1 Hazzan & Pompeo CAPITULO 4 Juros Compostos · M taxa de serviço = = + → Exercício 22:)...
Transcript of 1 Hazzan & Pompeo CAPITULO 4 Juros Compostos · M taxa de serviço = = + → Exercício 22:)...
1
Hazzan & Pompeo CAPITULO 4 Juros Compostos Exercício 1:
12,308.56)02,01(00,000.50 6 =+×=M Exercício 2:
00,968.147)36,01(00,000.80) 2 =+×=Ma
46,674.92)03,01(00,000.65) 12 =+×=Mb
56,525.52)07,01(00,000.35) 6 =+×=Mc Exercício 3:
61,917.300,000.7)025,01(00,000.7 18
=−+×=−=
JCMJ
Exercício 4:
54,626.1755,960.12)026,01(00,000.12
99,665.4)026,01(00,000.4
21
32
61
=+==+×=
=+×=
MMMMM
Exercício 5:
08,217.743579,2.)10,01.(000.175 9
==+=
CCC
2
Exercício 6:
..%55,101556,01)167,1(
)1(167,1)1(000.35000.3
101
10
10
maiii
ii
=→=+=
+=
+×=
Exercício 7:
..%18,70718,012)1(2
)1.(.2)1.(
.2
101
10
10
maiiii
iCCiCM
CMCJCMJ
n
=→=+=→+=
+=
+=
=→=−=
Exercício 8:
..%22,444422,013)1(3
)1.(.3)1.(
.3
31
3
3
taiiii
iCCiCM
CMn
=→=+=→+=
+=
+=
=
Exercício 9:
..%04,70704,0
)1(1458,1)1.(480550
2
2
maii
ii
==
+=
+=
3
Exercício 10:
mesesnnn
n
n
n
8)0178,0.1427,0)018,1ln(.1427,0)018,1ln(1534,1ln)018,01(1534,1
)018,01(000.5767.5
====
+=
+×=
Exercício 11:
mesesnnn
CCiCM
n
n
n
85,3102176,0.6931,0022,1ln.2ln
)022,1(2)022,01.(.2
)1.(
=→==
=
+=
+=
Exercício 12:
..%809,101809,01018,1)1(24,1)1.(00,000.600,440.7)
00,440.7)24,1(000.6)24,01(000.6)
12
12
1
maiiii
ib
MMa
=→=+=→+=
+=
=×=+×=
..%36,111136,011136,1)1(24,1
)1(00,000.600,440.7)2
2
saiiii
ic
=→=+=→+=
+×=
4
Exercício 13:
73,955.2;27,044.300,000.6.9709,0
.9709,00934,1.1262,1.
)015,01.()02,01.(
00,000.6
6
6
===+
==+=
+=
==+
ABBBBABA
BMAMMM
BA
B
A
BA
Exercício 14:
..%46,10146,010146,1)1(0909,1
)1(00,000.5500,000.606
6
maiiii
i
=→=→+=+=
+×=
Exercício 15:
93,900)02,01(00,800 6 =+×=M Exercício 16:
..%06,20206,010206,1)1(0417,1
)1.(1922002
2
maiiii
i
=→=→+=+=
+=
Exercício 17:
..%38,60638,0)1(0638,1..%08,20208,010208,1
)1(0638,1)1.(.094
1
3
3
taiiimaiii
iiMM
=→=→+=
=→=→+=+=
+=
5
Exercício 18: 2,3%a.m. 18.000 2 meses
..%41,22
%82,404822,0172.17
172.17000.18)
00,172.7
046,02023,0000.18
000.18)
mab
x
xa
=→=−
=
=×=−
..%38,20238,010238,1)1(0482,1
)1(00,172.1700,000.18)2
2
maiii
ic
→=→+=+=
+×=
Exercício 19: 3,5%a.m. 100.000 3 meses
..%77,30377,010377,1)1(1173,1
)1(00,500.8900,000.100)
00,500.89
105,03035,0000.100
000.100)
3
3
maiii
ib
x
xa
→=→+=+=
+×=
=
=×=−
Exercício 20:
.15,518.99)036,01(00,500.89 3
BBancooéopçãomelhorAM =+×=
6
Exercício 21:
.,15,116.100
)%1(00,89515,518.99
ABancooéopçãomelhoracasoNesteM
serviçodetaxaM=
→+=
Exercício 22:
41,170.16)22,01(00,000.12) 1218
=+×=Ma Convenção Exponencial
40,250.165,022,000,640.1400,640.1400,640.14)22,01(00,000.12)
2
11
=××+==+×=
MMb
Convenção Exponencial Exercício 23:
50,3.107301702,080,120.10680,120.106
80,120.106)02,01(00,000.100
2
2
31
=
××+=
=+×=
M
M
M
Exercício 24:
34,318.107)02,01(00,000.100 30107
=+×=M
Exercício 25:
39,477.10)75,01(00,000.10 36030
=+×=M
7
Exercício 26:
02,592.10)75,01(00,000.10 36037
=+×=M
Exercício 27: a) 3,5%a.m.
