Times; 0.2

3agaua 4.

Bms+aumwm +apoye+y cyuy 6opry, e›y ogepwmwa æ›nag+m›, æ›naæmm 7

wmc. rp+. uig 12% piu+mx, uepes 6 uiceyiæ.

Posæ'esa++e:

Bm›opmcwoæyDum Øopuyny 1.1, pospaxycuo +apoye+y cyuy 6opry:

FV = PVF

(1 + iF

n)=7F

(1+0,12F

0,5)=7,42 muc. spn.

3agaua 5.

B+eco› y cyui 3,5 wmc. rp+. upmu+ewmu 1 6epes+e uig 16% piu+mx. Æ›y cyuy ogepwmwa æ›nag+m› 16 æepec+e woro w po›y?

Posæ’esa++e: Mepiog +apaxyæa++e cwa+oæmwa:

6F30 + 15 = 195 6niø.

3a ØopuynoD 1.1 ogepwycuo:

FV = PVF

(1 + iF

n)=3,5(1+0,16F·

3agaua 6.

195/360)=3,9 muc. spn.

Ha c›ina›m po›iæ uoæm+e+ 6ywm æ›nage+mu ›auiwan uig 22% piu+mx, yo6 uepæic+a cyua s6inammnace æ 3,5 pasm?

Posæ'esa++e: Bm›opmcwoæyDum Øopuyny 1.1 i s ornegy +a we, yo

FV = 3,5 PV,

posæ'esycuo wa›e piæ+e++e:

3,5 PV = PVF

(1 + 0,22F

n),

3,5 = 1 + 0,22Fn

i ogepwycuo:

n = 2,5

0,22

= 11,36 _ muc.spn.

3agaua 7.

8ipua y›nana yrogy s 6a+›ou upo +aga++e uosmu›m æ 200 wmc. rp+. wepui+ou +a 2 po›m sa wa›mum yuoæaum: sa uepmmu pi› unawa sa uosmu›y cwa+oæmwa 20% piu+mx uo upocwiu cwaæyi, a æ ›ow+iu +acwyu+ouy uiæpiuui uosmu›oæmu æigcowo› spocwac +a 5%. Pospaxyæawm +apoye+y cyuy 6opry +a

›i+eya 2-ro po›y.

Posæ'esa++e:

3a ØopuynoD 1.2 pospaxoæycuo:

FV = 200 × (1 + 0,2 ×1 + 0,25 × 6 + 0,3× 6) = 295 _ muc.spn.

12 12

3agaua 8.

Kpegmw+mu goroæip uepeg6auac æmgauy uosmu›m æ cyui 150 wmc. rp+. wepui+ou +a 3 po›m sa wa›mum yuoæaum: sa uepmmu pi› unawa sa ›pegmw cwa+oæmwa 19% piu+mx, a æ ›ow+iu +acwyu+ouy ›æapwani uosmu›oæmu æigcowo› spocwac +a 1,5%. Pospaxyæawm +apoye+y cyuy 6opry +a ›i+eya 3-ro po›y.

Posæ'esa++e:

3a ØopuynoD 1.2 ogepwycuo:

FV=150(1+0,19F

1+0,195F

0.25+0,21F

0,25+0,225F

0,25+0,24F

0,25+

+0,255F

0,25+0,27F

0,25+0,295F

0,25 + 0,30F

0,25)=251,25 muc. spn.

Hapoye+a cyua 6opry (æ+ec›y) æms+auacwace sa ØopuynoD:

FV = PV × (1 + i )n×m,

M

ge (11.1.4)

m – ›ina›icwa pasiæ +apaxyæa++e % æ poyi.

Bmxogeum s sas+aue+oï Øopuynm uow+a s+auwm uepæic+y cyuy:

PV = FV

(1 + i )n×m

M

. (11.1.5)

3agaua 9.

Bms+aumwm +apoye+y cyuy ›auiwany, e›yo uepæic+a uoro cyua cwa+oæmwa 1000 rp+., c›nag+a upoye+w+a cwaæ›a - 5%, uepiog +apaxyæa++e - 7 po›iæ. Mopiæ+ewm owpmua+mu pesynawaw s æenmum+oD +apoye+oï cyum, pospaxoæa+oï s æm›opmcwa++eu cwaæ›m upocwmx %.

Posæ'esa++e:

Hapoye+a cyua, yo pospaxoæycwace sa uewogou c›nag+mx %,

æms+auacwace sa ØopuynoD 1.4:

FV= 1000(1+ 0,05)7 =1407,1 rp+.

Hapoye+a cyua, yo pospaxoæycwace sa uewogou upocwmx %,

æms+auacwace sa ØopuynoD 1.1:

FV =1000(1 + 0,05F7)= 1350 rp+.

3po6ne+i pospaxy+›m gosæoneDwa spo6mwm æmc+oæo› upo uepeæmye++e cyum ›auiwany, pospaxoæa+oï sa uewogou c›nag+mx %.

3agaua 10.

Æ›y cyuy æapwo æ›nacwm æ 6a+› uig 7% piu+mx sa c›nag+oD cwaæ›oD +a 3 po›m, yo6 go ›i+ye sas+aue+oro wepui+y ogepwawm 2000 rp+.? 3giuc+mwm uepeæip›y pospaxy+›y.

Posæ'esa++e:

Mepæic+y cyuy ›auiwany pospaxycuo sa ØopuynoD 1.5:

PV = 2000 = 1632,6 _ spn. (1+ 0,07)3

Mepeæip›y uow+a sgiuc+mwm, sacwocyæaæmm Øopuyny 1.4:

FV = 1632,6 × (1 + 0,07)3

3agaua 11.

= 2000 _ spn.

Bms+aumwm +apoye+y cyuy æ+ec›y, e›yo ›auiwan y cyui 2900 rp+. æ›nage+mu +a 3 po›m uig 24% sa c›nag+oD cwaæ›oD. Bigcow›m +apaxoæyDwace:

a) 1 pas y pi›;

6) ›ow+e uiæpiuue; æ) yo›æapwany;

r) youiceye.

Posæ'esa++e:

3a ØopuynoD 1.4 pospaxoæycuo +apoye+y cyuy, æmxogeum s yuoæ æ›nage++e:

a) _ P n

= 2800 (1 + 0,24 ) 3

= 5338 ,55 _ spn .;

6 ) _ Pn

ø ) _ Pn

= 2800 (1 +

= 2800 (1 +

0,24 )3×2

0,24 )3×4

= 5526 ,70 _ spn .;

= 5634 ,15 _ spn .;

s ) _ P n

= 2800

(1 +

0,24 ) 3×12

= 5711

,68

_ spn .;

3agaua 12.

Æ›y cyuy æapwo æ›nacwm æ 6a+›, yo6 uo sa›i+ue++i 2-x po›iæ +apoye+a cyua c›nana 9000 rp+. upm cwaæyi c›nag+mx % 9%. Hapaxyæa++e % sgiuc+Dcwace:

a) ›ow+e uiæpiuue;

6) yoݾapwany.

Posæ'esa++e:

Mepewæopmæmm Øopuyny 1.4, s+augeuo uepæic+y cyuy æ+ec›y:

P = 8000 = 6708,60spn.;

a) 0



1 +

2×2

0,09 



 2 

P 0 =

8000

2×4

= 6695,68spn.;

1 +

0,09 

 4 

3agaua 13.

Bms+aumwm +au6inam æmrig+mu æapia+w æ›nage++e ›omwiæ +a

3 po›m:

1) ›auiwan æ›nagacwace uig 11,9% piu+mx sa c›nag+oD cwaæ›oD upm

+apaxyæa++i % 1 pas y pi›;

2) ›auiwan æ›nagacwace uig 11,5% piu+mx sa c›nag+oD cwaæ›oD upm

+apaxyæa++i % ›ow+e uiæpiuue;

3) ›auiwan æ›nagacwace uig 11,3% piu+mx sa c›nag+oD cwaæ›oD upm

+apaxyæa++i % yo›æapwany;

4) ›auiwan æ›nagacwace uig 11,2% piu+mx sa c›nag+oD cwaæ›oD upm

+apaxyæa++i % youiceye.

1) P n

= 1000 (1 + 0,118 )3

Posæ'esa++e:

= 1397 ,42 spn .;

2) P n

= 1000 1 +

0,115

3×2







= 1398 ,56 spn .;

3) P n

= 1000



 1 +



0,113

3 × 4







= 1396

,96 spn .;

4) P n

= 1000 1 +

0,112

3×12







= 1397 ,16 spn .

Ouwmuana+mu æapia+w æ›nage++e ›owiæ sa6esueuyc ua›cmuana+y

+apoye+y cyuy, e›y pospaxycuo sa Øopuynaum 1.4, s ornegy +a yuoæm æ›nage++e. Mpmuuacuo uepæic+y cyuy æ posuipi 1000 rp+.

