1
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Ne videon e fundit, ne biseduam pak per interesin e përbërë

2
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Shembulli yne ishte interesi qe perbehet

3
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çdo vit, jo në menyre te vazhdueshme ashtu siç

4
00:00:17,830 --> 00:00:18,790
do ta shihnim në shume banka.

5
00:00:18,790 --> 00:00:21,390
Ne te vertete vetem desha t'ju le te kuptoni qe

6
00:00:21,390 --> 00:00:22,290
idea eshte e thjeshte.

7
00:00:22,290 --> 00:00:25,040
çdo vit ti merr 10% prej parave qe fillove te kesh

8
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atë vit.

9
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Dhe quhet i perbere sepse vitin tjeter ti merr

10
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parate dhe jo vetem nga depozita fillestare, por ti merr gjithashtu

11
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nga parate ose interesi mbi interesin e gjeneruar prej viteve te meparshme.

12
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Prandaj, quhet interes i perbere.

13
00:00:37,470 --> 00:00:40,290
Edhe pse ajo ide eshte kogja e thjeshte, ne pame qe matematika

14
00:00:40,290 --> 00:00:41,420
mund te behet e nderlikuar.

15
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Nese ke nje kalkulator te arsyeshem, ti mund t'i zgjidhesh

16
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disa nga gjerat nese di ti besh ato.

17
00:00:46,870 --> 00:00:50,550
Por, eshte gati se e pamundur ta besh permendesh.

18
00:00:50,550 --> 00:00:53,640
Per shembull, ne fund te videos se fundit, ne thame qe

19
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nese i kemi njeqind dollar.

20
00:00:54,700 --> 00:00:57,860
Dhe jam duke i kalkuluar ne menyre te perbere me 10% interes ne vit,

21
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ja prej aty vjen 1, sa kohe me nevojitet mua te dyfishoj parate

22
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dhe te perfundoj me kete ekuacion.

23
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Dhe per ta zgjidhur ate ekuacion, shumica e kalkulatoreve nuk kane

24
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bazen logaritmike 1.1

25
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Dhe e kam treguar kete ne videot e tjera

26
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Mund te thuash, x eshte i barabarte me logaritmin me baze 10 prej 2,

27
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e ndare me logaritmin me baze te 1.1 prej 2.

28
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Kjo eshte nje menyre tjeter per te kalkuluar log me baze 1.1 prej 2.

29
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Kjo duhet te ishte logaritmi me baze 10 prej 1.1.

30
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Them kete meqe shumica e kalkulatoreve kane

31
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logaritmin me baze 10.

32
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Kjo dhe kjo jane te barabarta.

33
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Kam vertetuar kete ne videot tjera.

34
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Keshtu qe ne vend se te themi sa gjate merr kohe per te dyfishuar

35
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parate e mia me 10% çdo vit.

36
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Ti e kalkulon kete me kalkulator.

37
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Dhe ta provojme

38
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Ta provojme ketu

39
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Do te kemi, 2, dhe do te marrim

40
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logaritmin e tij, ku kemi 0.3, i ndare me 1.1, dhe

41
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gjejme logaritmin e saj.

42
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Mbyllim kllapat.

43
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Eshte e barabarte me 7.27 vite.

44
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Afersisht 7.3 vite.

45
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Pra, kjo eshte afersisht e barabarte me 7.3 vite.

46
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Ashtu siç pame ne videot e tjera, kjo nuk eshte domosdoshmerisht

47
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e lehte per ta formuluar, por edhe nese ti kupton matematiken ketu,

48
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nuk eshte e lehte ta besh permendesh.

49
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Eshte thjesht gati se e pamundur ta besh kete permendesh.

50
00:02:20,720 --> 00:02:23,640
Keshtu qe dua tju tregoj nje rregull

51
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per t'ju afruar kesaj pyetje.

52
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Sa gjate te merr kohe per ta dyfishuar kete shume?

53
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Dhe kjo rregull quhet rregulla numer 72.

54
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Ndonjehere, eshte rregulla e 70 ose rregulla 69.

55
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Mirepo, rregulla 72 eshte me tipike, sidomos

56
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nese je duke kalkuluar perberjen neper

57
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nje periudhe kohore.

58
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Ndoshta kjo perberjen e vazhdueshme.

59
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Perberja e vazhdueshme do te sjell afer 69 ose 70.

60
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Por do ta shpjegoj kete pas pak

61
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Per t'ju pergjigjur pyetjes se njejte, themi qe kam 10%

62
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qe perbehen çdo vit.

63
00:03:06,990 --> 00:03:10,470
Duke perdorur rregullen 72, them sa gjate me merr kohe mua

64
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te dyfishoj parate?

65
00:03:11,740 --> 00:03:16,500
Marr thjeshte 72, prandaj quhet rregulla numer 72

66
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dhe e ndaj me perqindjen.

67
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Pra, perqindja eshte 10.

68
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Ne vlere decimale eshte 0.1.

69
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Pra, eshte 10 thye per 100.