3 meses
17,104100.96,0
04,0100
==
=−
xx
xx
)().00,104)04,01.(100) 1
girodecapitalbaéopçãomelhorAMb =+=
Exercício 28:
..%17,40417,017,104)1.(100 1
maiii
=→==+
Exercício 29:
51,371.1511231,1.)022,01.(00,000.170
)1.(23,960.152
1114,1.)02,01.(00,000.170
)1.(
30160
30160
==+=
+=
==+=
+=
CCC
iCMC
CC
iCM
n
n
8
Exercício 30:
..%64,404064,0)1(0625,1
)1(000.8500.8
..%88,20288,0)1(0625,1
)1(000.8500.8
18,0
36064
13,2
3064
aaiii
i
maiii
i
=→=+=
+×=
=→=+=
+×=
Exercício 31:
..%03,30303,0)1(0625,1
)1(000.8500.8033,2
3061
maiii
i
=→=+=
+×=
Exercício 32: 2,8%a.m. 102,88
30 dias 100
88,102100972,0.
028,0100
==
=−
xx
xx
..%61,404061,014061,1)1(0288,1
)1(10088,101
..%88,20288,0100
10088,102
0833,0
36030
aaiii
i
ma
→=→+=+=
+×=
→=−
9
Exercício 33: 45%a.a. 106,72
63 dias 100
)(%62,00062,0100
62,062,010062,1000606,1
)40,01).(100(72,106
72,106)45,01.(100
36063
36063
créditodeaberturadetaxa
x
x
M
→=
=−=
+−=
=+=
Exercício 34:
)(%49,0004922,01004922,0
4922,01004922,100
)41,01).(100(72,106 36063
créditodeaberturadetaxa
xx
x
→=
=−=
+−=
Exercício 35:
..%18,838318,010606,1)1(0606,1)1.(99105
)35(10505,1.100)05,01.(
288,10
0972,0
36035
)35(1
aaii
ii
diasMCM dias
→=+=
+=
+=
==+=
10
95,10335→
dias
..%97,484897,0148967,110395,1)1(0395,1
)1.(10095,103
288,10
0972,0
36035
aaiii
ii
→=→+=+=
+=
+=
Exercício 36:
.%.39,414139,014139,1)1(03425,1
)1.(100)1.(100425,103
425,1035,985,98)100%(5,1
)35(105)05,01.(100)1.(
09722,0
09722,036035
%5
1
aaiii
ii
flatdiasM
iCM n
→=→+=+=
+=+=
⎯→⎯
→=+=
+=
Exercício 37: 100 35 dias
96,92 38%a.a.
..%64,20264,03035
03080,0
35%08,303080,0100
92,9610092,96
0318,1.)38,01.(100 36035
ma
diasem
CCC
→=×
→=−
==+=
11
Exercício 38: 100 32 dias
96,99 41%a.a.