B e›o+ouiu+iu niwepawypi sycwpiuacwace ›ina›a upaæmn, uo e›mx uow+a æig+oc+o wou+o pospaxyæawm wepui+ uogæoc++e ›auiwany.

Mpaæmno “72”: gne æms+aue++e wepui+y uogæoc++e ›auiwany +eo6xig+o

72 uoginmwm +a æigouy upoye+w+y cwaæ›y i.

n = 72 .

i

(11.1.6)

Mpaæmno «69»: wepui+ uogæoc++e ›auiwany o6umcnDcwace uo Øopuyni:

n = 69 + 0,35 . (11.1.7)

I

3agaua 14.

Bms+aumwm uepes e›mu uac uogæoïwace ›auiwan, e›yo upoye+w+a cwaæ›a c›nagac 29%.

n = 69

Posæ'esa++e:

+ 0,35 = 2,81 _ so6a

um

n = 72 = 2,57 _ so6a

5agaui gne camocwiu+oro potæ'eta++e:

1.B›nag+m› posuiyac æ 6a+› 10000 rp+. 15% piu+mx. Bms+aumwm e›y cyuy ogepwmwa æ›nag+m› sa upaæmnou upocworo æigcow›a uepes:

a) 2 po›m;

6) 3 po›m; æ) 5 po›iæ.

2.B›nag+m› posuiyac 1000 rp+. uig 14% piu+mx y 6a+› +a 2 po›m. Bms+aumwm sa upaæmnou c›nag+oro æigcow›a e›y cyuy æi+ ogepwmwa upm

+apaxyæa++i æigcow›a.

a) 2 pasm +a pi›;

6) 4 pasm +a pi›.

3.B›nag+m› posuiyac 15000 rp+. uig 24% piu+mx y 6a+› +a 3 po›m. Bms+aumwm sa upaæmnou c›nag+oro æigcow›a e›y cyuy æi+ ogepwmwa upm

+apaxyæa++i æigcow›a yo›æapwana+o.

4.B›nag+m› posuiyac æ 6a+› 5000 rp+. uig 15% piu+mx. Bms+aumwe e›y cyuy ogepwmwa æ›nag+m› sa upaæmnou upocworo æigcow›a:

a) uepes 3 po›m;

6) uepes 240 g+iæ.

5.B›nag+m› posuiyac 1000 rp+. uig 16% piu+mx y 6a+› +a 2 po›m.

Bms+aumwm sa upaæmnou c›nag+oro æigcow›a e›y cyuy æi+ ogepwmwa:

a) uepes 2 po›m;

6) upm +apaxyæa++i æigcow›a 2 pasm +a pi›; æ) upm +apaxyæa++i æigcow›a yo›æapwana+o.

6.I+æecwop uac 15000 rp+., æms+aumwe uau6yw+D æapwicwa rpomiæ uepes:

a) 3 po›m upm cwaæyi æigcow›a 20%;

6) 5 po›iæ upm cwaæyi æigcow›a 15%;

æ) 4 po›iæ upm cwaæyi æigcow›a 25%.

7.Æ›y cyuy uoæm+e+ æ›nacwm i+æecwop uig 19 % piu+mx, yo6 uepes 3 po›m æi+ ogepwaæ 10000 rp+., sa upaæmnou upocworo æigcow›y.

8.I+æecwop uac 20000 rp+., æms+aumwe uau6yw+D æapwicwa rpomeu uepes:

a) 3 po›m upm cwaæyi upocworo æigcow›a 20% ;

6) 5 po›iæ upm cwaæyi c›nag+oro æigcow›a 15%.

9.I+æecwop upmg6aæ yi++mu uauip sa yi+oD 534 rp+. fepes 3 po›m æi+ 6yge ›omwyæawm 999 rp+. O6umcnmwe upoye+w+y cwaæ›y, yo sa6esueumwa goxog uo i+æecwmyiex.

10.Æ›y cyuy uoæm+e+ æ›nacwm i+æecwop uig 20 % piu+mx, yo6 uepes 3

po›m æi+ ogepwaæ 10000 rp+. sa upaæmnou c›nag+oro æigcow›a.

11. Bms+aumwe uau6yw+D æapwicwa 1000 rp+., e›yo æm i+æecwycwe rpomi

+a gæa po›m uo cwaæyi 6,5 % piu+mx.

12. Pospaxyuwe, e›y cyuy owpmuac i+æecwop, e›yo æi+ i+æecwyc 1100 rp+.

+a gæa po›m uo cwaæyi 5,6 % piu+mx.

13. Bm una+ycwe upmg6awm ›ouu'Dwep i uowewe sapas gne yaoro æig›nacwm 3000 rp+. Bms+aumwe, e›oD cyuoD æm poswamoæyæawmuewe gne yicï uo›yu›m uepes wpm po›m, e›yo i+æecwycwe yi rpomi uig piu+y upoye+w+y cwaæ›y 7,2 %.

14. Bm s6mpacwece upmg6awm weneæisop, upm yaouy sapas æm uowewe æig›nacwm wina›m 4000 rp+. Pospaxyuwe cyuy, e›y æm uawmuewe æ cæocuy posuopegwe++i æ yinex peanisayiï ga+oï uo›yu›m uepes gæa po›m, e›yo piu+a upoye+w+a cwaæ›a upm yo›æapwana+ouy +apaxyæa++i c›nagac 12%.

15. Bms+aumwe uau6yw+D æapwicwa 1700 rp+., i+æecwoæa+mx +a wpm po›m, e›yo piu+a upoye+w+a cwaæ›a c›nagac 9% upm +apaxyæa++i ›ow+i 6 uiceyiæ.

16. Bm i+æecwycwe rpomoæi ›omwm +a gæa po›m uig 11% piu+mx, wa›mx, yo +apaxoæyDwace ›ow+oro ›æapwany. Bms+aumwe uau6yw+D æapwicwa æamoro

›auiwany, yo cwa+oæmwa sapas 900 rp+.

17. fepes gæa po›m æm una+ycwe, yo æam Øi+a+coæmu ›auiwany c›nage 3120 rp+. Bms+aumwe uowou+mu posuip æamoro ›auiwana, e›yo æigouo, yo æi+ upm+ocmwa 11,9% piu+mx.

18. Bms+aumwe uowou+y æapwicwa i+æecwmyiu, e›yo æigouo, yo æo+m upm cwaæyi 9,9% upm+ecywa æau uepes wpm po›m 1919 rp+.

19.Bm una+ycwe uepes wpm po›m ›yumwm cwepeocmcweuy sa 3200 rp+. Bms+aumwe, e›y cyuy æm uoæm++i i+æecwyæawm sapas, yo6 spo6mwm yD uo›yu›y, e›yo piu+a upoye+w+a cwaæ›a c›nagac 9%.

20.Pospaxyuwe uowou+y æapwicwa 1300 rp+., owpmua+mx uepes gæa po›m, e›yo piu+a æigcow›oæa cwaæ›a c›nagac 9,6%.

21.Bms+aumwe, e›y cyuy æm uoæm++i uawm sapas, yo6 upm cwaæyi 9,9%

uepes wpm po›m æo+a c›nana 920 rp+.

22.Æ›yo i+æecwmyiï upm cwaæyi 11,4% upm+ecywa æau 2940 rp+. uepes uowmpm po›m, wo e›a ïx uowou+a æapwicwa.

23.Bms+aumwe uowou+y æapwicwa i+æecwmyiu, e›yo æo+m upm piu+iu æigcow›oæiu cwaæyi æ 13%, yo +apaxoæycwace ›ow+i 6 uiceyiæ, uepes 3,5 po›m c›nagywa 3950 rp+.

24. Æ›y cyuy uoæm+e+ æ›nacwm i+æecwop uig 20 % piu+mx, yo6 uepes 3

po›m æi+ owpmuaæ 10 000 rp+.

11.2.A++yïwew.Cyuac+a wa mau6yw+e æapwicwa a++yïwewy

Annyïmem – ye uocnigoæ+icwa unawewiæ sa æms+aue+i perynep+i upouiw›m uacy. I+ogi uo+ewwe a++yïwewy saui+ecwace uo+ewweu pe+wa. BmgineDwa gæa æmgm a++yïwewy: æigınage+uu i +erau+uu. Mpm æig›nage+ouy a++yïwewy unawewi sgiuc+DDwace +aupm›i+yi uepiogy, a upm +erau+ouy – +a uouaw›y.

