
Aiciiaeiua aa?eaiou aica?aoa aeieaa:
1. A ?an/ao i?eieiathony oi/iua i?ioeaiou e oi/iia /enei aeiae nnoaeu:
S = 5 • (1 + 181:365 • 0,6) = 6,487 iei.?oa.
2. A ?an/ao i?eieiathony iaueiiaaiiua i?ioeaiou e oi/iia /enei aeiae:
S = 5 • (1 + 181:360 • 0,6) = 6,508 iei.?oa.
3. A ?an/ao i?eieiathony iaueiiaaiiua i?ioeaiou e i?eaeeaeaiiia /enei
aeiae:
S = 5 • (1 + 180:360 • 0,6) = 6,5 iei.?oa.
Ae?oaie aanueia ?ani?ino?aiaiiie iia?aoeeae e?aoein?i/iiai oa?aeoa?a,
aeey ioeaiee eioi?ie eniieuecothony ?anniio?aiiua oi?ioeu, yaeyaony
iia?aoeey ii o/aoo aaenaeae aaieii. A yoii neo/aa iieuecothony
aeeneiioiie noaaeie. Iaeia ec i?e/ei ninoieo a oii, /oi aaenaey iiaoo
ioi?ieyoueny ii-?aciiio, iaeiaei /aua anaai aaieo i?eoiaeeony eiaoue
aeaei n noiiie e iiaaoaieth, o.a. n aaee/eiie FV. Noaia aeaenoaee a yoii
neo/aa iiaeao auoue neaaeothuae. Aeaaeaeaoe aaenaey ia noiio FV
i?aaeuyaeyao aaenaeue aaieo, eioi?ue niaeaoaaony aai o/anoue, o.a.
eoieoue, oaea?aeeaay a naith iieueco /anoue aaenaeueiie noiiu, eioi?ay
ia?aaeei oaeaea iacuaaaony aeeneiioii. A yoii neo/aa aaie i?aaeeaaaao
aeaaeaeueoeo noiio (PV), en/eneyaioth enoiaey ec iauyaeaiiie aaieii
noaaee aeeneiioe?iaaiey (d). I/aaeaeii, /oi /ai auoa cia/aiea
aeeneiioiie noaaee, oai aieueooth noiio oaea?aeeaaao aaie a naith
iieueco. ?an/ao i?aaeinoaaeyaiie aaieii noiiu aaaeaony ii oi?ioea:
PV == FV* (1 —f*d), eee PV = FV • (1 —t/T*d),
aaea f — ioiineoaeueiay aeeeia ia?eiaea aei iiaaoaiey nnoaeu (ioiaoei,
/oi iia?aoeey eiaao niune, eiaaea /enei a neiaeao ia io?eoeaoaeueii).
I?eia?
Aaenaeaaea?aeaoaeue i?aaeuyaee aeey o/aoa aaenaeue ia noiio 5 iei. ?oa.
ni n?ieii iiaaoaiey 28.09.1997 a. Aaenaeue i?aaeuyaeai 13.09.1997 a.
Aaie niaeaneeny o/anoue aaenaeue n aeeneiioii a 75% aiaeiauo. Oiaaea
noiia, eioi?oth aaenaeaaea?aeaoaeue iiaeao iieo/eoue io aaiea,
?ann/eouaaaony ii oi?ioea (4.6) e ninoaaeo:
PV = 5 • (1 —15:360 • 0,75) = 4,844 iei.?oa.
?aciinoue iaaeaeo aaee/eiaie FV e PV i?aaenoaaeyao niaie eiienneiiiua,
oaea?aeeaaaiua aaieii a naith iieueco, ca i?aaeinoaaeaiioth oneoao; a
aeaiiii i?eia?a iia ninoaaeea 156 oun. ?oa.
3.4. Aioo?eaiaeiaua i?ioeaioiua ia/eneaiey
A i?aeoeea auieaou aeeaeaeaiaeia ia?aaeei iaiaa?eaaaony aaee/eia
aiaeiaiai i?ioeaioa e /anoioa auieaou. A yoii neo/aa ?an/ao aaaeaony ii
oi?ioea neiaeiuo i?ioeaioia ii iiaeuioa?aaeai e ii noaaea, ?aaiie
i?iii?oeeiiaeueiie aeiea enoiaeiie aiaeiaie noaaee ii oi?ioea:
Fn =P*(1+r/m)k*m
aaea r—iauyaeaiiay aiaeiaay noaaea;
m—eiee/anoai ia/eneaiee a aiaeo;
k—eiee/anoai eao.
I?eia?: Aeiaeaiu aeaiueae a aaie a noiia 5 iei. ?oa ia aeaa aiaea n
iieoaiaeiaui ia/eneaieai i?ioeaioia iiae 20% aiaeiauo. A yoii neo/aa
ia/eneaiea i?ioeaioia i?iecaiaeeony /aou?a ?aca ii noaaea 10% (20% : 2),
a noaia aic?anoaiey eaieoaea aoaeao eiaoue aeae:
Ia?eiae (ianyoeaa) Noiia n eioi?ie eaeao ia/eneaiea Noaaea (a aeieyo
aae.) Noiia e eiioeo ia?eiaea
6 5.000 1.1 5.500
12 5.500 1.1 6.050
18 6.050 1.1 6.655
24 6.655 1.1 7.321
Anee ainiieueciaaoueny i?eaaaeaiiie oi?ioeie, oi m = 2, k = 2,
neaaeiaaoaeueii:
Fn = 5 * (1+20%/100%/2)4 = 7,3205 iei. ?oa.
I?eia?: A oneiaeyo i?aaeuaeouaai i?eia?a i?iaiaeece?iaaoue, eciaieony ee
aaee/eia eaieoaea e eiioeo aeaooeaoiaai ia?eiaea, anee au i?ioeaiou
ia/eneyeenue aaeaeaa?oaeueii.
A yoii neo/aa ia/eneaiea aoaeao i?iecaiaeeoueny ainaiue ?ac ii noaaea 5%
(20%: 4), a noiia e eiioeo aeaooeaoiaai ia?eiaea ninoaaeo:
Fn = 5 • (1 + 0,05)8 = 7,387 iei.?oa.
Oaeei ia?acii, iiaeii naeaeaoue ianeieueei i?inouo i?aeoe/aneeo
auaiaeia:
i?e ia/eneaiee i?ioeaioia: 12% aiaeiauo ia yeaeaaeaioii 1% a ianyoe (yoa
ioeaea i/aiue ?ani?ino?aiaia n?aaee ia/eiathueo aecianiaiia);
/ai /aua eaeao ia/eneaiea ii noaia neiaeiuo i?ioeaioia, oai aieueoa
eoiaiaay iaeiieaiiay noiia.
