Caaea/a 1.
Aeeaae 300 ?oa. aue iieiaeai a aaie 20.05.2000 a. ii noaaea 30%
aiaeiauo. N 1 naioya?y aaie niecee noaaeo ii aeeaaeai aei 20%. 25
ieoya?y aeeaae aue cae?uo.
Ii?aaeaeeoue noiio ia/eneaiiuo i?ioeaioia i?e aiaeeeneie e i?e
aa?iaineie i?aeoeeao ia/eneaiey.
?aoaiea:
1) i?e aiaeeeneie i?aeoeea: ia?eiae ia/eneaiey ii noaaea 30%
t1 = 11+30+31+31 +103 aeiy;
ia?eiae ia/eneaiey ii noaaea 20%
t2 = 30+25-1= 54 aeiy;
I = 300(103 365*0,3+5465*0,2) = 36.
2) i?e aa?iaineie i?aeoeea: ia?eiae ia/eneaiey ii noaaea 30%
t1 = 10+30+30+30 =100 aeiae;
ia?eiae ia/eneaiey ii noaaea 20%
t2 = 30+25-1 = 54 aeiy;
I =300(100360*0.3+54360*0.2) = 33 ?oaey 90 eii.
Caaea/a 2.
2.07.99 a: aaie i?eiye a iaaeaaieianeee aeaiiceo aeaiaaeiua n?aaenoaa a
noiia 80 oun. ?oa. n?ieii ia 7 aeiae ii noaaea 24, 9%.
Ii?aaeaeeoue noiio aica?aoa aaieii ii oeacaiiiio aeaiiceoo.
?aoaiea:
· iieiue n?ie aeaiiceoa 8 aeiae ni 2 ii 9.07.99 a.;
· ia?eiae ia/eneaiey i?ioeaioia 7 aeiae (n-1);
S = (1 + i*tk), S = 80000(1+0.249*7365) = 80384 ?oaey.
Caaea/a 3.
11.08.2000 a. aaie auaeaao i?aaei?eyoeth e?aaeeo a cyiie 280 oun. ?oa.
n?ieii ia 1 ianyoe ii noaaea 25%. N?ie aica?aoa e?aaeeoa e i?ioeaioia ii
iaio 11.09.2000 a. Ii?aaeaeeoue noiio oiea/aiiuo i?ioeaioia.
?aoaiea:
Iieiue n?ie e?aaeeoa n 11.08. ii 11.09. – 32 aeiy (n), ia?eiae
ia/eneaiey
i?ioeaioia ii e?aaeeoo (n-1) = 31aeaiue.
Oiaaea noiia oiea/aiiuo i?ioeaioia – yoi I, iieo/aiiia aaieii:
I = P * i%100% * tk,
I = 280000 * 2,5 * 31365 = 5964 ?oaey.
Caaea/a 4.
I. A. Naeoueia – Uaae?ei iienuaaao a «Ainiiaeao Aieiae?auo» oaeoth
noeaio: «Ii?oe?ee Aeaaeeie?iae/ … neaeeo o naay a eaaeiaoa, enienuaay
oeeoe?iuie aeeaaeeaie eenou aoiaae. Ia yoio ?ac aai caieiaao aii?in:
neieueei auei au o iaai oaia?ue aeaiaa, anee a iaiaiueea … iiaea?aiiua
aio i?e ?iaeaeaiee aeaaeooeie …, ia coaie noi ?oaeae … ia i?enaieea
naaa, a iieiaeeea au aeeaaeii a eiiaa?ae ia eiy iaeieaoiaai Ii?oe?ey?
Auoiaeeo, iaeiaei, iaiiiai: ainaiuenio ?oaeae…».
Ii?aaeaeeoa neiaeioth noaaeo i?ioeaioia aiaeiauo eiiaa?aea ii aeeaaeai,
anee Ii?oe?eth a iiiaio aai ?an/aoia auei 50 eao.
?aoaiea:
n = 50, ? = 100 ?oa., S=800 ?oa.,
Ii oi?ioea neiaeiuo i?ioeaioia ia?auaiiay noiia ?aaia:
S = P * (1+ic )n
ioeoaea noaaea neiaeiuo i?ioeaioia ninoaaeo:
ic = n? SP – 1 = 50?800100 – 1= 0.0425 = 4.25%
Caaea/a 5.