3a uacou æmunawm uepmoro a++yïwew+oro unawewy pospis+eDwa:

a++yïwew uocw+yuepa+go - æmunawa sgiuc+Dcwace +aupm›i+yi uepmoro uepiogy,

a++yïwew upe+yuepa+go - æmunawa sgiuc+Dcwace +a uouaw›y uepmoro uepiogy.

Mau6ymne øapmicma mepuinoøoso annyïmemy nocmnyuepan6o

¶ne oyi+›m pyxy Øi+a+coæmx uowo›iæ y uaci sacwocoæyDwa pis+i Øopuynm Øi+a+coæoï uaweuawm›m, y wouy umcni u pospaxy+o› uau6yw+aoï æapwocwi wepui+oæoro a++yïwewy uocw+yuepa+go.

Cyw+icwa pospaxy+›y y›nagacwace æ wiu, yo rpomoæmu uowi›, yo c›nagacwace s og+a›oæmx uo æenmum+i æmunaw u ic+yDumu ueæ+mu uac uow+a uepepaxyæawm æ uau6yw+D æapwicwa, uigcyuyæaæmm æci +apaxoæa+i æmunawm s ypaxyæa++eu yuoæm uocw+yuepa+go.

8opuyna uau6yw+aoï æapwocwi wepui+oæoro a++yiwewy uocw+yuepa+go:

(1 + i)n-1

FV = PMT ×

i

. (11.2.1)

3agaua 15.

Heo6xig+o pospaxyæawm uau6yw+D æapwicwa wepui+oæoro a++yïwewya upm 100 rp+. yopiu+mx æmunaw, cwaæyi piæ+oï 12%, upowerou 5 po›iæ sa cxeuoD uocw+yuepa+go.

FV = 100 ×

(1 + 0,12)5-1 0,12

= 635,28 _ spn.

Mau6ymne øapmicma mepuinoøoso annyïmemy npenyuepan6o

¶ne oyi+›m pyxy Øi+a+coæmx uowo›iæ y uaci sacwocoæyDwa pis+i Øopuynm Øi+a+coæoï uaweuawm›m, y wouy umcni u pospaxy+o› uau6yw+aoï æapwocwi wepui+oæoro a++yïwewy upe+yuepa+go.

Cyw+icwa pospaxy+›y y›nagacwace æ wiu, yo rpomoæmu uowi›, yo c›nagacwace s og+a›oæmx uo æenmum+i æmunaw u ic+yDumu ueæ+mu uac uow+a uepepaxyæawm æ uau6yw+D æapwicwa, uigcyuyæaæmm æci +apoye+i æmunawm s ypaxyæa++eu yuoæm upe+yuepa+go.

8opuyna +aæege+oï æapwocwi wepui+oæoro a++yïwewy upe+yuepa+go:

(1 + i)n-1

FV = PMT × (1 + i) ×

i

3agaua 16.

. (11.2.2)

Heo6xig+o pospaxyæawm uau6yw+D æapwicwa wepui+oæoro a++yïwewy upm

100 rp+. yopiu+mx æmunaw, cwaæyi piæ+oï 12%, upowerou 5 po›iæ sa cxeuoD

upe+yuepa+go.

FV = 100 × (1+ 0,12) ×

(1+ 0,12)5-1 0,12

= 712,1 _ spn.

Mpuøe6ena øapmicma mepuinoøoso annyïmemy nocmnyuepan6o

¶ne oyi+›m pyxy Øi+a+coæmx uowo›iæ y uaci sacwocoæyDwa pis+i Øopuynm Øi+a+coæoï uaweuawm›m, y wouy umcni u pospaxy+o› +aæege+oï æapwocwi wepui+oæoro a++yïwewy uocw+yuepa+go.

Cyw+icwa pospaxy+›y y›nagacwace æ wiu, yo rpomoæmu uowi›, yo c›nagacwace s og+a›oæmx uo æenmum+i æmunaw u ic+yDumu ueæ+mu uac uow+a uepepaxyæawm +a giuc+mu uoue+w, uigcyuyæaæmm æci upogmc›o+woæa+i æmunawm s ypaxyæa++eu yuoæm uocw+yuepa+go.

8opuyna +aæege+oï æapwocwi wepui+oæoro a++yïwewy uocw+yuepa+go:

1 - 1

PV = PMT × ( i). (11.2.3)

1 + n

i

3agaua 17.

Heo6xig+o pospaxyæawm +aæege+y æapwicwa wepui+oæoro a++yïwewy upm 100 rp+. yopiu+mx æmunaw, cwaæyi piæ+oï 12%, upowerou 5 po›iæ sa cxeuoD uocw+yuepa+go.

PV = 100 ×

1 - 1

(1 + 0,12)5

0,12

= 360,47 _ spn.

Haøe6ena øapmicma mepuinoøoso annyïmemy npenyuepan6o

¶ne oyi+›m pyxy Øi+a+coæmx uowo›iæ y uaci sacwocoæyDwa pis+i Øopuynm Øi+a+coæoï uaweuawm›m, y wouy umcni u pospaxy+o› +aæege+oï æapwocwi wepui+oæoro a++yïwewy upe+yuepa+go.

Cyw+icwa pospaxy+›y y›nagacwace æ wiu, yo rpomoæmu uowi›, yo c›nagacwace s og+a›oæmx uo æenmum+i æmunaw u ic+yDumu ueæ+mu uac uow+a uepepaxyæawm +a giuc+mu uoue+w, uigcyuyæaæmm æci upogmc›o+woæa+i æmunawm s ypaxyæa++eu yuoæm upe+yuepa+go.

8opuyna +aæege+oï æapwocwi wepui+oæoro a++yïwewy upe+yuepa+go:

1 - 1

PV = PMT × (1 + i)× ( i). (11.2.4)

3agaua 18.

1 + n

i

Heo6xig+o pospaxyæawm +aæege+y æapwicwa wepui+oæoro a++yïwewy upm 100 rp+. yopiu+mx æmunaw, cwaæyi piæ+oï 12%, upowerou 5 po›iæ sa cxeuoD upe+yuepa+go.

PV = 100 × (1 + 0,12) ×

1 - 1

(1 + 0,12)5

0,12

= 403,73 _ spn.

Mpuøe6ena øapmicma 6etcmpo1oøoso annyïmemy

¶ne oyi+›m pyxy Øi+a+coæmx uowo›iæ y uaci sacwocoæyDwa pis+i Øopuynm Øi+a+coæoï uaweuawm›m, y wouy umcni u pospaxy+o› +aæege+oï æapwocwi 6escwpo›oæoro a++yïwewy.

Cyw+icwa pospaxy+›y y›nagacwace æ wiu, yo rpomoæmu uowi›, yo c›nagacwace s og+a›oæmx uo æenmum+i æmunaw i +eo6uewe+mu sa uacou uac

›i+yeæy caorog+im+D æapwicwa, wouy yo upm i+Øneyiï 6iname +yne caorog+im+e æapwicwa uepiogmu+oï æmunawm uocwiu+o sue+mycwace u y

+ec›i+ue++ocwi upar+e go +yne.

8opuyna +aæege+oï æapwocwi 6escwpo›oæoro a++yïwewy:

PV = PMT .

i

3agaua 19.

(11.2.5)

Heo6xig+o pospaxyæawm æapwicwa 6escwpo›oæoro a++yïwewy upm 100 rp+. yopiu+mx æmunaw i cwaæyi piæ+oï 12%.

PV = 100 / 0,12 = 833,33 rp+.

Mpm æm›opmcwa++i ga+oro Øi+a+coæoro i+cwpyue+wa +eo6xig+o æpaxoæyæawm, yo upmu+ew+a cwaæ›a gmc›o+wyæa++e (upoye+w+a cwaæ›a) uoæm++a uicwmwm æ co6i 6espmsm›oæy cwaæ›y u upeuiD sa pmsm›.

5agaui gne camocwiu+oro potæ'eta++e:

1. Pospaxyuwe caorog+im+D æapwicwa wepui+oæoro a++yïwewy upe+yuepa+go sa yuoæm, yo æenmum+a piæ+ouip+oro +agxogwe++e cwa+oæmwa 2200 rp+. y pi›.

2. Bms+aumwe, e›e s+aue++e yopiu+oro æ+ec›y (æ+eco› po6mwace +a uouaw›y po›y), 6yge æiguoæigawm uowou+iu æapwocwi a++yïwewy æ 12300 rp+., e›yo cwpo› æ+ec›y 6 po›iæ upm upoye+w+iu cwaæyi 19,2%.

3. C›ina›m uacy 6yge uowpi6+o, yo6 uowou+a æapwicwa a++yïwewy æiguoæigana cyui æ 36000 rp+., e›yo +a uouaw›y ›ow+oro po›y +a paxy+o› ›nacwm 5900 rp+. uig 13,7% piu+mx?