3.5. Ia/eneaiea i?ioeaioia ca ae?iaiia /enei eao
Aeinoaoi/ii iauaeaiiuie yaeythony oeiainiaua eiio?aeou, caeeth/aaiua ia
ia?eiae, ioee/athueeny io oeaeiai /enea eao. A yoii neo/aa i?ioeaiou
iiaoo ia/eneyoueny iaeiei ec aeaoo iaoiaeia:
ii noaia neiaeiuo i?ioeaioia:
Fn = P * (1+r)(w+f)
ii niaoaiiie noaia (eniieuecoaony noaia neiaeiuo i?ioeaioia aeey oeaeiai
/enea eao e noaia i?inouo i?ioeaioia — aeey ae?iaiie /anoe aiaea):
?n=?*(1+r)w*(1+f*r),
Iineieueeo f (1 + a)f, neaaeiaaoaeueii ia?auaiiay
noiia aoaeao aieueoa i?e eniieueciaaiee niaoaiiie noaiu.
Aiciiaeiu oeiainiaua eiio?aeou, a eioi?uo ia/eneaiea i?ioeaioia
inouanoaeyaony ii aioo?eaiaeiaui iiaeia?eiaeai, a i?iaeieaeeoaeueiinoue
iauaai ia?eiaea aeaenoaey eiio?aeoa ia ?aaia oeaeiio /eneo
iiaeia?eiaeia. A yoii neo/aa oaeaea aiciiaeii eniieueciaaiea aeaoo noai:
a) noaia neiaeiuo i?ioeaioia:
Fn=P•(l+a/m)m*k•(l+r/m)f
a) niaoaiiay noaia:
Fn = ?*(1 + r/m) m*k * (1 + f*r),
aaea k — eiee/anoai eao;
m – eiee/anoai ia/eneaiee a aiaeo;
r — aiaeiaay noaaea;
f — ae?iaiay /anoue iiaeia?eiaea.
I?eia?: Aaie i?aaeinoaaee nnoaeo a ?acia?a 120 iei. ?oa. ia 27 ianyoeaa
(o.a. 9 eaa?oaeia, eee 2,25 aiaea) iiae 16% aiaeiauo ia oneiaeyo
aaeeiia?aiaiiiai aica?aoa iniiaiie noiiu aeieaa e ia/eneaiiuo
i?ioeaioia. I?iaiaeece?iaaoue, eaeoth noiio i?aaenoieo aa?iooue aaieo
i?e ?acee/iuo aa?eaioao e noaiao ia/eneaiey i?ioeaioia: a) aiaeiaia; a)
iieoaiaeiaia; a) eaa?oaeueiia.
a) a yoii neo/aa i?iaeieaeeoaeueiinoue nnoaeu ia yaeyaony e?aoiie
i?iaeieaeeoaeueiinoe aaceniiai ia?eiaea, o.a. aiaea. Iiyoiio aiciiaeii
i?eiaiaiea ethaie ec noai, oa?aeoa?ecoaiuo oi?ioeaie, i?eaaaeaiiuie
auoa, e cia/aieyie niioaaonoaothueo ia?aiao?ia: w = 2; f=0,25;r= 16%.
I?e ?aaeecaoeee noaiu neiaeiuo i?ioeaioia:
Fn = ?-(1 + r)w+f= 120 *(1 + 0,16)2.25 = 167,58 iei. ?oa.
I?e ?aaeecaoeee niaoaiiie noaiu:
Fn = ? • (1 + r)w * (1 + f * r) = 120 * (1 + 0,16)2 * 1,04 == 167,93
iei. ?oa.
a) a yoii neo/aa iu eiaai aeaei n neooaoeeae, eiaaea ia/eneaiea
i?ioeaioia inouanoaeyaony ii aioo?eaiaeiaui iiaeia?eiaeai, a
i?iaeieaeeoaeueiinoue iauaai ia?eiaea aeaenoaey eiio?aeoa ia ?aaia
oeaeiio /eneo iiaeia?eiaeia. Neaaeiaaoaeueii, ioaeii ainiieueciaaoueny
oi?ioeaie, eiaaea aaceniue ia?eiae ?aaai iieoaiaeeth, a ia?aiao?u oi?ioe
eiatho neaaeothuea cia/aiey: k = 2; f = 0,5; m = 2; r = 16%.
I?e ?aaeecaoeee noaiu neiaeiuo i?ioeaioia:
Fn=P*(1 +r/m)m*k*(l+r/m)f= 120*(l+0,08)4.5 = 169,66 iei. ?oa.
I?e ?aaeecaoeee niaoaiiie noaiu:
Fn = ?*(1 + a/m) m*k *(1+ f*r/m) = 120*(1 + 0.08)4*(1 + 1/2*0,16/2) =
169, 79 iei. ?oa
a) a yoii neo/aa i?iaeieaeeoaeueiinoue nnoaeu e?aoia
i?iaeieaeeoaeueiinoe aaceniiai ia?eiaea e iiaeii ainiieueciaaoueny
iau/iie oi?ioeie neiaeiuo i?ioeaioia, a eioi?ie n = 9, a r = 0,16/4 =
0,04.
Fn = 120* (1 + 0,04)9 = 170,8 iei.?oa.
A caaeneiinoe io /anoiou ia/eneaiey i?ioeaioia ia?auaiea noiiu
inouanoaeyaony ?acee/iuie oaiiaie, i?e/ai n aic?anoaieai /anoiou
iaeiieaiiay noiia oaaee/eaaaony. Iaeneiaeueii aiciiaeiia ia?auaiea
inouanoaeyaony i?e aaneiia/iii ae?iaeaiee aiaeiaiai eioa?aaea.
3.6. Yooaeoeaiay aiaeiaay i?ioeaioiay noaaea
?acee/iua aeaeu oeiainiauo eiio?aeoia iiaoo i?aaeoniao?eaaoue ?acee/iua
noaiu ia/eneaiey i?ioeaioia. Eae i?aaeei, a yoeo eiio?aeoao
iaiaa?eaaaony iiieiaeueiay i?ioeaioiay noaaea, iau/ii aiaeiaay. Yoa
noaaea, ai-ia?auo, ia io?aaeaao ?aaeueiie yooaeoeaiinoe naeaeee e,
ai-aoi?uo, ia iiaeao auoue eniieueciaaia aeey niiinoaaeaiee. Aeey
iaania/aiey n?aaieoaeueiiai aiaeeca yooaeoeaiinoe oaeeo eiio?aeoia
iaiaoiaeeii aua?aoue iaeee iieacaoaeue, eioi?ue aue au oieaa?naeueiui
aeey ethaie noaiu ia/eneaiey. Oaeei iieacaoaeai yaeyaony yooaeoeaiay
aiaeiaay i?ioeaioiay noaaea Ra, iaania/eaathuay ia?aoiae io ? e Fn i?e
caaeaiiuo cia/aieyo yoeo iieacaoaeae e iaeiie?aoiii ia/eneaiee
i?ioeaioia.