70
00:03:25,460 --> 00:03:27,490
Prandaj, 72 thye per 10.

71
00:03:27,490 --> 00:03:33,380
Dhe fitoj, 7.2, eshte vjetore, pra 7.2 vite.

72
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Nese kjo do te ishte 10% interes qe perbehet çdo muaj

73
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do te ishte 7.2 muaj.

74
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Prandaj, kam 7.2 vite, qe eshte mjaft e perafert me

75
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ate se çka gjeta me heret me menyrat matematikore.

76
00:03:44,910 --> 00:03:47,460
Ngjajshem me te, themi qe jam duke zgjidhur nje

77
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problem tjeter te perbere.

78
00:03:49,230 --> 00:03:55,420
Themi qe kam 6% interes vjetor te perbere.

79
00:04:04,370 --> 00:04:11,020
Duke perdorur rregullen 72, vetem kalkuloj 72 thye per 6.

80
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The fitoj qe 6 shkon ne 72, 12 here.

81
00:04:14,465 --> 00:04:19,060
Keshtu qe do te me duhen 12 vite per ta dyfishuar shumen e parave,

82
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nese kalkuloj 6% ne parate e mia si interes vjetor i perbere.

83
00:04:22,350 --> 00:04:23,570
Ta shohim nese kjo funksionon.

84
00:04:23,570 --> 00:04:26,530
Keshtu pra, kuptuam heren e fundit qe menyra tjeter

85
00:04:26,530 --> 00:04:30,490
per ta zgjidhur kete do te ishte, nese marrim x

86
00:04:30,490 --> 00:04:38,310
qe do te ishte afer 2 thye per-- kjo eshte ku

87
00:04:38,310 --> 00:04:41,150
kemi dyfishimin e parase, 2 dmth 2 here parate tona

88
00:04:41,150 --> 00:04:45,880
thye per logaritmin e cfardo baze qe jep 10.

89
00:04:45,880 --> 00:04:49,780
Ne kete rast ne vend te 1.1 do te jete 1.06

90
00:04:49,780 --> 00:04:52,270
Pra, mund ta shohesh qe eshte pak me veshtire.

91
00:04:52,270 --> 00:04:54,460
Prandaj marrim kalkulatorin.

92
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Pra, kemi 2, logaritmi i tij, i ndare me 1.06, logaritmi i kesaj shprehje

93
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qe eshte 11.89.

94
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Pra, afersisht 1.9

95
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Pra, me matematike, gjetem 11.9

96
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Pra, prap shohim qe eshte nje matje e perafert e mire.

97
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dhe kjo matje eshte shume me e thjeshte se kjo matematike.

98
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Dhe mendoj qe shume prej nesh mund ta llogarisin kete permendesh.

99
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Pra, kjo eshte nje menyre e mire per ti impresionuar njerezit.

100
00:05:27,960 --> 00:05:31,890
Dhe per te pare sa i mire eshte ky numer

101
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une i kam vendosur ne nje databaze

102
00:05:35,690 --> 00:05:38,760
Shtypa OK, ja ketu kemi normat e ndryshme te interesit

103
00:05:38,760 --> 00:05:41,180
Kjo eshte koha e sakte sa do te duhej qe ti dyfishojme parate.

104
00:05:41,180 --> 00:05:45,340
Pra, jam duke perdorur kete formule ketu per ta llogaritur

105
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kohen e sakte qe nevojitet per ta dyfishuar.

106
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Themi qe kjo eshte ne vite nese perbejme interesin çdo vit.

107
00:05:52,790 --> 00:05:55,190
Pra nese interesi eshte 1% atehere do te nevojiten 70 vite

108
00:05:55,190 --> 00:05:55,980
per ti dyfishuar parate.

109
00:05:55,980 --> 00:05:59,460
Me 25% do te nevojiten mbi 3 vite per ti dyfishuar

110
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parate tuaja.

111
00:06:02,960 --> 00:06:10,870
Kjo eshte e sakte--dhe do ta bej kete me te kaltert--

112
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kete numer ketu.

113
00:06:11,970 --> 00:06:13,220
Kjo eshte e sakte.

114
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Dhe e vendosa ketu, gjithashtu.

115
00:06:21,310 --> 00:06:24,450
Nese e shikon kete vije te kaltert, kjo eshte e sakta.

116
00:06:24,450 --> 00:06:26,140
Nuk i kam vendosur te gjitha.

117
00:06:26,140 --> 00:06:28,600
Mendoj qe fillova me 4%.

118
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Pra, nese e sheh tek 4%, do te nevojiten 17.6 vite

119
00:06:32,560 --> 00:06:33,370
per ti dyfishuar parate.

120
00:06:33,370 --> 00:06:37,360
Pra, 4% do te nevojiten 17.6 vite per ti dyfishuar parate.

121
00:06:37,360 --> 00:06:39,450
Pra, kjo pika me te kaltert.

122
00:06:39,450 --> 00:06:46,270
Me 5%, do te nevojiten 14 vite per ta dyfishuar shumen e parave.