4. Mpm e›iu upoye+w+iu cwaæyi, æapwicwa a++yïwewy 6yge gopiæ+Dæawm 28000

rp+., e›yo +a uouaw›y ›ow+oro s 6 po›iæ +a paxy+o› ›nacwm 6600 rp+.?

5. Pospaxyuwe uau6yw+D æapwicwa wepui+oæoro a++yïwewy uocw+yuepa+go sa yuoæm, yo æenmum+a piæ+ouip+oro +agxogwe++e cwa+oæmwa 3000 rp+. y pi›, upoye+w+a cwaæ›a 12,33% i cwpo› 4 po›m.

6. Bms+aumwe, upm e›ouy s+aue++i yopiu+mx æ+ec›iæ (æ+eco› po6mwace

+aupm›i+yi po›y), æmuge uepes 5 po›iæ cyua æ 20000 rp+. upm æigcow›oæoï cwaæyi 21,5%.

7. C›ina›m yinmx po›iæ 6yge uowpi6+o, yo6 +arpouagmwm +a paxy+›y cyuy æ 45000 rp+., e›yo +aupm›i+yi ›ow+oro po›y +a paxy+o› ›nacwm 5000 rp+. uig 14,5% piu+mx.

8. Mpm e›iu æigcow›oæiu cwaæyi +arpouagmwace cyua æ 64000 rp+., e›yo

+aupm›i+yi ›ow+oro s 8 po›iæ +a paxy+o› ›nacwm 7300 rp+.?

9. Pospaxyuwe uau6yw+D æapwicwa wepui+oæoro a++yïwewy upe+yuepa+go sa yuoæm, yo æenmum+a piæ+ouip+oro +agxogwe++e cwa+oæmwa 1500 rp+. +a pi›, æigcow›oæa cwaæ›a 9,5% i cwpo› 5 po›iæ.

10. Bms+aumwe, upm e›ouy s+aue++i yopiu+mx æ+ec›iæ (æ+eco› po6mwace +a uouaw›y po›y), æmuge uepes 7 po›iæ cyua æ 14 000 rp+. upm æigcow›oæiu cwaæyi 4,6%.

11. C›ina›m yinmx po›iæ 6yge uowpi6+o, yo6 +arpouagmwm +a paxy+›y cyuy æ

53000 rp+., e›yo +a uouaw›y ›ow+oro po›y +a paxy+o› ›nacwm 2700 rp+. uig

10,1% piu+mx.

12. Mpm e›iu æigcow›oæiu cwaæyi +arpouagmwace cyua æ 48000 rp+., e›yo +a uouaw›y ›ow+oro s 6 po›iæ +a paxy+o› ›nacwm 6600 rp+.?

13. Pospaxyuwe caorog+im+D æapwicwa wepui+oæoro a++yïwewy uocw+yuepa+go sa yuoæm, yo æenmum+a piæ+ouip+oro +agxogwe++e cwa+oæmwa 1100 rp+. y pi›, upoye+w+a cwaæ›a 5,6% i cwpo› 6 po›iæ.

14. Bms+aumwe, e›e s+aue++e yopiu+oro æ+ec›y (æ+eco› po6mwace +aupm›i+yi po›y), 6yge æiguoæigawm uowou+iu æapwocwi a++yïwewy æ 41000 rp+., e›yo cwpo› æ+ec›y 5 po›iæ upm æigcow›oæiu cwaæyi 13,75%.

15. C›ina›m uacy 6yge uowpi6+o, yo6 uowou+a æapwicwa a++yïwewy æiguoæigana cyui æ 42000 rp+., e›yo +aupm›i+yi ›ow+oro po›y +a paxy+o› ›nacwm 5200 rp+. uig 8,8% piu+mx?

16. Mpm e›iu æigcow›oæiu cwaæyi, æapwicwa a++yïwewa 6yge gopiæ+Dc 17000 rp+., e›yo +aupm›i+yi ›ow+oro s 9 po›iæ +a paxy+o› ›nacwm 2300 rp+.?

17. Pospaxyuwe caorog+im+D æapwicwa 6escwpo›oæoro a++yïwewy sa yuoæm, yo æenmum+a piæ+ouip+oro +agxogwe++e cwa+oæmwa 3200 rp+. y pi›, æigcow›oæa cwaæ›a 14,4%.

18. Bms+aumwe, e›e s+aue++e yopiu+oro æ+ec›y 6yge æiguoæigawm uowou+iu æapwocwi 6escwpo›oæoro a++yïwewy æ 37100 rp+., upm æigcow›oæiu cwaæyi 7,25%.

19. Mpm e›iu æigcow›oæiu cwaæyi, æapwicwa 6escwpo›oæoro a++yïwewy 6yge gopiæ+Dæawm 51000 rp+., e›yo yopo›y +a paxy+o› ›nacwm 5500 rp+.?

11.3.Bapwic+a oyi+ıa aıyiu wa ïx+e upu6ywıoæicwa.

Mpm yxæane++i i+æecwmyiu+mx pime+a æ upoyeci a+anisy pm+›y yi++mx uauepiæ æm›opmcwoæyDwace pis+i æapwic+i oyi+›m a›yiu. V upa›wmu+iu giena+ocwi pospis+eDwa +acwyu+i ïx æmgm:

1) +oui+ana+a æapwicwa;

2) euiciu+a æapwicwa (yi+a posuiye++e);

3) 6yxranwepca›a (6ana+coæa, ›+mw+a) æapwicwa;

4) pm+›oæa æapwicwa;

5) ›ypcoæa æapwicwa.

Houi+ana+a æapwicwa a›yiï - ye æapwicwa, æ›asa+a +a nmyaoæiu cwopo+i a›yiï a6o ïï cepwmØi›awy. Ounawa a›yiu upm ycwa+oæi woæapmcwæa upoæogmwace sac+oæ+m›aum sa ïx +oui+ana+oD æapwicwD. V uouaw›oæmu uepiog Øy+›yio+yæa++e woæapmcwæa æapwicwa uoro uau+a gopiæ+Dc æenmum+i cwawyw+oro ›auiwany.

B upoyeci cæocï giena+ocwi æapwicwa uau+a uigupmcucwæa uowe s6inamyæawmce a6o sue+myæawmce. Ta›mu um+ou, s uacou peana+a æapwicwa uau+a a›yio+ep+oro woæapmcwæa (AT) æigpis+ewmuewace æig æenmum+m cwawyw+oro ›auiwany. B sæ'es›y s ymu æm+m›ac +eo6xig+icwa y æms+aue++i 6yxranwepca›oï æapwocwi a›yiï, e›a c æig+ome++eu æapwocwi umcwmx a›wmæiæ

›ouua+iï go ›ina›ocwi posuiye+mx a›yiu. bana+coæa æapwicwa sasæmuau pospaxoæycwace yo›æapwany i æ ›i+yi po›y upm c›naga++i 6ana+cy.

Mig æapwicwD umcwmx a›wmæiæ AT posyuicwace æenmum+a, yo o6umcnDcwace æig+iua++eu s cyum a›wmæiæ AT, yo upmuuaDwace go pospaxy+›y, cyum uoro uacmæiæ, yo upmuuaDwace go pospaxy+›y. ¶o c›nagy a›wmæiæ, yo upmuuaDwace go pospaxy+›y, æig+ocewa: +eo6opow+i i o6opow+i a›wmæm, sa æm+ew›ou cyu, æmwpaue+mx +a æm›yu ænac+mx a›yiu i sa6oproæa+ocwi sac+oæ+m›iæ uo æ+ec›ax æ cwawyw+mu ›auiwan. ¶o c›nagy uacmæiæ, yo æ›nDuaDwace æ pospaxy+o›, æ›nDuaDwa: goærocwpo›oæi i ›opow›ocwpo›oæi so6oæ'esa++e AT.

B upoyeci cæoro posæmw›y AT uepiogmu+o ygacwace go euiciï a›yiu s uewoD owpmua++e gogaw›oæoro ›auiwany. ]i+a, uo e›iu peanisyDwace a›yiï

+oæoro æmuyc›y, +asmæacwace yi+oD posuiye++e (euiciu+oD yi+oD). 3a pociuca›mu sa›o+ogaæcwæou posuiye++e a›yiu uoæm++e sgiuc+Dæawmce sa pm+›oæoD yi+oD, e›a uowe æigpis+ewmce æig +oui+ana+oï. Æ›yo æ upoyeci sæep+e++e +a æwopm++ouy pm+›y ouepayiï uo ›yuiæni-upogawy a›yiu uowywa sgiuc+Dæawmce sa yi+oD æmye a6o +mwue sa ïx +oui+ana+y æapwicwa, wo upm euiciï a›yiu yi+a ïx posuiye++e uoæm++a 6ywm +e +mwue +oui+ana+oD.