..%82,202822,03032
03001,0
32%01,30301,0100
99,9610099,96
031,1.)41,01.(100 36032
ma
diasem
CCC
→=×
→=−
==+=
Exercício 39: 1,9%a.m. 100 42 dias
97,34
..%99,252599,0)1(02732,1
)1.(34,97100
34,9766,2100
0266,04230019,0
100100
11666,0
36042
aaii
i
xx
x
→=+=
+=
=→=−
=×=−
Exercício 40:
..%09,292909,0)1(02732,1
)1.(34,9710010555,0
36038
aaii
i
→=+=
+=
12
Exercício 41:
..%87,30387,010387,1)1(06,1
..%63,30363,010363,1)1(06,1
)1(000.500000.530
)1.(
3046
6333,1
3049
maiii
maiii
i
iCM n
→=→+=+=
→=→+=+=
+×=
+=
Exercício 42:
..%27,404271,0)1(0707,1
)1.(99,0.5005306333,1
3049
maiii
i
=→=+=
+=
Exercício 43:
aaiid
aaiic
aaiib
aaiia
a
a
a
a
a
a
a
a
.%24,393924,01)018,01()
.%25,191925,01)045,01()
.%97,151597,01)025,01()
.%87,232387,01)018,01()
180360
90360
60360
30360
==−+=
==−+=
==−+=
==−+=
13
Exercício 44:
maiie
maiid
maiic
maiib
maiia
m
m
m
m
m
m
m
m
m
m
.%66,30366,01)0012,01()
.%19,30319,01)065,01()
.%56,60656,01)21,01()
.%99,60699,01)50,01()
.%77,40477,01)75,01()
130
6030
9030
18030
36030
==−+=
==−+=
==−+=
==−+=
==−+=
14
Exercício 45:
..%4040,01)96,01()
..%37,80837,01)041,01()
..%32,80832,01)027,01()
..%99,90999,01)016,01()
..%64,282864,01)0014,01()
360180
90180
60180
30180
1180
saiie
saiid
saiic
saiib
saiia
s
s
s
s
s
s
s
s
s
s
==−+=
==−+=
==−+=
==−+=
==−+=
Exercício 46:
diasemii
d
d
40%35,303347,01)025,01(
40
3040
40
==−+=
Exercício 47:
diasemii
d
d
65%38,40438,01)02,01(
65
3065
65
==−+=
tt
nn
iCiC
anopadrãoprazodiast
ndiasq
n
iCiC
360360
21
21
)1.()1.(
1:)(
360;)(
360)1.()1.( 21
+=+
==
+=+
15
1)1(
)1(1
])1[(])1[( 360360
360
360
−+=
+=+
+=+
tq
tq
tq
tq
qt
t
q
ii
ii
ii
Exercício 48:
..%1,2
32,128)021,01.(100126)26,01.(100
122
11
madetaxaàaplicarpreferívelÉ
MM
=+=
=+=
Exercício 49:
..%5,269,107)025,01.(100
39,107)33,01.(1003
2
123
1
madetaxaàaplicaréaalternativmelhorAMM
=+=
=+=
Exercício 50:
..%5,413,109)06,01.(100
20,109)045,01.(100
46
2
36
1
tadetaxaàaplicaréaalternativmelhorAM
M
=+=
=+=
16
Exercício 51: 100 90 dias
97,34
..%72,10172,01)0526,01()
90%26,50526,0955
9595100)
9030
30 maib
diasema
→=−+=
→==−
Exercício 52:
..%16,10116,000,000.8
00,000.845,093.8)
45,093.826,2381,118.8)
26,2320,0)00,000.881,116.8()
81,116.8)19,01(000.8) 36030
mad
Mc
IRb
Ma
líq
→=−
=−=
=×−=
=+×=
Exercício 53:
..%35,20235,000,000.8
00,000.815,188.8)
15,188.807,4733,235.8)
07,4720,0)00,000.833,235.8()
33,235.8)19,01(000.8) 36060
mad
Mc
IRb
Ma
líq
→=−
=−=
=×−=
=+×=
17
Exercício 54:
..%28,10128,000,000.8
00,000.887,102.8)
87,102.872,2559,128.8)
72,2520,0)00,000.859,128.8()
59,128.8)19,01(000.8) 36033
mad
Mc
IRb
Ma
líq
→=−
=−=
=×−=
=+×=
Exercício 55:
..%41,202041,01)0156,01(
30%56,10156,0)1.(10056,101
56,10125,818,0
25,10120.2,025,10120,0)100(