Iauay iinoaiiaea caaea/e iiaeao auoue noi?ioee?iaaia neaaeothuei
ia?acii. Caaeaia enoiaeiay noiia ?, aiaeiaay i?ioeaioiay noaaea
(iiieiaeueiay) r, /enei ia/eneaiee neiaeiuo i?ioeaioia m. Yoiio iaai?o
enoiaeiuo aaee/ei a ?aieao iaeiiai aiaea niioaaonoaoao aiieia
ii?aaeaeaiiia cia/aiea ia?auaiiie aaee/eiu F1. O?aaoaony iaeoe oaeoth
aiaeiaoth noaaeo Re, eioi?ay iaania/eea au oi/ii oaeia aea ia?auaiea,
eae e enoiaeiay noaia, ii i?e iaeiie?aoiii ia/eneaiee i?ioeaioia, o.a. m
= 1. Eiuie neiaaie, noaiu {?, F1, a, m > 1} e {?, F1, Ra, m = 1}
aeieaeiu auoue ?aaiineeueiuie.
Ec oi?ioeu (4.7) neaaeoao, /oi a ?aieao iaeiiai aiaea:
F1=P*(1+r/m)m.
Niaeanii ii?aaeaeaieth yooaeoeaiie aiaeiaie i?ioeaioiie noaaee:
F1=P+P*Re=P*(l+Ra)
ionthaea:
Re=(1+r/m)m-1
Ec oi?ioeu neaaeoao, /oi yooaeoeaiay noaaea caaeneo io eiee/anoaa
aioo?eaiaeiauo ia/eneaiee, i?e/ai n ?inoii m iia oaaee/eaaaony. E?iia
oiai, aeey eaaeaeie iiieiaeueiie noaaee iiaeii iaeoe niioaaonoaothuoth
ae yooaeoeaioth noaaeo; aeaa yoe noaaee niaiaaeatho eeoue i?e m = 1.
Eiaiii noaaea Re yaeyaony e?eoa?eai yooaeoeaiinoe oeiainiaie naeaeee e
iiaeao auoue eniieueciaaia aeey i?ino?ainoaaiii-a?aiaiiuo niiinoaaeaiee.
I?eia?: I?aaei?eieiaoaeue iiaeao iieo/eoue nnoaeo
a) eeai ia oneiaeyo aaeaeaa?oaeueiiai ia/eneaiey i?ioeaioia ec ?an/aoa
75% aiaeiauo,
a) eeai ia oneiaeyo iieoaiaeiaiai ia/eneaiey i?ioeaioia ec ?an/aoa 80%
aiaeiauo. Eaeie aa?eaio aieaa i?aaeii/oeoaeai?
Ioiineoaeueiua ?anoiaeu i?aaei?eieiaoaey ii ianeoaeeaaieth nnoaeu iiaoo
auoue ii?aaeaeaiu n iiiiuueth ?an/aoa yooaeoeaiie aiaeiaie i?ioeaioiie
noaaee — /ai iia auoa, oai aieueoa o?iaaiue ?anoiaeia. aa?eaio (a)
a(a) = (1 + 0,75/4)4 – 1 = 0,99,
aa?eaio (a)
r(e) = (1 + 0,80/2)2 – 1 = 0,96.
Oaeei ia?acii, aa?eaio (a) yaeyaony aieaa i?aaeii/oeoaeueiui aeey
i?aaei?eieiaoaey. Iaiaoiaeeii ioiaoeoue, /oi i?eiyoea ?aoaiey ia caaeneo
io aaee/eiu e?aaeeoa, iineieueeo e?eoa?eai yaeyaony ioiineoaeueiue
iieacaoaeue — yooaeoeaiay noaaea, a iia, caaeneo eeoue io iiieiaeueiie
noaaee e eiee/anoaa ia/eneaiee.
Iiieiaiea ?iee yooaeoeaiie i?ioeaioiie noaaee /?acau/aeii aaaeii aeey
oeiainiaiai iaiaaeaea?a, iineieueeo i?eiyoea ?aoaiey i i?eaea/aiee
n?aaenoa, iai?eia?, aaieianeie nnoaeu ia oao eee eiuo oneiaeyo,
aeaeaaony /aua anaai enoiaey ec i?eaieaiinoe i?aaeeaaaaiie i?ioeaioiie
noaaee, eioi?ay a yoii neo/aa oa?aeoa?ecoao ioiineoaeueiua ?anoiaeu
caaiueea. A ?aeeaiiuo i?iniaeoao iai?iecaieueii eee oiuoeaiii aieiaiea
ia i?e?iaea noaaee iau/ii ia aeoeaioe?oaony, oioy a iiaeaaeythuai /enea
neo/aaa ?a/ue eaeao i iiieiaeueiie noaaea, eioi?ay iiaeao aanueia
nouanoaaiii ioee/aoueny io yooaeoeaiie noaaee. ?anniio?ei i?inoaeoee
i?eia?.
I?eia?: ?ann/eoaoue yooaeoeaioth aiaeiaoth i?ioeaioioth noaaeo i?e
?acee/iie /anoioa ia/eneaiey i?ioeaioia, anee iiieiaeueiay noaaea ?aaia
10%.:
m I 2 4 12
365
Re 0,10 0,1025 0,10381 0,10471 0,10516
?acee/ea iaaeaeo aeaoiy noaaeaie iiaeao auoue ai?acaei aieaa
?aceoaeueiui i?e caeeth/aiee iaeioi?uo niaoeeaeueiuo e?aaeeoiuo
aeiaiai?ia, iai?eia?, i?e ioi?ieaiee e?aaeeoa ia oneiaeyo aeiaaaeaiiiai
i?ioeaioa.
3.7. Iiiyoea i?eaaaeaiiie noieiinoe
Ioeaieaay oeaeaniia?aciinoue oeiainiauo aeiaeaiee a oio eee eiie aeae
aeciana, enoiaeyo ec oiai, yaeyaony yoi aeiaeaiea aieaa i?eaueueiui (i?e
aeiionoeiii o?iaia ?enea), /ai aeiaeaiey a ainoaea?noaaiiua oeaiiua
aoiaae, eee iao. Eniieuecoy ianeiaeiua iaoiaeu, iuoathony aiaeece?iaaoue
aoaeouea aeioiaeu i?e ieieiaeueiii, “aaciianiii” o?iaia aeioiaeiinoe.
Iniiaiay eaeay yoeo iaoiaeia caeeth/aaony a ioeaiea aoaeoueo iinooieaiee
Fn (iai?eia?, a aeaea i?eauee, i?ioeaioia, aeeaeaeaiaeia) n iiceoeee
oaeouaai iiiaioa. I?e yoii, naeaeaa oeiainiaua aeiaeaiey, eiaanoi?
iau/ii ?oeiaiaenoaoaony o?aiy iinueaie:
a) i?ienoiaeeo ia?iaiaioiia iaanoeaiaiea aeaiaa (eioeyoeey);
a) oaii eciaiaiey oeai ia nu?uea, iaoa?eaeu e iniiaiua n?aaenoaa,
eniieuecoaiua i?aaei?eyoeai, iiaeao nouanoaaiii ioee/aoueny io oaiia
eioeyoeee;
a) aeaeaoaeueii ia?eiaee/aneia ia/eneaiea (eee iinooieaiea) aeioiaea,
i?e/ai a ?acia?a, ia ieaea ii?aaeaeaiiiai ieieioia.