Pm+›oæa yi+a - ye yi+a, uo e›iu a›yie ›yuycwace i upogacwace +a æwopm++ouy pm+›y. ]e yi+a Øopuycwace uig æunmæou pm+›oæoï ›o+'D+›wypm i æms+auacwace uoumwou i upouosmyicD, piæ+eu upm6yw›oæocwi +a cyuiw+mx cerue+wax Øi+a+coæoro pm+›y, i+Øneyiu+mum oui›yæa++eum i i+mmum um++m›aum. Pm+›oæa yi+a sasæmuau æcwa+oænDcwace +a woprax +a Øo+goæiu 6ipwi i æigo6pawac giuc+y yi+y a›yiï sa yuoæm æenm›oro o6'cuy ouepayiu.

Ha æigui+y æig i+mmx yi++mx uauepiæ oyi+›a sæmuau+mx a›yiu +ece æ co6i ueæ+i wpyg+oyi gne i+æecwopa. ]e uoæ'esa+o s wmu, yo:

uo-uepme, ic+yDwa wpyg+oyi æ oyi+yi uepmoï c›nagoæoï goxogy ænac+m›a a›yiï - gmæige+giæ. Posuip gmæige+giæ uo sæmuau+mx a›yiex +e æigoumu, i wouy uowou+a oyi+›a uau6yw+ix gmæige+giæ 6ygycwace +a upmuyye++ex i+æecwopa;

uo-gpyre, +eæms+aue+icwa æ pyci ›ypcy a›yiï. Ha æigui+y æig 6oproæmx yi++mx uauepiæ, y e›mx pm+›oæa yi+a uoæ'esa+a s +oui+anou i uocwiu+o upmæogmwace æiguoæig+o go +eo6xig+oï upm6yw›oæocwi i pmsm›y go +eï, yi+a a›yiï +e +ocmwa wa›oï sanew+ocwi. Pm+›oæa yi+a a›yiï 6inamoD uipoD æms+auacwace spocwa++eu umcwmx a›wmæiæ ›ouua+iï, i ïï ua›cmuana+e s+aue++e

+e o6uewe+e. Mpm yaouy æo+a uowe e› pocwm, wa› i s+mwyæawmce, upmwouy, yo

+aupeu ïï pyxy 6ygycwace wa›ow +a upor+osax i+æecwopiæ;

uo-wpewc, 6escwpo›oæmu xapa›wep a›yiï æmuarac o6ni›y una+iæ i+æecwopa uo æig+ome++D go +eï. ]e uoæ'esa+o s uigxogou go oyi+›m yi++mx uauepiæ s ueæ+mu i +eæms+aue+mu wepui+ou æonogi++e, oc›ina›m oyi+›a æig6yæacwace +a oc+oæi gmc›o+wyæa++e uau6yw+ix uowo›iæ unawewiæ.

Bms+aue++e yi+m a›yiï, e› i 6inamocwi yi++mx uauepiæ, 6asycwace +a uowou+iu oyi+yi rpomoæmx uowo›iæ, e›i i+æecwop owpmuac æ uau6yw+aouy. Ta› upm æms+aue++i yi+m a›yiï i+æecwop æpaxoæyc posuip uau6yw+ix gmæige+giæ i oui›yæa+y æapwicwa a›yiï æ ›i+yi i+æecwmyiu+oro uepiogy. Mpmuouy upor+os i uau6yw+ix gmæige+giæ, i sui+a yi+m a›yiï 6ygyDwace +a uigcwaæi uoniwm›m a›yio+ep+oro woæapmcwæa æig+oc+o ymx uo›as+m›iæ i a+anisi gm+aui›m sui+ ïx sa uouepeg+iu uepiog. Touy oyi+›m uau6yw+ix goxogiæ æig a›yiu +ocewa

yuoæ+mu xapa›wep. Bm+ewo› cwa+oænewa upmæineuoæa+i a›yiï, posuip gmæige+giæ uo e›mx æms+aue+mu æ cwawywi.

Bigs+aumuo, yo goxig y Øopui gmæige+giæ uowe 6ywm upegcwaæne+mu y æmrnegi cepiï piæ+mx unawewiæ i unawewiæ goæina+oï Øopum. V sæ'es›y s ymu pospis+eDwace uewogm oyi+›m a›yiu. Æ›yo i+æecwop, +a6yæaDum a›yiï +a

+eæms+aue+mu uepiog, pospaxoæyc wina›m +a goxig y Øopui gmæige+giæ, wo upmu+ew+a yi+a a›yie gne +aoro æms+auawmuewace e›

¥ Divt

(11.3.1)

ge t - uepiog, æ e›ouy 6ynm æmunaue+i gmæige+gm;

Div - cyua gmæige+giæ.

Mpm yaouy e›yo gmæige+gm æmunauyDwace piæ+mum unawewaum, wo æm›opmcwoæyDwa +acwyu+y Øopuyny:

PV =

Div ,

i

(11.3.2)

3agaua 20.

¶mæige+g +a og+y a›yiD æ piu+ouy æmuipi c›nagac 10 rpmæe+a, uepeg6auyæa+mu upm6yw›oæicwa ga+oï a›yiï – 15%. Oyi+mwm æapwicwa a›yiï, e›yo upmuycwmwm yo gmæige+gm +a uocwiu+ouy piæ+i.

Posæ'esa++e:

PV =

10 = 67 ,7 spuøena .

0,15

Æ›yo posuip gmæige+giæ spocwac is cepeg+aopiu+mu weuuou (g ), wo oyi+›a a›yiï sgiuc+Dæawmuewace sa ØopuynoD:

D (1+ g ) D

PV = iv0 =

i - g

3agaua 21.

iv1

i - g

, (11.3.3)

Ocwa++iu pi› a›yio+ep+e woæapmcwæo æmunawmno gmæige+gm æ posuipi 0,5 rpmæe+a +a a›yiD. Mpor+osycwace, yo gmæige+gm yopiu+o 6ygywa spocwawm +a 4,5%. Bms+aumwm yi+y a›yiï, e›yo +eo6xig+a cwaæ›a goxogy c›nagac 12%.

PV =

Posæ'esa++e:

0,5 × (1+ 0,045)

= 6,97spuøen.

0,12 - 0,045

V cmwyayiï ›onm +apaxyæa++e i æmunawa gmæige+giæ upoæogewace ›ina›a pasiæ æ pi›, wo æapwicwa a›yiï gne i+æecwopa æms+auacwace e›

(11.3.4)

ge m - umcno æmunaw gmæige+giæ +a pi›.

V æmuag›y e›yo i+æecwop, yo æonogic a›yicD, una+yc wpmuawm ïï upowerou ueæ+oro uepiogy uacy, owpmuyDum gmæige+gm, a uowiu upogawm ïï, wo æapwicwa wa›oï a›yiï o6umcnDcwace e›

n Divt FV

+

(1 + i)n

. (11.3.5)

Mpm yaouy e›yo gmæige+gm æmunauyDwace piæ+mum unawewaum i uepes piæ+i upouiw›m uacy, wo Øopuyny uow+a æmpasmwm wa›mu um+ou:

1  FV

 + . (11.3.6)

r  

(1 + i)n

Pm+›oæa yi+a s pospaxy+›y +a 100 rpomoæmx ogm+mya (r.o.) +oui+any

+asmæacwace ›ypcou (›ypcoæoD æapwicwD):

ge Pa – ›ypc a›yiï;

P - pm+›oæa yi+a;

N – +oui+ana+a yi+a.

K = P

a N

×100,

(11.3.7)

I+æecwmyiï æ a›yiï pis+oæmg Øi+a+coæmx i+æecwmyiu, wo6wo æ›nage++e rpomeu y Øi+a+coæi a›wmæm s uewoD owpmua++e goxogy. Ha6yæaDum a›yiu, i+æecwop upmuyc›ac owpmuawm goxig æig cæoïx i+æecwmyiu æmye cepeg+aopm+›oæoro. ¶oxig æig æ›nage+a æ a›yiï c›nagacwace s:

3)gmæige+giæ;

4) sui+m ›ypcoæiu æapwocwi.

Æ›yo i+æecwop sgiuc+Dc goærocwpo›oæi i+æecwmyiï i æ i+æecwmyiu+mu uepiog, uo e›ouy æig6yæacwace oyi+›a upm6yw›oæocwi a›yiï, +e æxogmwa ïï upogaw, wo uowou+mu goxig æms+auacwace æenmum+oD æmunauyæa+mx gmæige+giæ. V wa›iu cmwyayiï posrnegaDwa uowou+y upm6yw›oæicwa, wo6wo 6es ypaxyæa++e peanisayiï a›yiï, e›y pospaxoæyDwa e› æig+ome++e owpmua+oro gmæige+gy go yi+m upmg6a++e a›yiï:

Yn =

Div ×100

B

, (11.3.9)

ge Yn- uowou+a upm6yw›oæicwa;

Div - cyua gmæige+gy sa pi›;

B - yi+a upmg6a++e a›yiï.