25,10125,1100
0125,0100
100
30360
360
30
1
aai
diasemiiM
MM
MMMMM
M
Mi
BR
BR
BR
BRBR
BRBRlíq
líq
líqlíq
→=−+=
→=+==
==
=+−
=×−−=
=+=
=−
=
Exercício 56:
..%404,909404,01)0156,01( 62360
360 aai →=−+=
18
Exercício 57:
diasemiid
Mc
IRb
M
Ma
líqlíq
líq
BR
120%98,505987,000,000.25
00,000.2593,496.26)
93,496.2623,37416,871.26)
23,37420,0)00,000.2516,871.26()
16,871.26)12,01(00,875.25
00,875.25035,100,000.25)
360120
1
=→=−
=
=−=
=×−=
=+×=
=×=
Exercício 58:
diasemiid
Mc
IRb
Ma
líqlíq
líq
BR
150%80,606803,000,000.25
00,000.2590,700.26)
90,700.2623,42513,126.27)
23,42520,0)00,000.2513,126.27()
13,126.27)12,01(00,875.25) 360150
=→=−
=
=−=
=×−=
=+×=
19
Exercício 59:
períodonoCMCMCM
CMCM
IRMM
MMMMM
M
Mi
CMM
BRBR
BRBR
BRBRlíq
líq
líqlíq
BR
%91,20291,101029,010001029,0
46,104).(075,1)14,1).(.(10050,107
50,120,0)00,10050,107(50,10700,86.8,0
00,1062020,000,10620,0)100(
00,106
06,0100
100)14,01).(.(100
360120
360120
==×=→=
==
=×−==→=
=+−
=×−−=
=
=−
=
+=
Exercício 60: 1,3%a.m. 100 5 meses
87,959.77)013,01(
00,000.80)
39,959.76)013,01(
00,000.80
39,959.76)013,01.(80,996.74)
80,996.74)013,01(
00,000.80)
2
3
22
5
=+
=
=+
=
=+=
=+
=
A
A
mesesA
A
Vc
V
ouVb
Va
20
Exercício 61:
87,207.26)015,01(
00,000.272=
+=V
Exercício 62:
09,450.25)03,01(
00,000.27)
56,951.25)02,01(
00,000.27)
30,156.26)016,01(
00,000.27)
2
2
2
=+
=
=+
=
=+
=
Vc
Vb
Va
Exercício 63: 2 meses 50.000 4 meses 60.000 1,8%a.m.
07,115.104
62,867.5546,247.48)018,01(
00,000.60)018,01(
00,000.5042
=
+=+
++
=
V
V
Exercício 64:
32,540.19763,907.7356,962.6513,670.57
)02,01(00,000.80
)02,01(00,000.70
)02,01(00,000.60
432
=++=
++
++
+=
VV
V
21
Exercício 65: 2 meses 50.000,00 48.250,00 ( 3% sobre 50.000,00 )
prazoàéaalternativmelhorAespostaRM
:63,002.50)018,01(00,250.48 2 =+×=
Exercício 66:
vistaàéaalternativmelhorAespostaRM
:45,610.49)014,01(00,250.48 2 =+×=
Exercício 67: 45 dias 1.000,00 970,00 ( 3% de 1.000,00 )
vistaàpagarécompradoroparamelhorOespostaRM
:98,988)013,01(00,970 30
45
=+×=
Exercício 68:
..%05,20205,0)1(0309,1
)1(00,97000,000.15,1
3045
maii
i
→=+=
+×=
22
Exercício 69: 1 ano 50
CaAlternativespostaRManosManos
AtualcC
aaia
:99,409.146)010,1(09,909.90)5(99,999.109)010,1(09,909.90)2(
)(09,909.90)10,01.(00,000.100
..%10
5
2
1
=+×=
=+×=
=+=
=
Exercício 70 85.000,00 6 meses 75.000,00 3 meses
( )
( ) 69,564.7504,0173,176.67
73,176.6704,0100,000.85
31
6
=+⋅=
=+=
M
CC
Resposta: A troca sim é vantajosa para Rogério Exercício 71
( ) ( )37,806.25
017,01015,0100,000.25)=
+⋅+⋅=M
Ma
( )
( ) ( )mesesnosi
iou
mesesnosib
2%22,30322,01017,01015,01
2%22,30322,000,000.25
00,000.2537,806.25)
==−+⋅+=
=−
=
23
Exercício 72
( ) ( ) ( )( )trimestrenoi
ia%68,50568,0
1018,01019,01027,01)=