Aace?oynue ia yoeo iinueao, eiaanoi? aeieaeai ioeaieoue, eaeeie aoaeoo
aai aeioiaeu a aoaeouai, eaeoth iaeneiaeueii aiciiaeioth noiio
aeiionoeii aeiaeeoue a aeaiiia aeaei enoiaey ec i?iaiice?oaiie aai
?aioaaaeueiinoe.
Aaciaay ?an/aoiay oi?ioea aeey oaeiai aiaeeca:
P=Fn/(1+d)n=Fn*FM2(d;n)
aaea Fn — aeioiae, ieaie?oaiue e iieo/aieth a i-i aiaeo;
? — oaeouay (eee i?eaaaeaiiay) noieiinoue, o.a. ioeaiea aaee/eiu Fn n
iiceoeee oaeouaai iiiaioa;
d — eiyooeoeeaio aeeneiioe?iaaiey.
Yeiiiie/aneee niune oaeiai i?aaenoaaeaiey caeeth/aaony a neaaeothuai:
i?iaiice?oaiay aaee/eia aeaiaaeiuo iinooieaiee /a?ac i eao (Fn) n
iiceoeee oaeouaai iiiaioa aoaeao iaiueoa e ?aaia ? (iineieueeo
ciaiaiaoaeue ae?iae aieueoa aaeeieoeu). Yoi icia/aao oaeaea, /oi aeey
eiaanoi?a noiia ? a aeaiiue iiiaio a?aiaie e noiia Fn /a?ac n eao
iaeeiaeiau ii naiae oeaiiinoe. Eniieuecoy yoo oi?ioeo, iiaeii
i?eaiaeeoue a niiinoaaeiue aeae ioeaieo aeioiaeia io eiaanoeoeee,
iaeeaeaaiuo e iinooieaieth a oa/aiea ?yaea eao. Eaaei aeaeaoue, /oi a
yoii neo/aa eiyooeoeeaio aeeneiioe?iaaiey /eneaiii ?aaai i?ioeaioiie
noaaea, onoaiaaeeaaaiie eiaanoi?ii, o.a. oiio ioiineoaeueiiio ?acia?o
aeioiaea, eioi?ue eiaanoi? oi/ao eee iiaeao iieo/eoue ia eiaanoe?oaiue
ei eaieoae.
Ii?aaeaeyy eiyooeoeeaio aeeneiioe?iaaiey, iau/ii enoiaeyo ec oae
iacuaaaiiai aaciianiiai eee aa?aioe?iaaiiiai o?iaiy aeioiaeiinoe
oeiainiauo eiaanoeoeee, eioi?ue iaania/eaaaony ainoaea?noaaiiui aaieii
ii aeeaaeai eee i?e iia?aoeeyo n oeaiiuie aoiaaaie. I?e yoii iiaeao
aeaaaoueny iaaeaaaea ca ?ene, i?e/ai, /ai aieaa ?eneiaui n/eoaaony
?anniao?eaaaiue i?iaeo eee oeiainiaue eiio?aeo, oai aieueoa ?acia?
i?aiee ca ?ene. Eiuie neiaaie, i?ioeaioiay noaaea aae, eniieuecoaiay a
ea/anoaa eiyooeoeeaioa aeeneiioe?iaaiey, aoaeao a yoii neo/aa eiaoue
neaaeothuee aeae:
d = rf + ra ,
aaea rf — aac?eneiaay aeioiaeiinoue;
ra — i?aiey ca ?ene.
I?eia?: Ia aaoai n/aoa a aaiea 2 iei. ?oa. Aaie ieaoeo 18% aiaeiauo. Aai
i?aaeeaaatho aieoe anai eaieoaeii a i?aaiecaoeeth aai/o?iiai
i?aaei?eyoey. I?aaenoaaeaiiua yeiiiie/aneea ?an/aou iieacuaatho, /oi
/a?ac oanoue eao aao eaieoae oo?ieony. Noieo ee i?eieiaoue yoi
i?aaeeiaeaiea?
Ioeaiea aeaiiie neooaoeee iiaeao auoue naeaeaia eeai n iiceoeee
aoaeouaai, eeai n iiceoeee ianoiyuaai. A ia?aii neo/aa aiaeec iniiaai ia
n?aaiaiee aeaoo noii, iieo/aaiuo io aeiaeaiey a ?eneiaia i?aaei?eyoea e
a aaieianeia o/?aaeaeaiea n aa?aioe?iaaiiui aeioiaeii. Ia?aay noiia
?aaia 6 iei. ?oa., aoi?ay iaoiaeeony ii oi?ioea:
F6=?*(1 + 0,18)6= 2*2,7 =5,4 iei. ?oa.
I?eaaaeaiiue ?an/ao naeaeaoaeuenoaoao ia yeiiiie/aneie auaiaea
naeaeaiiiai aai i?aaeeiaeaiey. Iaeiaei i?e i?eiyoee ieii/aoaeueiiai
?aoaiey iaiaoiaeeii ii aiciiaeiinoe o/anoue oaeoi? ?enea.
Aoi?ie aa?eaio aiaeeca iniiaai ia aeeneiioe?iaaiiuo ioeaieao. Aeiionoei,
/oi oeiainiaue eiinoeueoaio ?aeiiaiaeoao ioeaieoue ?ene o/anoey a
aai/o?iii i?aaei?eyoee iooai aaaaeaiey i?aiee a ?acia?a 5%. Oaeei
ia?acii, eiyooeoeeaio aeeneiioe?iaaiey aoaeao ?aaai 23%. Oiaaea iiaeii
?ann/eoaoue i?eaaaeaiioth noieiinoue PV iaeeaeaaiiai iinooieaiey i?e
o/anoee a aai/o?iii i?aaei?eyoee:
PV = 6 * 1 /(1 + 0,23)6 = 1,73 iei. ?oa.
I?e oaeeo enoiaeiuo iinueao i?aaeeiaeaiea ia o/anoee a aai/o?iii
i?aaei?eyoee noaiiaeony iaauaiaeiui.