Kpiu woro, uow+a pospaxyæawm pm+›oæy uowou+y upm6yw›oæicwa. e›a sanewawmue æig piæ+e yi+m, yo ic+yc +a pm+›y æ ›owe+ uoue+w uacy:

ge P - pm+›oæa yi+a a›yiï.

Y = Div ×100

n P

, (11.3.10)

V æmuag›y s uocwiu+mu spocwa++eu gmæige+giæ:

D

(1 + g)

+ g

B

, (11.3.11)

3agaua 22.

Hexau uowou+a pm+›oæa yi+a a›yiï c›nagac 15 rp+., posuip gmæige+giæ y 6asoæouy poyi c›nagac 3,2 rp+., upor+osycwace cepeg+aopiu+mu weuu pocwy gmæige+giæ – 3%.

Yn =

Posæ’esa++e:

3,2 × (1 + 0,03)

+ 0,03 = 0,2497

, u 24,97%.

Micne peanisayiï ywpmuyæau a›yiï uowe owpmuawm, upm cupmewnmæiu sui+i yi+m, gpyry c›nagoæy cy›yu+oro goxogy - upmpicw ›ypcoæoï æapwocwi. Kina›ic+o ye uos+auacwace e› goxig, piæ+mu pis+myi uiw yi+oD peanisayiï i yi+oD upmg6a++e. Mpm yaouy upm uepeæmye++i yi+m upogawy +ag yi+oD uo›yu›m i+æecwop owpmuyc goxig, a upm s+mwe++i yi+ +a Øo+goæouy pm+›y i æiguoæig+o

yi+m peanisayiï æ uopiæ+e++i s yi+oD upmg6a++e i+æecwop sas+ac s6mw›iæ.

Æ›yo i+æecwmyiu+mu uepiog +e æ›nDuac æmunawm gmæige+giæ, wo goxig ywæopDcwace e› pis+mye uiw yi+oD uo›yu›m i yi+oD upogawy. Mpm yaouy upm6yw›oæicwa pospaxoæycwace e› æig+ome++e pis+myi æ yi+i upogawy i yi+i uo›yu›m go æmwpaw i+æecwopau. Ta›a upm6yw›oæicwa +asmæacwace ›i+yeæoD, oc›ina›m æi+ peanisyæaæ cæiu yi++mu uauip i, owwe, goxig uo +iu +i æ e›iu Øopui æwe +e owpmuac:

Y1

ge Y1- ›i+yeæa upm6yw›oæicwa;

S - yi+a upogawy a›yiï.

= S - B ×100

B

, (11.3.12)

Æ›yo i+æecwmyiu+mu uepiog, uo e›ouy oyi+DDwace a›yiï, æ›nDuac æmunawy gmæige+giæ i sa›i+uycwace ïx peanisayicD, wo goxig æms+auacwace e› cyua cy›yu+mx gmæige+giæ i sui+m ›ypcoæiu æapwocwi. Mpm6yw›oæicwa sasæmuau

+asmæacwace cy›yu+oD i pospaxoæycwace uo Øopuyni

Div + (S - B)

Yc =

B ×100. (11.3.13)

V æmuag›y e›yo i+æecwmyiu+mu uepiog uepeæmyyc 1 pi›, wo Øopuyna

›i+yeæoï upm6yw›oæocwi +a6epe +acwyu+oro æmrnegy:

Div + (S - B)

a6o

Y = ∑ ×100

c B × n

Div + (S - B)

, (11.3.14)

Y = ∑ × 365 ×100

c B T

. (11.3.15)

ge T- ›ina›icwa g+iæ æonogi++e yi++mu uauepou.

3agaua 23.

I+æecwop upmg6aæ a›yiD i uepes 60 g+iæ ïï upogaæ. ]i+a uo›yu›m c›nana 3,5 rp+., yi+a upogawy 3,7 rp+., gmæige+gm +e æmunauyæanmce. Bms+aumwm upm6yw›oæicwa ouepayiï s a›yicD.

Posæ’esa++e:

Y = 3,7 - 3,5 × 365 = 0,348

c 3,5 60

, u 34,9%

5agaui gne camocwiu+oro potæ’eta++e:

1. Cwawyw+mu Øo+g sa›pmworo a›yio+ep+oro woæapmcwæa c›nagac 100000 rp+. Bi+ cØopuoæa+mu sa paxy+o› upocwmx a›yiu. Toæapmcwæou upoæogmwace gogaw›oæa euicie upmæineuoæa+mx a›yiu +a upeg'eæ+m›a +a cyuy 9500 rp+. fm upaæouip+i giï 3AT?

2. Cwawyw+mu Øo+g sa›pmworo a›yio+ep+oro woæapmcwæa c›nagac 90000 rp+. Toæapmcwæou gne s6iname++e cwawyw+oro Øo+gy æmpo6necwace euicie o6nirayiu +a cyuy 20000 rp+. fm upaæouip+i giï 3AT?

3. Cwawyw+mu Øo+g æig›pmworo a›yio+ep+oro woæapmcwæa c›nagac 950000 rp+. (uacw›a upmæineuoæa+mx a›yiu – 5 %). Toæapmcwæo una+yc gogaw›oæy euiciD a›yiu +a cyuy 250000 rp+. Æ›mu upm yaouy uownmæmu ua›cmuana+mu o6cer upmæineuoæa+mx a›yiu?

4. Bms+aumwm pm+›oæy æapwicwa upmæineuoæa+oï a›yiï, e›yo yi+a ïï uo›yu›m c›nana 1900 rp+., +oui+ana+a æapwicwa 1000 rp+., gmæige+gm 200% piu+mx, pm+›oæa cwaæ›a 14 % piu+mx.

5. Oyi+mwm upocwy a›yiD, e›yo æ ocwa++iu pi› uo +iu 6ynm æmunaue+i gmæige+gm æ posuipi 1,3 rp+., oui›yæa+mu weuu pocwy gmæige+giæ 5%, pm+›oæa cwaæ›a 12 % piu+mx.

6. Ocwa++iu pi› a›yio+ep+e woæapmcwæo æmunawmno gmæige+gm æ posuipi 0,6 rp+. +a a›yiD. Mpor+osycwace, yo yopiu+o gmæige+gm 6ygywa spocwawm +a 2,5%. Bms+aumwm yi+y a›yiï, e›yo +eo6xig+a cwaæ›a goxogy 15%.

7. I+æecwop æonogic a›yieum +oui+ana+oD æapwicwD 1000 rp+. i uo e›mu æi+ ogepwaæ wopi› gmæige+gm æ posuipi 120%. A+anis ga+mx sa 2 po›m uo›asaæ, yo cepeg+aopiu+mu picw gmæige+giæ 50%, upm cwaæyi goxogy 0,9. Bms+aumwm pm+›oæy æapwicwa a›yiï.

8. Mowou+a pm+›oæa yi+a a›yiï c›nagac 20 rp+., posuip gmæige+giæ y

6asoæouy poyi c›naæ 2,5 rp+., upor+osoæa+mu cepeg+aopiu+mu weuu pocwy gmæige+giæ 5%. Bms+aumwm upm6yw›oæicwa a›yiï.

9. I+æecwop ›yumæ a›yiD 01.06.2005 po›y sa yi+oD 10 rp+., a upogaæ 31.12.2007 p. sa yi+oD 25 rp+. V 2005 p. gmæige+gm +a a›yiD c›nanm 2 rp+., y 2006 p. – 2,5 rp+., y 2007 p. – 2,9 rp+. Bms+aumwm upm6yw›oæicwa ouepayiï s a›yicD.

10. I+æecwop upmg6aæ 120 a›yiu ›ouua+iï A +oui+ana+oD æapwicwD 10 rp+. sa yi+oD 500 rp+. sa a›yiD. fepes 10 g+iæ æi+ ›yumæ 150 a›yiu ›ouua+iï B sa yi+oD 320 rp+. sa a›yiD. [e uepes 10 g+iæ ›yumæ 210 a›yiu ›ouua+iï A sa yi+oD 540 rp+. sa a›yiD. Bms+aumwe cy›yu+y upm6yw›oæicwa ouepayiu i+æecwopa, e›yo æigouo, yo uepes pi› æi+ upogaæ æci a›yiï ›ouua+iï A sa yi+oD 530 rp+. sa a›yiD, a a›yiï ›ouua+iï B-uo yi+i 343 rp+. sa a›yiD i upm yaouy owpmuaæ gmæige+gm uo a›yiex ›ouua+iï B y posuipi 5 rp+. sa a›yiD.