05,09,98 a. aaie caeeth/ee n aeeaae/eeii aeiaiai? n?i/iiai aeeaaea ia 21
aeeiue (n?ie aica?aoa aeeaaea -.26.09.98 a.). Noiia aeeaaea – 15 oun.
?oa. I?ioeaioiay noaaea – 15% ii oneiaeyi aeiaiai?a, ia/eneaiiua ii
eoiaai eaaeaeiai aeiy n?iea aeaenoaey aeiaiai?a i?ioeaiou oaaee/eaatho
noiio aeeaaea.
Ii?aaeaeeoue noiio, eioi?oth iieo/eo aeeaae/ee ii ieii/aiee n?iea
aeaiiceoa.
?aoaiea:
Iieiue n?ie aeeaaea – 22 aeiy, ia?eiae ia/eneaiey i?ioeaioia – 21aeaiue,
i?ioeaiou ia/eneythony aaeaaeiaaii e eaieoaeece?othony, oiaaea:
S = 15000*(1 + 15%100% * 1365)21 = 15129 ?oa. 99 eii.
Caaea/a 6.
Aeaoa iiaaoaiey aeeneiioiiai aaenaey – 22 ethey oaeouaai aiaea.
Ii?aaeaeeoue aueoiioth oeaio e aeeneiio ia 2 ethey aaenaey iiieiaeii 100
iei. ?oaeae, anee aaenaeueiay noaaea ninoaaeyao 40% aiaeiauo, a /enei
aeiae a aiaeo i?eiyoue ca 360.
?aoaiea:
S = 100 000 000 ?oa.; d = 0.4; t = 20 aeiae; E = 360.
Aueoiiay oeaia aeeneiioiiai aaenaey:
P = S-D = S * (1-20360 * 40%100%) = 977 777 777 ?oa. 78 eii.
Caaea/a 7.
Eeeaio eiaao aaenaeue ia 10000 ?oa., eioi?ue ii oi/ao o/anoue 01.03.98
a. a aaiea ii neiaeiie o/?oiie noaaea, ?aaiie 7%. Eaeoth noiio ii
iieo/eo, anee n?ie iiaaoaiey aaenaey 01.08.98 a.?
?aoaiea:
N?ie io aeaou o/aoa aei aeaou iiaaoaiey aaena6ey ?aaai:
t = 31 + 30 + C1 + C0 + C1 = 15C aeiy
*enei aeiae a aiaeo E = 365, d = 0.07. Eeeaio iieo/eo noiio:
P = S * (1-dc)tk = 10000 * (1-0.07)153365 = 9700 ?oa. 38 eii.
Caaea/a 8.
Ii?aaeaeeoue iaeeaeaaiue o?iaaiue eioeyoeee ca aiae i?e aaeaiany/iii
o?iaia eioeyoeee 6%.
?aoaiea:
?% = 6%, N=12.
Eiaeaen eioeyoeee ca roae ninoaaeo:
Iu = (1+ a)N = (1 + 0.06)12 = 2.012
O?iaaiue eioeyoeee ca aiae ninoaaeo:
a = Iu – 1 = 2.012-1 = 1.012, eee a% = 101,2%.
Caaea/a 9.
Aaie auaeae eeeaioo e?aaeeo ia iaeei aiae a ?acia?a 2000 ?oa. ii noaaea
6% aiaeiauo. O?iaaiue eioeyoeee ca aiae ninoaaee 40%. Ii?aaeaeeoue n
o/?oii eioeyoeee ?aaeueioth noaaeo i?ioeaioia ii e?aaeeoo, iiaaoaaioth
noiio e noiio i?ioeaioia ca e?aaeeo.
?aoaiea:
P = 2000 ?oa., i = 0,06, a = 0,4, n = l aiae.
Noiia iiaaoaiey e?aaeeoa n i?ioeaioaie aac o/aoa eioeyoeee ninoaaeo:
S = ?(1+ni) = 2000(1+0,06) = 2120 ?oa.,
Coiia i?ioeaioia niioaaonoaaiii ?aaia 120 ?oa., aica?auaaiay noiia n i?i
oeaioaie n o/aoii eioeyoeee:
Pa = SIu = S1+a = 21201.4 = 1514 ?oa. 29 eii.,
?aaeueiue aeioiae aaiea
Ae = ?a –? = 1514,29-2000 = – 485,71,
oi anoue ?aaeueii aeioiae aaiea, i?eaaaeaiiue e iiiaioo auaea/e e?aaeeoa
n o/aoii eioeyoeee, – yoi oauoie.