Iiiaeeoaeue FM2(d, k) = 1/(1 + d)k iacuaaaony aeeneiioe?othuei
iiiaeeoaeai. Yeiiiie/aneee niune aeeneiioe?othuaai iiiaeeoaey FM2(d,k)
caeeth/aaony a neaaeothuai: ii iieacuaaao “naaiaeiyoithth” oeaio iaeiie
aeaiaaeiie aaeeieoeu aoaeouaai, o.a. /aio n iiceoeee oaeouaai iiiaioa
?aaia iaeia aeaiaaeiay aaeeieoea (iai?eia?, iaeei ?oaeue),
oee?eoee?othuay a noa?a aeciana k ia?eiaeia nionoy io iiiaioa ?an/aoa,
i?e caaeaiiuo i?ioeaioiie noaaea (aeioiaeiinoe) a e /anoioa ia/eneaiey
i?ioeaioa.
4. Aeaeu aeaiaaeiuo iioieia
Iaeiei ec iniiaiuo yeaiaioia oeiainiaiai aiaeeca yaeyaony ioeaiea
aeaiaaeiiai iioiea C1, N2, … , Nn, aaia?e?oaiiai a oa/aiea ?yaea
a?aiaiiuo ia?eiaeia a ?acoeueoaoa ?aaeecaoeee eaeiai-eeai i?iaeoa eee
ooieoeeiie?iaaiey oiai eee eiiai aeaea aeoeaia.
Yeaiaiou iioiea Ni iiaoo auoue eeai iacaaeneiuie, eeai naycaiiuie
iaaeaeo niaie ii?aaeaeaiiui aeai?eoiii. A?aiaiiua ia?eiaeu /aua anaai
i?aaeiieaaathony ?aaiuie. E?iia oiai, aeey i?inoiou eceiaeaiey iaoa?eaea
i?aaeiieaaaaony, /oi yeaiaiou aeaiaaeiiai iioiea yaeythony
iaeiiiai?aaeaiiuie, o.a. iao /a?aaeiaaiey iooieia e i?eoieia aeaiaaeiuo
n?aaenoa. Oaeaea n/eoaaony, /oi aaia?e?oaiua a ?aieao iaeiiai a?aiaiiiai
ia?eiaea iinooieaiey eiatho ianoi eeai a aai ia/aea, eeai a aai eiioea,
o.a. iie ia ?ani?aaeaeaiu aioo?e ia?eiaea, a neiioeaio?e?iaaiu ia iaeiie
ec aai a?aieoe. A ia?aii neo/aa iioie iacuaaaony iioieii i?aioia?aiaei.
eee aaainiaui, ai aoi?ii — iioieii iinoioia?aiaei..
Iioie i?aioia?aaei Iioie iinoioia?aaei
Ia i?aeoeea aieueoaa ?ani?ino?aiaiea iieo/ee iioie iinoioia?aiaei, a
/anoiinoe, eiaiii yoio iioie eaaeeo a iniiaa iaoiaeee aiaeeca
eiaanoeoeeiiiuo i?iaeoia. Iaeioi?ua iauyniaiey yoiio iiaeii aeaoue
enoiaey ec iaueo i?eioeeiia o/aoa, niaeanii eioi?ui i?eiyoi iiaeaiaeeoue
eoiae e ioeaieaaoue oeiainiaue ?acoeueoao oiai eee eiiai aeaenoaey ii
ieii/aiee i/a?aaeiiai io/aoiiai ia?eiaea. *oi eanaaony iinooieaiey
aeaiaaeiuo n?aaenoa a n/ao iieaou, oi ia i?aeoeea iii /aua anaai
?ani?aaeaeaii ai a?aiaie ia?aaiiia?ii e iioiio oaeiaiaa oneiaii ioianoe
ana iinooieaiey e eiioeo ia?eiaea. Aeaaiaea?y yoiio niaeaoaieth
oi?ie?othony ?aaiua a?aiaiiua ia?eiaeu, /oi iicaieyao ?ac?aaioaoue
oaeiaiua oi?iaeeciaaiiua aeai?eoiu ioeaiee. Iioie i?aioia?aiaei eiaao
cia/aiea i?e aiaeeca ?acee/iuo noai iaeiieaiey aeaiaaeiuo n?aaenoa aeey
iineaaeothuaai eo eiaanoe?iaaiey.
Ioeaiea aeaiaaeiiai iioiea iiaeao auiieiyoueny a ?aieao ?aoaiey aeaoo
caaea/:
a) i?yiie, o.a. i?iaiaeeony ioeaiea n iiceoeee aoaeouaai (?aaeecoaony
noaia ia?auaiey);
a) ia?aoiie, o.a. i?iaiaeeony ioeaiea n iiceoeee ianoiyuaai (?aaeecoaony
noaia aeeneiioe?iaaiey).
I?yiay caaea/a i?aaeiieaaaao noiia?ioth ioeaieo ia?auaiiiai aeaiaaeiiai
iioiea, o.a. a aa iniiaa eaaeeo aoaeouay noieiinoue. Ia?aoiay caaea/a
i?aaeiieaaaao noiia?ioth ioeaieo aeeneiioe?iaaiiiai (i?eaaaeaiiiai)
aeaiaaeiiai iioiea. Iineieueeo ioaeaeueiua yeaiaiou aeaiaaeiiai iioiea
aaia?e?othony a ?acee/iua a?aiaiiua eioa?aaeu, a aeaiueae eiatho
a?aiaiioth oeaiiinoue, iaiin?aaenoaaiiia eo noiie?iaaiea iaaiciiaeii.
Iniiaiui ?acoeueoaoii ?an/aoa yaeyaony ii?aaeaeaiea iauae aaee/eiu
i?eaaaeaiiiai aeaiaaeiiai iioiea. Eniieuecoaiua i?e yoii ?an/aoiua
oi?ioeu ?acee/iu a caaeneiinoe io aeaea iioiea — iinoioia?aiaei eee
i?aioia?aiaei.
Iaiaoiaeeii ioiaoeoue, /oi eeth/aaui iiiaioii a ?anniio?aiiuo noaiao
yaeyaony i?aaeiinueea i oii, /oi aiaeec aaaeaony n iiceoeee “?acoiiiai
eiaanoi?a”, o.a. eiaanoi?a, iaiaaeeaiii eiaanoe?othuaai n?aaenoaa n
oeaeueth iieo/aiey aeiiieieoaeueiiai aeioiaea. Eiaiii yoei iauyniyaony
oio oaeo, /oi i?e ioeaiea iioieia a iaieo neo/ayo, o.a. e i?e ia?auaiee,
e i?e aeeneiioe?iaaiee, i?aaeiieaaaaony eaieoaeecaoeey ii noaia neiaeiuo
i?ioeaioia.
4.1. Ioeaiea aeaiaaeiiai iioiea n ia?aaiuie iinooieaieyie
Neooaoeey, eiaaea aeaiaaeiua iinooieaiey ii aiaeai aa?uee?otho, yaeyaony
iaeaieaa ?ani?ino?aiaiiie. Iauay iinoaiiaea caaea/e a yoii neo/aa
oaeiaa.