−+⋅+⋅+=
( ) ( ) ( )( )
( )Abrilemi
iib
%20,202198,010567,10232,0
10567,108,110098,01019,01027,0108,0)
=⋅=+⋅=
−+⋅+⋅+==
Exercício 73
( )mesesemii
4%09,50509,01015,1012,1012,1011,1
=−×××=
Exercício 74
( ) ( ) ( )( )mesesemi
i3%79,60679,0
104,0108,0103,01=
−−⋅+⋅+=
Exercício 75
( ) ( )( )
..%11,11111,0
1,09,0119,0
1110,01
maii
ii
ii
maio ==
=⋅=+⋅
−+⋅−=
Exercício 76
( ) ( ) ( )( )trimestrenoi
i%26,141426,0
105,0105,0105,01−−=
−−⋅−⋅−=
24
Exercício 77
( ) ( )( )bimestreaoi
i%49,00049,0
107,0207,01−−=
−−⋅+=
Exercício 78
( ) ( )
( )Novembroemii
iii
738,303738,09626,01
03,01107,01
−−==+
=−+⋅+=
Exercício 79
( ) ( ) ( )
( )Junhoemii
iii
%66,4046627,0046627,11
055,01104,0105,01
==+
=−+⋅−⋅+=
Exercício 80
( )diasemii
i
2%21,0002134,01001133,1001,1
130034,01
3003,01
=−×=
−⎟⎠⎞
⎜⎝⎛ +⋅⎟
⎠⎞
⎜⎝⎛ +=
Exercício 81
( )diasemii
i
3%2702,0002702,010009,10009,10009,1
130027,01
30027,01
30027,01
=−××=
−⎟⎠⎞
⎜⎝⎛ +⋅⎟
⎠⎞
⎜⎝⎛ +⋅⎟
⎠⎞
⎜⎝⎛ +=
25
Exercício 82
( )diasemii
i
5%4776,0004776,01001,1000933,1000967,1000967,10009,1
13003,01
30028,01
30029,01
30029,01
30027,01
=−××××=
−⎟⎠⎞
⎜⎝⎛ +⋅⎟
⎠⎞
⎜⎝⎛ +⋅⎟
⎠⎞
⎜⎝⎛ +⋅⎟
⎠⎞
⎜⎝⎛ +⋅⎟
⎠⎞
⎜⎝⎛ +=
Exercício 83
( )diasemi
i
10%07,10107,0
130032,01
10
=
−⎟⎠⎞
⎜⎝⎛ +=
Exercício 84
( )diasemi
i
22%37,20237,0
130032,01
22
=
−⎟⎠⎞
⎜⎝⎛ +=
Exercício 85
( )diasemi
i
20%8155,1018155,0
130027,01
20
=
−⎟⎠⎞
⎜⎝⎛ +=
Exercício 86 1.000,00 35dias 980,00
períodonoia %04,200204,00,980
00,98000,000.1) →=−
=
26
( ) ( )
..%0808,0000808,0
10204,1100,98000,000.1) 2525
udii
iib
==
+=→+⋅=
..%42,20808,030) maic mensalover =×=
Exercício 87 1.000,00 35dias 970,00
( )períodonoia %09,30309,000,970
00,97000,000.1) =−
=
( ) ( )
..%65,31218,030)
...%1218,0001218,0
1039,1100,97000,000.1) 2525
maic
udaii
iib
mensalover =×=
==
+=→+⋅=
Exercício 89
( )61,642.9
0008666,0100,000.10
0008666,000,000.3
6,2..%6,2
42
...
=+⋅=
==→=
XX
imai udaover
Exercício 90
70,409.930022,0100,000.10
83
=
⎟⎠⎞
⎜⎝⎛ +⋅=
X
X
27
( )
( ) 00,736.2300073279,0100,000.23
00,736.23032,0100,000.23)
cot92,924.2863455,7
00,000.23)
43
1
=+⋅=
=+=
=
ouMd
asc
Exercício 91
( )( )..267,101267,0101267,1
01267,10006,01 21
mamestaxa
=−=+⇒
Exercício 92
( ) ( )..%4165,1014165,0100067,01 21 ma=−+
Exercício 93 120.000,00 60 dias (8,115086) 43 du 23.000,00
( )
( )( )...%073279,000073279,0
1863455,7115086,8)
%2,3032,0863455,7
863455,7115086,8)
43
udaiib
períodonoa
=+⋅=
=−
00,147$20,000,73600,000.2300,736.23
R×
−
ase
cot06,428.1115086,880,588.1180,588.1120,14700,000.1200,736.23)
=÷=−−
28
Exercício 94
( )71,085.008.12
185,0100,000.000.12) 2521
=+⋅=
MMa
( )( )
mensaloverc
udaiib
%0202,030678,0)
...%678,00006738,0100,000.000.1271,085.008.12) 1
=×
=+⋅=
Exercício 95
( )70,478.007.12
17,0100,000.000.12) 2521