11. I+æecwop upmg6aæ ua›ew s 300 a›yiu sarana+oD pm+›oæoD æapwicwD

150 wmc. rp+. s +oui+ana+oD æapwicwD og+icï a›yiï 200 rp+. Micne yaoro

›ouua+ie sgiuc+mna gpo6ne++e a›yiu: is cuiææig+ome++e 1:4. Bms+aumwe

›ina›icwa a›yiu æ ua›ewi i+æecwopa uicne gpo6ne++e i sarana+y +oui+ana+y æapwicwa.

12. I+æecwop upmg6aæ 25 a›yiu +oui+ana+oD æapwicwD 100 rp+. sa a›yiD uo ›ypcy 130 i upogaæ ïx uepes wpm po›m uicne upmg6a++e go gawm æmunawm gmæige+giæ. 3a uepmmu pi› cwaæ›a gmæige+giæ c›nana 13 %, sa gpyrmu pi› - 19, sa wpewiu pi› – 23 % Bms+auwe cy›yu+y upm6yw›oæicwa a›yiu gne i+æecwopa, e›yo æigouo, yo yi+a upogawy a›yiï uo æig+ome++D go yi+m upmg6a++e c›nagac 1,4.

13. Kouua+ie A c mæmg›o spocwaDuoD ›ouua+icD s æenm›mu uowe+yianou. Mpm yaouy cwaæ›a upm6yw›oæocwi æ ranysi c›nagac 20 % +a pi›. Bm una+ycwe ›yumwm a›yiï yicï ›ouua+iï i æonogiwm +mum upowerou 3 po›iæ, uicne uoro upogawm sa 45 rp+. sa a›yiD. 3a e›oD yi+oD æm uorogmwece ›yumwm a›yiï ›ouua+iï A, e›yo æigouo, yo ›ouua+ie +i›onm +e unawmna gmæige+gm i +e una+yc yaoro po6mwm?

rp+.;

14. Pospaxyuwe posuip gmæige+giæ uo upocwmx a›yiex, e›yo æigouo, yo: upm6ywo› AT, yo +aupaænecwace +a æmunawy gmæige+giæ, c›nagac 9 unpg.

a›yiï æmuyye+i +a cyuy 4500 un+. rp+., s +mx +a 500 un+. rp+.

upmæineuoæa+mx s gmæige+gou, piæ+mu 200% go +oui+any;

+oui+ana+a æapwicwa upocwoï a›yiï c›nagac 5000 rp+.

15. I+æecwop upmg6aæ ua›ew s 240 a›yiu sarana+oD æapwicwD 12 wmc. rp+.

+oui+ana+oD æapwicwD og+icï a›yiï 10 rp+. Micne yaoro ›ouua+ie upoæena

›o+conigayiD a›yiu is cuiææig+ome++e 4:1. Bms+aumwe ›ina›icwa a›yiï æ ua›ewi i+æecwopa, uicne ›o+conigayiï i sarana+y +oui+ana+y æapwicwa ua›ewy.

16. Bms+aumwe cy›yu+y upm6yw›oæicwa a›yiï, e›yo æigouo, yo a›yie upmg6a+a sa +oui+ana+oD æapwicwD 100 rp+. upm cwaæyi gmæige+gy 60% piu+mx, a pm+›oæa æapwicwa, a›yiï uepes pi› uicne æmuyc›y c›nana 190 rp+.

17. I+æecwop upmg6aæ 15 a›yiu +oui+ana+oD æapwicwD 10 rp+. sa yi+oD 30 rp+. sa a›yiD. fepes pi› pm+›oæa yi+a og+icï a›yiï c›nana 45 rp+., a i+æecwop owpmuaæ gmæige+gm y posuipi 6 rp+. +a a›yiD. Bms+aumwe uowou+y, ›i+yeæy i cy›yu+y upm6yw›oæicwa a›yiu.

18. V ciu+i æm s6mpacwece upmg6awm a›yiï ›ouua+iï A. Kouua+ie unawmwa gmæige+gm y posuipi 20 rp+. sa a›yiD ›ow+oro ›æapwany. Bm rowoæi wpmuawm a›yiï upowerou uowmpaox ›æapwaniæ i upogawm ïx uicne owpmua++e gmæige+giæ sa yi+oD 450 rp+. 3a e›oD yi+oD æm uorogmwece upmg6awm a›yiï, e›yo oui›yæa+a upm6yw›oæicwa c›nagac 20%.

19. BAT «Pe›opg» upm ycwa+oæi æmuycwmno upocwi i upmæineuoæa+i a›yiï og+icï +oui+ana+oï æapwocwi æ cuiææig+ome++i, yo upmuyc›ac ua›cmuana+o uownmæy srig+o is sa›o+ou ›ina›icwa upmæineuoæa+mx a›yiu æ o6iry. V cwawywi AT posuip gmæige+giæ uo upmæineuoæa+mx a›yiex saØi›coæa+mu y posuipi 30% piu+mx. Bms+aumwe posuip cwawyw+oro ›auiwany AT, e›yo æigouo, yo cyua,

+eo6xig+a gne æmunawm gmæige+giæ uo upmæineuoæa+mx a›yiex, c›nagac 600000

rp+.

20. I+æecwop upmg6aæ a›yiD uo ›ypcy 150. fepes pi› æi+ upogaæ a›yiD sa

yi+oD 600 rp+. uicne owpmua++e gmæige+giæ y posuipi 20% piu+mx. Bms+aumwe, sa e›oD yi+oD i+æecwop ›yumæ a›yiD, e›yo æigouo, yo cy›yu+a upm6yw›oæicwa uoro ouepayiï c›nana 70%.

21. Bm una+ycwe ›yumwm a›yiï ›ouua+iï A, e›a +egaæ+o æmunawmna gmæige+gm æ cyui 50 rp+. +a a›yiD. Mo æammx upor+osax gmæige+gm æ +acwyu+i gæa po›m 6ygywa 6inami +a 20%. ¶o sa›i+ue++e yaoro uepiogy æm pospaxoæycwe upogawm a›yiï sa yi+oD 790 rp+. Bms+aumwe yi+y, uo e›iu æm uorogmwece ›yumwm a›yiï, e›yo pospaxoæycwe +a upm6yw›oæicwa æ 10%.

11.4.Bapwic+a oyi+ıa wa upu6ywıoæicwa 6oproæux yi++ux uauepiæ

O6nirayiï uaDwa +oui+ana+y i pm+›oæy yi+y. Houi+ana+a æapwicwa o6nirayiï +agpy›oæa+a +a nmyaoæiu cwopo+i +auyi++imoro uauepy i uos+auac cyuy, e›a 6epewace y uosm›y i uignerac uoæep+e++D uicne sa›i+ue++e wepui+y sæep+e++e. Æ› upaæmno, o6nirayiï æmuyc›aDwace s æmco›oD +oui+ana+oD æapwicwD i pospaxoæa+i +a 6arawmx i+æecwopiæ. ]mu æo+m wa›ow æigpis+eDwace æig a›yiu, æapwicwa e›mx pospaxoæa+a +a upmg6a++e mmpo›mu goæ›ona oci6, upm yaouy e›yo gne a›yiu +oui+ana+a æapwicwa - æenmum+a gocmwa yuoæ+a (oc›ina›m a›yiï upogaDwace i ›yuyDwace sa yi+oD, +ie› +e uoæ'esa+oD s

+oui+anou), wo gne o6nirayiu +oui+ana+a æapwicwa c gywe æawnmæmu uapauewpou. ]e uoæ'esa+o s wmu, yo uo cuouaw›y saØi›coæa+iu æenmum+i

+oui+any o6nirayiï uoramawmuywace uicne sa›i+ue++e wepui+y ïx sæep+e++e.

3 uoue+wy euiciï i go uorame++e o6nirayiï upogaDwace i ›yuyDwace uo cwanmx +a pm+›y yi+ax. Pm+›oæa yi+a y uoue+w euiciï uowe 6ywm +mwue sa

+oui+an, piæ+mu uouy a6o 6ywm æmye. 3 uoue+wy euiciï pm+›oæa yi+a o6nirayiu æms+auacwace æmxogeum s cmwyayiï, yo c›nanace +a pm+›y, a wa›ow gæox ronoæ+mx eneue+wiæ:

uepcue›wmæm owpmuawm upm uorame++i +oui+ana+y æapwicwa (umu 6nmwue wepui+ uorame++e, wmu æmye pm+›oæa yi+a o6nirayiï);

upaæa +a perynep+mu Øi›coæa+mu goxig (umu æmye upoye+w+mu goxig,

wmu æmye pm+›oæa yi+a).