Ionoue C1, N2, … , Nn — aeaiaaeiue iioie; d — eiyooeoeeaio
aeeneiioe?iaaiey. Iioie, ana yeaiaiou eioi?iai n iiiiuueth
aeeneiioe?othueo iiiaeeoaeae i?eaaaeaiu e iaeiiio iiiaioo a?aiaie, a
eiaiii — e ianoiyuaio iiiaioo, iacuaaaony i?eaaaeaiiui. O?aaoaony iaeoe
noieiinoue aeaiiiai aeaiaaeiiai iioiea n iiceoeee aoaeouaai e n iiceoeee
ianoiyuaai.
4.1.1. Ioeaiea iioiea iinoioia?aiaei
I?yiay caaea/a i?aaeiieaaaao ioeaieo n iiceoeee aoaeouaai, o.a. ia
eiiaoe ia?eiaea. Aoaeouay noieiinoue enoiaeiiai aeaiaaeiiai iioiea
iinoioia?aiaei FVpst iiaeao auoue ioeaiaia eae noiia ia?auaiiuo
iinooieaiee, o.a. a iauai aeaea oi?ioea eiaao aeae:
n
FVpst=(Ck*(1+d)n-k
k=1
Ia?aoiay caaea/a iiae?acoiaaaao ioeaieo n iiceoeee oaeouaai iiiaioa,
o.a. ia eiiaoe ia?eiaea 0. A yoii neo/aa ?aaeecoaony noaia
aeeneiioe?iaaiey, a ?an/aou iaiaoiaeeii aanoe ii i?eaaaeaiiiio iioieo.
Yeaiaiou i?eaaaeaiiiai aeaiaaeiiai iioiea oaea iiaeii noiie?iaaoue; eo
noiia oa?aeoa?ecoao i?eaaaeaiioth, eee oaeouoth, noieiinoue aeaiaaeiiai
iioiea, eioi?oth i?e iaiaoiaeeiinoe iiaeii n?aaieaaoue n aaee/eiie
ia?aiia/aeueiie eiaanoeoeee. Oaeei ia?acii, i?eaaaeaiiue aeaiaaeiue
iioie aeey enoiaeiiai iioiea iinoioia?aiaei eiaao aeae:
C1/(1+d) C2/(1+d)2 C3/(1+d)3 …… Cn/(1+d)n
I?eaaaeaiiay noieiinoue aeaiaaeiiai iioiea iinoioia?aiaei PVpst a iauai
neo/aa iiaeao auoue ?ann/eoaia ii oi?ioea:
n
PVpst = (Ck/(1+d)k
k=1
Anee eniieueciaaoue aeeneiioe?othuee iiiaeeoaeue, oi oi?ioeo iiaeii
ia?aienaoue a neaaeothuai aeaea:
n
PVpst = ( Ck*FM2(r,k).
k=l
I?eia?: ?ann/eoaoue i?eaaaeaiioth noieiinoue aeaiaaeiiai iioiea
iinoioia?aiaei (oun. ?oa.): 12, 15, 9, 25, anee eiyooeoeeaio
aeeneiioe?iaaiey = 12%.
Aiae Aeaiaaeiue iioie Aeeneiioe?othuee iiiaeeoaeue i?e d = 12%
I?eaaaeaiiue iioie
1 12 0,8929 10,71
2 15 0,7972 11,96
3 9 0,7118 6,41
4 25 0,6355 15,89
Eoiai 61
44,97
4.1.2. Ioeaiea iioiea i?aioia?aiaei
Eiaeea ioeaiee aeaiaaeiiai iioiea a yoii neo/aa aiaeiae/ia
auoaiienaiiie; iaeioi?ia ?anoiaeaeaiea a au/eneeoaeueiuo oi?ioeao
iauyniyaony naeaeaii yeaiaioia iioiea e ia/aeo niioaaonoaothueo
iiaeuioa?aaeia. Aoaeouay noieiinoue enoiaeiiai aeaiaaeiiai iioiea
i?aioia?aiaei FVpre a iauai aeaea iiaeao auoue ?ann/eoaia ii oi?ioea:
n
FVpre=(Ck(1+d)n-k+1
k=l
I/aaeaeii, /oi FVpre = FVpst * (1 + d).
Aeey ia?aoiie caaea/e iiaeao auoue i?aaenoaaeaia neaaeothuay noaia
aeeneiioe?iaaiey
Oaeei ia?acii, i?eaaaeaiiue aeaiaaeiue iioie aeey enoiaeiiai iioiea
i?aioia?aiaei eiaao aeae:
C1 C2/(1+d) C3/(1+d)2 ……. Cn/(1+d)n-1
Neaaeiaaoaeueii, i?eaaaeaiiay noieiinoue iioiea i?aioia?aiaei PVpre a
iauai aeaea iiaeao auoue ?ann/eoaia ii oi?ioea:
n n
PVpre = (Ck/(1+d)k-1 = (1+d)*(Ck*FM2(d,k-1)
k=1 k=1
Eae e a neo/aa n aoaeouae noieiinoueth, i/aaeaeii, /oi
PVpre=PVpst*(1+d). Oae, anee a i?aaeuaeouae caaea/a i?aaeiieiaeeoue, /oi
enoiaeiie iioie i?aaenoaaeyao niaie iioie i?aioia?aiaei, oi aai
i?eaaaeaiiay noieiinoue aoaeao ?aaia:
PVpre=PVpst*(1+d) = 44,97*1,12 = 50,37 oun. ?oa.
4.2. Oeiainiaua iioiee i?aaei?eyoey
Iiae oeiainiaui iioieii i?aaei?eyoey aoaeai iiieiaoue niaieoiiinoue
ieaoaaeae ca ii?aaeaeaiiue ia?eiae, iauaaeeiaiiuo aaeeinoaii oi?iu
ieaoaaea e aeaeii ieaoaaea ( ca /oi e eae ieaoyo).
Ana oeiainiaua iioiee aeaeyonya:
—aoiaeiua – iinooieaiey aeaiaaeiuo n?aaenoa i?aaei?eyoeth
—auoiaeiua – aeaiaaeiua n?aaenoaa, auiea/eaaaiua i?aaei?eyoeai ii oai
eee eiui i?e/eiai
Ana oeiainiaua iioiee eiatho ianeieueei o?iaiae:
—eeanneoeeaoeey ca /oi ieaoyo eee ia /oi ?anoiaeothony aeaiueae
(aa?aae?iaaiiue o?iaaiue)
—iieaoa eaeiio-oi iinoaaueeo, caeac/eeo (iee?io?iaaiue), eiie?aoiua
ieaoaaee.
Oeiainiaua iioiee iae?io?iaiy aoaeai iacuaaoue oeiainiaui iioieii, a ia
n?aaeiai o?iaia iiaeiioieii.
4.2.1. Eeanneoeeaoeey aoiaeiuo oeiainiauo iioieia
1.Iioie aeaiaaeiuo n?aaenoa io ?aaeecaoeee iniiaiie i?iaeoeoeee.