Aeey oiai /oiau iaania/eoue aeioiaeiinoue aaieo a ?acia?a 6% aiaeiauo,
noaaea i?ioeaioia ii e?aaeeoo n o/aoii eioeyoeee aeieaeia auoue:
ia = (1+n)(1+a)n = i + a + i * a= 0.06 + 0.4+ 0.06 * 0.4 = 0.484, ia %
= 48.4%, iiaaoaaiay noiia niioaaonoaaiii aeieaeia ninoaaeyoue:
Sa = ?(l + ia) = 2000(1 +0,484)=2968 ?oa.;
?aaeueiue aeioiae aaiea ninoaaeo:
Ae == ?a- ? = SaIa – P = 29681.14 -200= 120 ?oa.,
/oi e iaania/eo ?aaeueioth aeioiaeiinoue iia?aoeee a 6% aiaeiauo.
Caaea/a 10.
Aeeaae/ee iaia?ai iieiaeeoue a aaie noiio, /oiau aai nui a oa/aiea
iyoeeaoiaai n?iea iao/aiey iia nieiaoue a eiioea eaaeaeiai aiaea ii
10000 ?oa. e ec?anoiaeiaaoue e eiioeo o/aau aanue aeeaae. Ii?aaeaeeoue
noiio aeeaaea, anee aiaeiaay noaaea neiaeiuo i?ioeaioia ninoaaeo 12%.
?aoaiea:
Noiia aeeaaea ?aaia, nia?aiaiiie oeaiiinoe ?aiou, ninoiyuae ec iyoe
ieaoaaeae:
A = R* (1-(1 + ic)-n) /ic =10000* (1-(1+0.12)-5) /0,12 = 104/0,12[1-
1/1,125] =
104[1-0.56742069]/0,12 = 36047 ?oa. 76 eii.
Caaea/a 11.
Caaiuee iieo/ee e?aaeeo 3 iei. ?oa. ia 5 ianyoeaa n oneiaeai iiaaoaiey
aeieaa a eiioea eaaeaeiai ianyoea ?aaiuie n?i/iuie ieaoaaeaie. Ia
aaee/eio aeieaa ia/eneythony neiaeiua i?ioeaiou ii noaaea 5% ca ianyoe.
Ii?aaeaeeoue noiio n?i/iiai ieaoaaea.
?aoaiea:
n = 5; A =.3000060 ?oa,; in = 0,05.
Noiia n?i/iiai ieaoaaea:
R = (A* in)/1-(1+ic)-n = ( 3 000 000 *0.05) / 1-(1+0,05)-5 = 692924
?oa.C9eii.
Caaea/a 12.
Aaie iauyaee, /oi aeeaeaeaiaeu ii aai aeoeeyi ca i?ioaaeoee aiae
ninoaaeytho 20% aiaeiauo ii iaueiiaaiiui aeoeeyi e 20% aiaeiauo ii
i?eaeeaae?iaaiiui aeoeeyi. Ii?aaeaeeoue noiio aeeaeaeaiaea ia iaeio
i?eaeeaae?iaaiioth aeoeeth iiieiaeii 3000 ?oa. e iaeio iaueiiaaiioth
aeoeeth iiieiaeii 1000 ?oa.
?aoaiea:
Noiia aeeaeaeaiaea ia iaeio i?eaeeaae?iaaiioth aeoeeth paaia
Di?= 0,3 o 3000 ?oa.
Noiia aeeaeaeaiaea ia iaeio iaueiiaaiioth aeoeeth ?aaia
Do = 0.2 o 1000 =200 ?oa.
Caaea/a 13.
Ii?aaeaeeoue iaeeaeaaiue aeioiae io iieoiee aeoeee iiieiaeii 1000 pya.,
aaeaaiaeiiai iieo/aiey aeeaeaeaiaeia a ?acia?a 20% aiaeiauo e
aaeaaiaeiiai pocra noieiinoe ia 10% io iiieiaea, anee aeoeey aoaeao
i?iaeaia /a?ac 5 eao, a oaeaea aeioiaeiinoue iia?aoeee.
