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

qq

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

qq

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