A ?aieao yoiai oeiainiaiai iioiea auaeaeythony iiaeiioiee:
—iioie ieaoaaeae ii oaeouei iia?aoeeyi, iiae eioi?ui iiieiaaony
n?aaenoaa au?o/aiiua i?aaei?eyoeai ca ?aaeecaoeeth oiaa?a, iieaoa
eioi?iai i?ienoiaeeo iaeiia?aiaiii eee ii/oe iaeiia?aiaiii n iinoaaeie
i?iaeoeoeee (einiioianeee iioie)
—iioie iiaaoaiey aeaaeoi?neie caaeieaeaiiinoe e oiaa?iuo e?aaeeoia, o.a.
yoi oa aeaiueae, eioi?ua iieo/athony io i?iaeaaee i?iaeoeoeee (oiaa?ia,
oneoa) a e?aaeeo. Oiaa? eee oneoaa ieacuaathony a ianoiyuaa a?aiy, a
aeaiueae iieo/athony /a?ac eaeia-oi a?aiy (iioie i?iaeaaee a e?aaeeo)
—iioie aaainiauo ieaoaaeae – iieo/athony n?aaenoaa ca aua ia
i?iecaaaeaiioth e ia?aaeeciaaiioth i?iaeoeoeeth
2.Iioie n?aaenoa io ?aaeecaoeee eiouanoaa i?aaei?eyoey
A ?aiee yoiai iioiea iiiaaeatho ana n?aaenoaa au?o/aiiua i?aaei?eyoeai
io i?iaeaaee eiathueony o iaai aeoeaia.
Iiaeiioiee:
—i?iaeaaea a e?aaeeo
—i?aaeiieaoa
—einiioiaue iaoiae
Ii aieaa nouanoaaiia eeanneoeeaoeey ii aeaeo ?aaeec. eiouanoaa
—io ?aaeecaoeee iniiaiuo n?aaenoa, eiaaoeony o i?aaei?eyoey
—io ?aaeecaoeee iaiaoa?eaeueiuo aeoeaia
—io i?iaeaaee eiaaoeony o i?aaei?eyoey aeoeee e ae?. oeaiiuo aoiaa,
i?eia?aoaaoeony i?aaei?eyoeai ia a niaeoeyoeaiuo oeaeyo
—aeioiaeu, iieo/aaiua io ?aaeecaoeee eiaaoeony caiania nu?uey e
iaoa?eaeia (iaeeeaeaeia)
3.Iioie n?aaenoa, iieo/aaiuo i?e aeaenoaee i?aaei?eyoey ia oeiainiaii
?uiea.
—%-iue aeioiae, iieo/aaiue ii oeaiiui aoiaaai (aeoeeyi, iaeeaaoeeyi e
o.ae.)
—%-iue aeioiae, iieo/aaiue io e?aaeeoiuo iia?aoeee
—aeaiaaeiua n?aaenoaa, iieo/aaiua i?aaei?eyoeai io niaeoeyoeaiuo
iia?aoeee ia oeiainiaii ?uiea (oeaiiua aoiaae i?eia?aoathony ia ei?ioeia
a?aiy)
—aica?ao aeaiaaeiuo n?aaenoa, o.a. aeaiaaeiua n?aaenoaa, eioi?ua
i?aaei?eyoea iieo/aao iinea aica?aoa aio nnoae, aeaiiceoia, n?aaenoa,
cao?a/aiiuo ia i?eia?aoaiea e?aoein?i/iuo oeaiiuo aoiaa
4.Aia?aaeecaoeeiiiua aeioiaeu i?aaei?eyoey (iaoi?aiaua aeioiaeu
i?aaei?eyoey)
—aeaiaaeiua n?aaenoaa, iieo/aiiua a aeaea ?acee/iiai ?iaea oo?aoia,
iieo/aaiuo i?aaei?eyoeai (iaie)
—aeaiaaeiua n?aaenoaa, iieo/aiiua a ?acoeueoaoa auea?uoa th?eaee/aneeo
i?ioeannia (enee)
—aeioiaeu io eniieueciaaiey eiouanoaa i?aaei?eyoey, a?aiaeiua ieaoaaee
5.Oeiainiaue iioie i?eaeaeaaiuo eee caieiaaiuo oeiainiauo n?aaenoa
—e?aaeeou e nnoaeu, iieo/aaiua aeaiiui i?aaei?eyoeai (n?aaenoaa, eioi?ua
i?eaeaeathony i?aaei?eyoeai ia aica?aoiie iniiaa ia no?iai ii?aaeaeaiiue
i?iiaaeooie a?aiaie ia ieaoaaeiie iniiaa)
—aeaiaaeiua n?aaenoaa, i?eaeaeaaiua i?aaei?eyoeai a onoaaiie eaieoae
(oeiainiaue iioie i?yiuo eiaanoeoeee), iau/iue niinia i?eaea/aiey –
i?iaeaaea aeoeee eee iaaa, oeene?. ieaoaaeae e no?iaeo oneiaee aica?aoa
ia i?aaeoniao?eaaaony
—aeaiaaeiua n?aaenoaa, iieo/aiiua a aeaea oeiainiaie iiiiue: aeaiaaeiua
n?aaenoaa, iieo/aaiua i?aaei?eyoeai eeai io ainoaea?noaaiiuo i?aaiia,
eeai io ae?oaeo i?aaei?eyoee ia neaaeothueo oneiaeyo: oai?aoe/anee
i?aaeiieaaaaony aica?aoiinoue n?aaenoa ( ii ia anaaaea), ca
eniieueciaaiea aeaiaaeiuo n?aaenoa (ii e?aeiae ia?a oi?iaeueii) ieaou ia
i?aaeoniao?eaaaony
—iiaeiioie noaneaeee – aeaiaaeiua n?aaenoaa, iieo/aaiua a aeaea
noaneaeee ainoaea?noaa eiie?aoiie i?aaiecaoeee (aeey athaeaeaoiuo
i?aaiecaoeee yoi iniiaiie iioie), eiiiainaoeee ni noi?iiu ainoaea?noaa,
aeai. n?aaenoaa, iieo/aiiua a ea/anoaa aeaaioai?eoaeueiie iiiiue
Oa?aeoa?iay /a?oa yoi iioiea – aacaica?aoiay iniiaa.
4.2.2. Auoiaeiua oeiainiaua iioiee
Iiae auoiaeiuie iioieaie iiieiathony oa aeaiaaeiua n?aaenoaa, eioi?ua
i?aaei?eyoea ?aaeueii ?anoiaeoao a oa/aiee ii?aaeaeaiiiai ia?eiaea.