Bms+aue++e pm+›oæoï yi+m o6nirayiï sanewmwa uepm sa æce æig Øopum goxogy, e›mu æo+a upm+ocmwa cæocuy ænac+m›oæi. B sæ'es›y s ymu pospis+eDwa: o6nirayiï s +ynaoæmu ›yuo+ou, a6o gmc›o+w+i, uo e›mx i+æecwop goxig owpmuyc y Øopui gmc›o+wy. ]i+oywæope++e 6es›yuo+oï o6nirayiï uonerac y æms+aue++i æenmum+m eneue+wap+oro uowo›y unawewiæ, uo æigoumx s+aue++ex

+oui+ana+oï æapwocwi, 6espmsm›oæoï upoye+w+oï cwaæ›m (a6o oui›yæa+iu upm6yw›oæocwi) i uepiogy i+æecwyæa++e. Ta›mu um+ou, uowou+a yi+a o6nirayiï

PV = FV = N

(1+ i)n

ge N - +oui+ana+a æapwicwa o6nirayiï.

(1+i)n, (11.4.1)

Mpm yaouy pm+›oæa yi+a ga+oï o6nirayiï +i›onm +e uepeæmymwa

+oui+ana+y, oc›ina›m upm uorame++i i+æecwop owpmuac wina›m +oui+ana+y æapwicwa o6nirayiï;

Æ›yo uepiog æonogi++e gmc›o+w+oï o6nirayiï ue+me sa pi›, wogi ïï æapwicwa pospaxoæycwace sa ØopuynoD

PV = N ×100,

1 + i t

(11.4.2)

ge t - ›ina›icwa g+iæ æig g+e upogawy o6nirayiï go ïï uorame++e.

i – æigcow›oæa cwaæ›a gmc›o+wyæa++e.

o6nirayiï s uocwiu+mu ›yuo++mu goxogou. Kyuo++a cwaæ›a uo wa›mx o6nirayiex saØi›coæa+a i c +esui++oD +a æcaouy upowesi wepui+y ïï o6iry. Pm+›oæa yi+a wa›oï o6nirayiï æms+auacwace e›

1  FV

 +

=i  (1 + i)n

(1 + i)n

. (11.4.3)

 

Pm+›oæa yi+a wa›mx o6nirayiu uowe 6ywm e› æmye, wa› i +mwue

+oui+ana+oï sanew+o æig oui›yæa+oï i+æecwopou upm6yw›oæocwi (i) i æig cwaæ›m

›yuo+a (k);

o6nirayiï s ›yuo++mu goxogou pis+oï æenmum+m. Kyuo++mu goxig uo

wa›mx o6nirayiex uowe 6ywm saØi›coæa+mu upm ïx æmuyc›y, ane 6ywm pis+mu æ pis+i ›yuo++i uepiogm, a uowe 6ywm sui++mu (sui++mu) sanew+o æig 6yga-e›oro um++m›a a6o uo›as+m›a. Oyi+›a æapwocwi wa›mx o6nirayiu uoæ'esa+a s wpyg+oyaum sa æms+aue++eu ›yuo++oro goxogy gne ›ow+oro uepiogy i uoro gmc›o+wyæa++eu. V sarana+ouy æmrnegi Øopuyna æmrnegac e›

n k FV

+

(1+ i)n

. (11.4.4)

Bigcow›m uo o6nirayiex uowywa æmunauyæawmce ›ina›a pasiæ +a pi›. Togi, Øopuyna uawmue wa›mu æmg:

k

m×n

PV = ∑ m +

t =1 (1+ i )t

m

N

(1+ i)n

, (11.4.5),

ge m – ›ina›icwa æmunaw % upowerou po›y.

3agaua 24.

Oyi+mwm æapwicwa ›yuo++oï o6nirayiï, æmuyye+oï +a 2 po›m, +oui+ana+a æapwicwa e›oï 1000 rpmæe+a, ›yuo++a cwaæ›a 16%, yo pm+›oæa – 20% i æigcow›m æmunauyDwace gæa pasm æ pi›.

Posæ’esa++e:

PV = 2 + 80 + 80 + 1080 = 80 + 80 + 80 + 1080 = 936,65spuøena.

(1+ 0,2)1

(1,1)2

(1,1)3

(1,1)4

1,1

1,21

1,331

1,464

Oc›ina›m +oui+anm y pis+mx o6nirayiu pospis+eDwace, wo gne sicwaæne++e

pm+›oæmx yi+ o6nirayiu æm›opmcwoæyDwa ›ypc. Kypcou o6nirayiï +asmæacwace s+aue++e pm+›oæoï yi+m o6nirayiï, æmpawe+e y æigcow›ax go ïï +oui+any:

ge P - ›ypc o6nirayiï;

P - pm+›oæa yi+a o6nirayiï;

K = P ×100, (11.4.6)

N

N - +oui+ana+a yi+a o6nirayiï.

O›piu +oui+ana+oï i pm+›oæoï yi+ upmæogmwace ye og+a æapwic+a

xapa›wepmcwm›a o6nirayiu - ïx æm›yu+a yi+a, uo e›iu euiwe+w uicne sa›i+ue++e wepui+y uosm›m uoramac o6nirayiï. Bm›yu+a yi+a uowe cuiæuagawm s

+oui+ana+oD, a uowe 6ywm æmye a6o +mwue. Biguoæig+o go 3a›o+y V›paï+m

«Mpo yi++i uauepm wa Øo+goæmu pm+o›» o6nirayiï uowywa uoramawmce wina›m sa +oui+ana+oD æapwicwD.

3arana+mu goxig æig o6nirayiï c›nagacwace s +acwyu+mx eneue+wiæ: uepiogmu+o æmunauyæa+mx %;

sui+m æapwocwi o6nirayiï sa æiguoæig+mu uepiog; goxogy æig pei+æecwmyiu owpmua+mx %.

O6nirayie upm+ocmwa cæocuy ænac+m›oæi Øi›coæa+mu goxig y æmrnegi %. 3asæmuau æigcow›m æmunauyDwace 1-2 pasm +a pi›. Mpm yaouy umu uacwime upoæogewace upoye+w+i æmunawm, wmu 6inammu goxig upm+ocmwa o6nirayie, agwe æigcow›m uowywa 6ywm pei+æecwoæa+i. Posuip ›yuo++oro goxogy uo o6nirayiex sanewmwa uepm sa æce æig +agiu+ocwi o6nirayiï, wo6wo æig woro, xwo 6yæ euiwe+wou. fmu cwiu›ime ›ouua+ie i +agiu+ime o6nirayie, wmu +mwue upouo+oæa+mu æigcowo›. Kpiu woro, ic+yc sanew+icwa uiw upoye+w+mu goxogou i wepui+ou sæep+e++e (umu 6iname wepui+ sæep+e++e, wmu æmye uoæm+e+ 6ywm æigcowo›), upm yaouy umu 6iname wepui+ sæep+e++e o6nirayiï, wmu icwow+ime goxig æig pei+æecwmyiu.

Mpowe icwow+imoD c›nagoæoD goxogy æig æonogi++e o6nirayicD c goxig æig sui+m æapwocwi o6nirayiï. Mpm yaouy gne ænac+m›iæ o6nirayiu s +ynaoæmu

›yuo+ou - ye cgm+e gwepeno goxogy. ¶oxig uo +mu ywæopDcwace e› pis+mye uiw +oui+ana+oD yi+oD i pm+›oæoD yi+oD.

3anew+o æig owpmuyæa+oro i+æecwopou goxogy pospis+eDwa: uowou+y upm6yw›oæicwa o6nirayiï;

uoæ+y a6o ›i+yeæy upm6yw›oæicwa o6nirayiï.

Mo›as+m› uowou+oï upm6yw›oæocwi xapa›wepmsyc piu+i (uowou+i)

+agxogwe++e uo o6nirayiï yogo spo6ne+mx æmwpaw +a ïï uo›yu›y. Mowou+a upm6yw›oæicwa ›yuo++oï o6nirayiï pospaxoæycwace uo Øopuyni

Y = k

n B

×100

, (11.4.7)

ge Yn - uowou+a upm6yw›oæicwa o6nirayiï %;

k – cyua æmunaue+mx æ pi› %, rp+.,

B – yi+a upmg6a++e o6nirayiï, rp+.

3agaua 25.

Bms+aumwm uowou+y upm6yw›oæicwa gne o6nirayiï +oui+ana+oï æapwocwi

190000 rp+. wa ›yuo++mu upm6yw›ou 35000 rp+.

Posæ’esa++e:

Y = 35000 ×100 = 19,4%

n 180000

Mowou+a upm6yw›oæicwa gmc›o+w+oï o6nirayiï æms+auacwace uo Øopuyni

Yn =

B - S B