?aoaiea:
N = 1000 ?oa.; f = 0,2; n = 5 eao; AeP1 = 0.1N.
Aaee/eia aiaeiauo aeeaeaeaiaeia ca 5 eao ninoaaeo
Ae = n * f * N=5 * 0,2 * 1000 = 1000 ?oa.
Noieiinoue aeoeee /a?ac 5 eao ninoaaeo
?a = N + n * AeP1 = N+0,l * N * 5 = N (1+ 0,5) = 1500 ?oa.
Iauee aeioiae nicoaaeo
Aea = D + Pa – N=1000 + 1500 – 1000 = 1500 ?oa.
Aeioiaeiinoue iieoiee aeoeee a aeaea yeaeaaeaioiie noaaee neiaeiuo
i?ioeaioia ninoaaeo iny = (n?(N + Aea)/N) – 1 =(5?(1000+1500)/1000) – 1
= 1,201-1 = 0,201 = 20,1%
Caaea/a 14.
AI n onoaaiui oiiaeii l iei. ?oa. eiaao neaaeothuoth no?oeoo?o eaieoaea:
85 iaueiiaaiiuo aeoeee e 15 i?eaeeaae?iaaiiuo. ?acia? i?eauee e
?ani?aaeaeaieth iaaeaeo aeoeeiia?aie ninoaaeyao 120 oun. ?oa.
Oeene?iaaiiue aeeaeaeaiae ii i?eaeeaae?iaaiiui aeoeeyi ninoaaeyao 10%.
Ii?aaeaeeoue aeeaeaeaiaeu aeey aeaaeaeueoea iaueiiaaiiie aeoeee.
?aoaiea:
*I =120000 ?oa., I0 = 85, Mi? = 15, OE = 100000 ?oa., f = 0,1
a) iiieiae oaeioe aeoeee iaoiaeei eae ioiioaiea onoaaiiai oiiaea e
iauaio /eneo aeoeee
N = OE/(Ii + Ii?) = 1000000/(85 + 15) = 10000 ?oa.
a) auieaou ii anai i?eaeeaae?iaaiiui. aeoeeyi ?aaiu
Aei? = Ii? * Ae1 =N * 15 *0,1 = 15000 ?oa.
a) auieaou ia iaeio iaueiiaaiioth aeoeeth ?aaiu
Aei = (*I –Aei?)/Ii = (120000-15000)/85 = 1235 ?oa. 29 eii.
Caaea/a 15.
Aaeainiaay i?eaueue AI n onoaaiui oiiaeii 2 iei. ?oa., iieo/aiiay io
i?iecaiaenoaaiiie aeayoaeueiinoe, ninoaaeea 10 iei. ?oa. Nia?aiea
aeoeeiia?ia iinoaiiaeei, /oi inoaaoothny iinea oieaou iaeiaia i?eaueue
neaaeoao ?ani?aaeaeeoue oae: 20% ia ?acaeoea i?iecaiaenoaa, a 80% ia
auieaoo aeeaeaeaiaeia. Ii?aaeaeeoue eo?n aeoeee, anee aaieianeee
i?ioeaio ninoaaeyao 80%, iiieiae aeoeee -100 ?oa., a noaaee iaeiaa ia
i?eaueue – 32%.
?aoaiea:.
OE = 2000000 ?oa., AI = 1000000 ?oa., Aeauo= 0,8; i = 0,8; N = 100 ?oa;
W = 0,32.
a) ii?aaeaeyai eiee/anoai aeoeee AI:
I = OE/N = 2000000/100 = 20000 oo.
a) au/eneei npeaueue iinea oieaou iaeiaia:
*I = AI(1- W) = 1000000(1 – 0.32) = 6800000 ?oa. = 6,8 iei. ?o6.
a) iaoiaeei aaee/eio aeeaeaeaiaeia ia auieaoo aeoeeiia?ai:
DO = *I * Aeauo = 6800000 * 0,8 = 5440000?oa.;
a) ii?aaeaeyai auieaoo aeeaeaeaiaeia ia iaeio aeoeeth:
D1 = DO /I = 5440000 /20000 = 272?oa/aeoeey.
Caaea/a 16.