123
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Dhe kjo do te jep nje vleresim

124
00:06:48,200 --> 00:06:50,780
çdo perqindje eshte e rendesishme nese flet per

125
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interesin e perbere. Kur e merr 2%, ju nevojiten 35 vite

126
00:06:54,490 --> 00:06:55,310
per t'o dyfishuar parate.

127
00:06:55,310 --> 00:06:57,490
Me 1% ju nevojiten 70 vite.

128
00:06:57,490 --> 00:07:00,900
Ti i dyfishon parate dy here me shpejte. Eshte ne te vertete

129
00:07:00,900 --> 00:07:02,680
e rendesishme, veçanerisht nese mendon per te dyfishuar

130
00:07:02,680 --> 00:07:05,230
parate, ose edhe per te trefishuar parate.

131
00:07:05,230 --> 00:07:13,200
Me te kuqe, thashe se çfare parashikon rregulla 72?

132
00:07:13,200 --> 00:07:17,280
Pra nese vetem merr numrin 72 dhe e ndane me 1%, ti fiton 72.

133
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Nese e merr 72 dhe e ndane me 4, ti fiton 18.

134
00:07:21,730 --> 00:07:25,100
Rregulla 72 thote qe do te nevojiten 18 vite per ti dyfishuar parate.

135
00:07:25,100 --> 00:07:27,580
Me 4% norme interesi, kur pergjigja e sakte eshte

136
00:07:27,580 --> 00:07:30,520
17.7 vite.

137
00:07:30,520 --> 00:07:31,420
Pra, eshte shume afer.

138
00:07:31,420 --> 00:07:34,455
Pra, çka eshte ajo me te kuqe aty?

139
00:07:37,490 --> 00:07:38,820
Pra, e kam vendosur ketu.

140
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Lakoret jane shume afer.

141
00:07:40,680 --> 00:07:45,510
Per norma te uleta te interesit, pra keto norma interesi,

142
00:07:45,510 --> 00:07:53,140
rregulla 72 e tejkalon per pak se sa kohe te nevojitet

143
00:07:53,140 --> 00:07:54,880
per ti dyfishuar parate.

144
00:07:54,880 --> 00:07:57,610
Dhe perderisa shkon tek normat me te larta, rregulla 72

145
00:07:57,610 --> 00:08:01,340
e nenvlereson per pak se sa kohe te nevojitet per te dyfishuar parate.

146
00:08:01,340 --> 00:08:05,090
A kishit menduar qe a eshte me te vertete numri 72 me i miri?

147
00:08:05,090 --> 00:08:06,840
Kjo eshte cka une bera.

148
00:08:06,840 --> 00:08:09,340
Nese e merr normen e interesit dhe e shumezon me

149
00:08:09,340 --> 00:08:11,270
kohen aktuale per dyfishim.

150
00:08:11,270 --> 00:08:12,790
Dhe ja ketu fiton nje mori numrash.

151
00:08:12,790 --> 00:08:14,940
Per norma te uleta te interesit 69 funksionon mire.

152
00:08:14,940 --> 00:08:17,360
Per norma te larta te interesit 78 funksionon mire.

153
00:08:17,360 --> 00:08:20,470
Mirepo po e shikove keshtu, 72 duket

154
00:08:20,470 --> 00:08:21,290
nje matje mjaft e perafert.

155
00:08:21,290 --> 00:08:26,150
Mund te shohesh qe nxorri mjaft mire prej 4%

156
00:08:26,150 --> 00:08:27,620
deri ne 25%.

157
00:08:27,620 --> 00:08:30,310
Qe jane normat me te shpeshta te interesit

158
00:08:30,310 --> 00:08:32,409
qe shume nga ne do ti perdorim gjate jetes.

159
00:08:32,409 --> 00:08:34,299
Shpresoj se ishte e vyeshme per ju.

160
00:08:34,299 --> 00:08:36,750
Eshte menyre shume e lehte per te pare sa shpejt

161
00:08:36,750 --> 00:08:37,530
ti do te mund ti dyfishosh parate.

162
00:08:37,530 --> 00:08:39,015
Ta bejme edhe nje veç per qef.

163
00:08:44,680 --> 00:08:50,480
Themi qe une kam 9% interes vjetor te perbere.

164
00:08:50,480 --> 00:08:53,500
Dhe sa gjate me duhet per ti dyfishuar parate?

165
00:08:53,500 --> 00:08:59,610
Pra, 72 thye per 9 eshte e barabarte me 8 vite.

166
00:08:59,610 --> 00:09:02,810
Do te me nevojiten 8 vite per ti dyfishuar parate.

167
00:09:02,810 --> 00:09:06,200
Dhe pergjigjja e sakte--sepse kjo ishte e perafert--

168
00:09:06,200 --> 00:09:12,190
me rregullen 72 eshte 9%, ndersa e tjetra 8.04 vite.

169
00:09:12,190 --> 00:09:15,940
Prap, permendesh ne mund ta bejme nje

170
00:09:15,940 --> 00:09:17,190
matje te perafert shume te mire.