1.N?aaenoaa, cao?a/eaaaiua ia iieaoo nu?uey iaoa?eaeia e oneoa
—iiaaoaiea e?aaeeoi?neie caaeieaeaiiinoe ii i?eia?aoaiiui oiaa?ai e
oneoaai
—aeaiaaeiua n?aaenoaa, ?anoiaeoaiua ia oiaa?u e oneoae i?eia?aoaaiua e
iiea/eaaaiua a oaeouai ia?eiaea (einiioiaue iioie)
—aaainiaua ieaoaaee
A ?aieao yoiai iioiea ?anniao?eaathony ana ieaoaaee ii iieaoa ana
oiaa?ia e oneoa, iaiaoiaeeiuo aeey ii?iaeueiie aeeciaaeayoaeueiinoe
i?aaei?eyoey, ieacuaaaiuo ei ae?oaeie i?aaei?eyoeyie
2.Oeiainiaue iioie iieaou ?aaioieeia
A ?aieao yoiai iioiea iiiaaeatho ana ieaoaaee, iacaaeneii io oiai,
aeeth/athony iie a naaanoieiinoue eee iao, naycaiiua n iieaoie o?oaea
eeoe, iaieiaaiuo aeaiiui i?aaei?eyoeai
—aaainiaua ieaoaaee
—einiioiaua ieaoaaee
—iiaaoaiea e?aaeeoi?neie caaeieaeaiiinoe
3.Oeiainiaue iioie iaeiaiauo ieaoaaeae
—iaeiae, aeeth/aaiua a naaanoieiinoue
—io/eneaiey ai aiaathaeaeaoiua oiiaeu (nioe. ia/eneaiey, eioi?ua oiaea
aeeth/athony a naaanoieiinoue)
—iai?ioiua ieaoaaee e aeoeecu, IAeN, oaiiaeaiiua aeaea
—iaeiaiaua ieaoaaee ec i?eauee
4.Iioie n?aaenoa nianoaaiieeai i?aaei?eyoey
—auieaoa aeeaeaeaiaeia
—oeaeaaua io/eneaiey a ain. i?aaei?eyoey
—aeaiaaeiua n?aaenoaa, ?anoiaeoaiua ia aueoi oeaiiuo aoiaa o
nianoaaiieeia i?aaei?eyoey
5.Iioie ianeoaeeaaiey caeiia, o.a. oa aeaiueae, eioi?ua ?anoiaeothony
i?aaei?eyoeai ia oi, /oiau auiea/eaaoue %, iiaaoaoue e?aaeeou e o.ae.
—%-ua ieaoaaee, o.a. n?aaenoaa, eioi?ua iai?aaeythony ii oai e?aaeeoai,
eioi?ua a?aei i?aaei?eyoea
—ieaoaaee ii iiaaoaieth iniiaiie nnoaeu
—auaea/a nnoae e ?aciauaiea n?aaenoa a oeaiiua aoiaae, ia aeaiiceou
(auaeaeythony a naiinoiyoaeueiue iioie aeey i?aaei?eyoee oeia aaie)
6.Eiaanoeoeeiiiue iioie i?aaeoniao?eaaao ?anoiaeiaaiea aeaiaaeiuo
n?aaenoa ia i?eia?aoaiea ?acee/iiai ?iaea eiouanoaa
—ia i?eia?aoaiea iniiaiuo n?aaenoa
—ia i?eia?aoaiea iaiaoa?eaeueiuo aeoeaia (iaoaioia, eeoeaicee)
—aeaiaaeiua n?aaenoaa, iai?aaeyaiua ia i?eia?aoaiea aeieain?i/iuo
oeiainiauo aeoeaia (n?aaenoaa, ?anoiaeoaiua ia iieoieo aeoeee,
iaeeaaoeee, iaaa)
7.Aia?aaeecaoeeiiiua ?anoiaeu – aeaiaaeiua n?aaenoaa, iai?aaeyaiua ia
iiaaoaiea ?acee/iiai ?iaea oo?aoia, iaie, auieaou ii noaeaaiui eneai,
?anoiaeu, naycaiiua n ianeoaeeaaieai th?eaee/aneeo i?ioeannia
(aaeaieaou)
8.Aacaiciacaeiia ?anoiaeiaaiea n?aaenoa
—aeaiaaeiua n?aaenoaa, iai?aaeyaiua a aeaea noaneaeee e ae?. oi?i
aacaiciacaeiie iiiiue ae?. th?eaee/aneei eee oece/aneei eeoeai
—?anoiaeu ia aeaaioai?eoaeueiinoue
—?anoiaeu, naycaiiua n i?eia?aoaieai iai?iecaiaenoaaiiiai eiouanoaa a
nioeeaeueiuo oeaeyo (?anoiaeu ia no?ieoaeuenoai aeeeuo aeiiia e o.ae.)
4.2.3. Aeaeaeaiea aeaiaaeiuo n?aaenoa
Iiae aeaeaeaieai aeaiaaeiuo n?aaenoa iiieiatho io?aaeaiea a
ii?aaeaeaiiie oi?ia anao aoiaeiuo e auoiaeiuo iioieia, eiathueony ia
i?aaei?eyoee.Nouanoaoao aeaa iniiaiua oi?iu io?aaeaiey:
—a?oooi-aaeain
—iaooi-aaeain
Iiae a?oooi-aaeainii iiieiatho:
Iioiee I II III IV …
Aeaiaaeiua n?aaenoaa ia ia/aei ia?eiaea
Aoiaeiua iioiee
1
…
5
Anaai aoiaeiuo
Auoiaeiua iioiee
1
…
8
Anaai auoiaeiuo
Inoaoie ia eiiaoe
Inoaoie ia eiiaoe ia?eiaea aeieaeai niioaaonoaiaaoue noaouea aaeaina
«Aeaiaaeiua n?aaenoaa i?aaei?eyoey»
Iaooi-aaeain ioee/aaony io a?oooi-aaeaina oai, /oi aianoi aoiaeiuo e
auoiaeiuo iioieia noaaeony eo naeueaee?iaaiiay aaee/eia, a eiaiii
.Aianoi au?o/ee io ?aaeecaoeee noaaeony
*I=A1-Auo1-Auo2-Auo3
naeueaee?iaaiiue iioie – iioie eiaanoeoeee
E=Auo6-A2
Caaiiue iioie
C=A5-Auo5-Auo4
Iioie aia?aaeecaoeeiiiuo ?anoiaeia
Ai=A4-Auo7
Oeiainiaue iioie
O=A3
?anoiaeu ia aeaaioai?eoaeueiinoue
A=Auo8
A
Anaai
Inoaoie ia eiiaoe
I?eia/aiea A – aii?oecaoeey ia/eneaiiay i?aaei?eyoeai a niioaanoaothoai
ia?eiaea
A a?oooi-aaeaina i?aaeiieaaaaony, /oi ana aaee/eiu iieiaeeoaeueiu
A iaooi-aaeaina aaee/eiu iiaoo auoue eae iieiaeeoaeueiua, oae e
io?eoeaoaeueiua
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