Eo?n iaeeaaoeee iiieiaeii 500 ?oa. ninoaaeyao 75. Ii?aaeaeeoue oeaio
iaeeaaoeee.
?aoaiea:
?e= 75; N=500 ?oa.
Oeaia iaeeaaoeee:
? = (75 * 500)/100 = 375?oa.
Caaea/a 17.
Aeioiae ii iaeeaaoeeyi iiieiaeii 1000 ?oa. auiea/eaaaony eaaeaeua
iieaiaea ii coaaee 50% aiaeiauo. Au/eneeoue noiio aeioiaea ii eaaeaeie
auieaoa.
?aoaiea:
N = l000 ?oa.; i=0,5; n = 0,5.
Noiia aeioiaea ii eaaeaeie auieaoa: I = Nni = 1000 * 0.5 * 0,5 = 250
?oa.
Caaea/a 18.
Iaeeaaoeee iiieiaeii 1000 ?oa. e ni n?ieii ia?auaiey 90 aeiae
i?iaeathony ii eo?no 85. Ii?aaeaeeoue noiio aeioiaea io iieoiee 5
iaeeaaoeee e aeioiaeiinoue oeiainiaie iia?aoeee i?e ?an/aoiii eiee/anoaa
aeiae a riaeo 360.
?aoaiea:
N = 1000 ?oa.; t = 90 aei.; E = 360; ?e=85.
Aeioiae io iieoiee iaeiie iaeeaaoeee i?e oneiaee a? iiaaoaiey ninoaaeo
Ae = N- Pk * N/100 = N(1-Pk/100) = 1000(1-85/100) = 150 ?oa.
Noiia aeioiaea io iieoiee 5 iaeeaaoeee ninoaaeo
W = 5W1 = 5 *150 = 750?oa.
Aeioiaeiinoue iaeeaaoeee e iiaaoaieth ii yeaeaaeaioiie noaaea i?inouo
i?ioeaioia ninoaaeyao
Iy= (N – ?)/? * E/t = (1000-850)|850 * 360|90 = 150/850 * 4 = 60/85 =
0.706 = 70.6%.
Caaea/a 19.
Iaeeaaoeey eoieaia ii eo?no 95 e aoaeao iiaaoaia /a?ac 10 eao. I?ioeaiou
ii iaeeaaoeee auiea/eaathony a eiioea n?iea ii neiaeiie noaaea 5%
aiaeiauo. Ii?aaeaeeoue aeioiaeiinoue i?eia?aoaiey iaeeaaoeee.
?aoaiea:
Pe = 95; q = 0;05; n = 10.
?= P1 * N /100 =0,95N.
I?ioeaioiue aeioiae ca 10 eao ninoaaeo
I = N(1+q)n – N = N[(1+q)n – 1] = N[(1+0.05)n -1] = N[1.0510 – 1] =
0.629.
Aeioiae io iiaaoaiey ninoaaee
Wn = N(1-0.01Pk) = N(1 -0.95)= 0.05N
Iauee aeioiae ninoaaee
W = I + Wn = 0.629N + 0.05N = 0.679N/
Aeioiaeiinoue iieoiee iaeeaaoeee ii yooaeoeaiie noaaea neiaeiuo
i?ioeaioia ?aaia iny = [n?(W+N)/N] – 1 = [10?(0.679N + N)/N] – 1 = 0.053
= 5.3%
Caaea/a 20.
Ii?aaeaeeoue noiio e?aaeeoa iiae oiaa?ii – iaoa?eaeueiua oeaiiinoe i?e
neaaeothueo oneiaeyo: inoaoie iaoa?eaeia ia neeaaea – 800 000?; inoaoie
iaoa?eaeia a iooe – 40 000?; caaeieaeaiiinoue iinoaaueeai ca iaoa?eaeu –
120 000?; nianoaaiiua iai?ioiua n?aaenoaa – 120 000?; eeieo
e?aaeeoiaaiey – 800 000?;Caaeieaeaiiinoue ii noaea – 70 000?.
?aoaiea:
1. ii?aaeaeeoue aaee/eio e?aaeeoa:
E? = 800 000+40 000-120 000-120 000-70 000 = 530 000?
2.N?aaieaaai aaee/eio e?aaeeoa n eeieoii e?aaeeoiaaiey:
530 000
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