=+⋅=
MMa
( )( )...%062322,000062322,0
100,000.000.1270,478.007.12)udai
ib=
+⋅=
mensaloverc %018696,030062322,0) =×
Exercício 96
( )
( )
( ) 72,015.012.2185,0150,967.007.6
50,967.007.6184,0111,942.003.6
11,942.003.618,0100,000.000.6)
2521
3
2521
2
2521
1
=+⋅=
=+⋅=
=+⋅=
M
M
Ma
( )( )
( )..3%20028,0
0020028,01183016,01
...3016,181002002,1
100,000.000.672,015.012.6)
3
2523
3
0119,0
2523
udemii
uaaii
ib
du
du
==−+=
=+=
+⋅=
Exercício 97
00,200.019.2430024,0100,000.000.24)
1
=⎟⎠⎞
⎜⎝⎛ +⋅=Ma
29
( ) 10008,01) 1252
252 −+=uib
..%32,22) 252 uaic u =
Exercício 98
00,600.021.2430027,0100,000.000.24)
1
=⎟⎠⎞
⎜⎝⎛ +⋅=Ma
( ) 10009,01) 1252
252 −+=uib
..%44,25) 252 uaic u =
Exercício 99
( ) ..53,1120,01) 36030
maia =−+=
( ) ( )...%0723,0000723,0193,98400,000.1
93,9840153,000,000.1)
21 udaii
XX
Xb
=→+⋅=
=→=−
overmac ..%17,2300723,0) =×
Exercício 100
( ) ( )..%67,101671,0122,01) 36030
maia =−+=
( ) ( )...%0789,00007894,0156,98300,000.1
56,98301671,000,000.1)
21 udaii
XX
Xb
=→+⋅=
=→=−
overmac ..%37,2300789,0) =×
Exercício 101
( )
( )IRdediasemdiasemi
ia
d
d
%2032%367,180,07088,132%7088,1
017088,0121,01)
32
36032
32
=×=
=−+=
30
( )( )udai
ib..%0617,00006173,0
100,000.167,013.1) 22
=+⋅=
overmac ..%85,130%0617,0) =×
Exercício 102
( ) ( )diasemia d 32%857,101857,0123,01) 36032
32 =−+=
( )( )...%083669,000083669,0
100,000.157,0118.1) 22
udaiib
=+⋅=
overmac ..%51,230%083669,0) =×
Exercício 103
85,333.61236,0100,000.5
8
=⎟⎠⎞
⎜⎝⎛ +⋅=M
Exercício 104
00,986.7220,0100,000.6
3
=⎟⎠⎞
⎜⎝⎛ +⋅=M
Exercício 105
78,030.1425,0100,000.1)
9045
1 =⎟⎠⎞
⎜⎝⎛ +⋅=Ma
→=⎟⎠⎞
⎜⎝⎛ +⋅= 91,025.1
421,0100,000.1)
9045
2Mb
esta é a melhor alternativa para tomar o empréstimo.
31
Exercício 106
59,214.101236,018100,000.6)
18
=⎟⎠⎞
⎜⎝⎛ ×+⋅=Ma
( ) 00,780.9035,018100,000.6) =×+⋅=Mb
É preferível aplicar a juros compostos
Exercício 107
96,876.31424,0100,000.20
35,252.38424,0100,000.24
8
8
=⎟⎠⎞
⎜⎝⎛ +⋅=
=⎟⎠⎞
⎜⎝⎛ +⋅=
M
M
Alternativa b
Exercício 108
( )
34,100.112096,0100,000.1
00,180.118,0100,000.1)12
2
1
=⎟⎠⎞
⎜⎝⎛ +⋅=
=+⋅=
M
Ma
para o tomador do empréstimo é preferível o banco B
( )..%67,161667,012
01389,012
101389,1
12118,1
12100,000.100,180.1)
12
12
aai
ii
i
ib
=
=→+=
⎟⎠⎞
⎜⎝⎛ +=
⎟⎠⎞
⎜⎝⎛ +⋅=
Exercício 109
63,585.1791260,0100,000.100)
12
=⎟⎠⎞
⎜⎝⎛ +⋅=Ma
32
92,120.182360
60,0100,000.100)360
=⎟⎠⎞
⎜⎝⎛ +⋅=Mb
38,207.182640.860,0100,000.100)
8640
=⎟⎠⎞
⎜⎝⎛ +⋅=Mc
88,211.18200,000.100
1limlim
1)
6,0 =⋅=
⋅=⎟⎠⎞
⎜⎝⎛ +⋅=
⎟⎠⎞
⎜⎝⎛ +⋅=
∞→∞→
eM
eCkiCM
kiCMd
ik
kk
k
Exercício 110
87,409.900,000.653,520.300,000.3
315,0
802,0
=⋅=
=⋅=⋅
⋅
eMeM
Exercício 111
53,520.300,000.3 802,0 =⋅= ⋅eM
Exercício 112
compostasjurosdetaxaaa
eM
→
=−
=⋅=
..%18,16
1618,000,000.1
00,000.183,161.183,161.100,000.1 15,0