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# SEMI Matematica Financeira 01

DisciplinaMatemática Financeira57.324 materiais1.486.878 seguidores
Pré-visualização3 páginas
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Autoria: Leonardo Takamasa Otsuka
Tema 01
Fundamentos da Matemática Financeira
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Fundamentos da Matemática Financeira
Autoria: Leonardo Takamasa Otsuka
Como citar esse documento:
OTSUKA, Leonardo Takamasa. Matemática Financeira: Fundamentos da Matemática Financeira. Caderno de Atividades. Valinhos: Anhanguera
Educacional, 2017.
Índice
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SRUWXJXHVD\ufffdRX\ufffdTXDOTXHU\ufffdRXWUR\ufffdLGLRPD\ufffd
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ACOMPANHENAWEB
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CONVITEÀLEITURA
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PORDENTRODOTEMA
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Fundamentos da Matemática Financeira
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GLQKHLUR\ufffdSDUD\ufffdDXPHQWDU\ufffdR\ufffdVHX\ufffdQHJyFLR\ufffd\ufffdTXDLV\ufffdVmR\ufffdRV\ufffd WLSRV\ufffdGH\ufffd¿\ufffdQDQFLDPHQWRV\ufffdPDLV\ufffdYLiYHLV&quot;\ufffd6H\ufffdYRFr\ufffdSUHVWD\ufffdVHUYLoRV
FRQWiEHLV\ufffdD\ufffdYiULRV\ufffdHPSUHViULRV\ufffd\ufffdTXDLV\ufffdGLFDV\ufffdGH\ufffdLQYHVWLPHQWRV\ufffdYRFr\ufffdGDULD&quot;\ufffd2X\ufffdDWp\ufffdPHVPR\ufffdVH\ufffdYRFr\ufffdHVWi\ufffdID]HQGR\ufffdXPD\ufffd
SHUtFLD\ufffdFRQWiELO\ufffdGH\ufffdXPD\ufffdDomR\ufffdMXGLFLDO\ufffdTXH\ufffdHQYROYH\ufffdMXURV\ufffdGR\ufffdFKHTXH\ufffdHVSHFLDO\ufffd\ufffdTXH\ufffdWLSR\ufffdGH\ufffdFiOFXOR\ufffdVHUi\ufffdQHFHVViULR&quot;
3DUD\ufffdUHVSRQGHU\ufffdHVWDV\ufffdSHUJXQWDV\ufffd\ufffdR\ufffdFRQKHFLPHQWR\ufffdGHVWD\ufffdGLVFLSOLQD\ufffdSRGH\ufffdID]HU\ufffdD\ufffdGLIHUHQoD\ufffdQD\ufffdVXD\ufffdYLGD\ufffdRX\ufffdFDUUHLUD\ufffdSUR¿\ufffdVVLRQDO\ufffd
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3RUWDQWR\ufffdQHVWH\ufffdWHPD\ufffdYDPRV\ufffdDSUHQGHU\ufffdGH\ufffdXPD\ufffdIRUPD\ufffdFODUD\ufffdH\ufffdREMHWLYD\ufffdRV\ufffdFRQFHLWRV\ufffdEiVLFRV\ufffd\ufffdD\ufffdOLQJXDJHP\ufffdXWLOL]DGD\ufffdH\ufffdDOJXQV\ufffd
FiOFXORV\ufffdVLPSOHV\ufffdTXH\ufffdVHUmR\ufffdXWLOL]DGRV\ufffdQD\ufffd0DWHPiWLFD\ufffd)LQDQFHLUD\ufffd
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á
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PORDENTRODOTEMA
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Terminologia
([LVWHP\ufffdYiULDV terminologias\ufffdXWLOL]DGDV\ufffdSDUD\ufffdGH¿\ufffdQLU\ufffdRV\ufffdFRPSRQHQWHV\ufffdGH\ufffdXPD\ufffdRSHUDomR\ufffd\ufffdVHMD\ufffdHP\ufffdMXURV\ufffdVLPSOHV\ufffdRX\ufffd
MXURV\ufffdFRPSRVWRV\ufffd\ufffd3DUD\ufffdIDFLOLWDU\ufffdR\ufffdXVR\ufffdGD\ufffdFDOFXODGRUD\ufffd+3\ufffd\ufffdF\ufffd\ufffd&DOFXODGRUD\ufffd¿\ufffdQDQFHLUD\ufffd\ufffd\ufffdXWLOL]DUHPRV\ufffdDV\ufffdPHVPDV\ufffdWHUPLQRORJLDV\ufffd
XWLOL]DGD\ufffdQHVWD\ufffdFDOFXODGRUD\ufffd
PV (Presente Value)\ufffd\ufffdVLJQL¿\ufffdFD\ufffd9DORU\ufffd3UHVHQWH\ufffd\ufffdRX\ufffdVHMD\ufffd\ufffdp\ufffdR\ufffdYDORU\ufffdLQLFLDO\ufffdGD\ufffdRSHUDomR\ufffd\ufffdQR\ufffdPRPHQWR\ufffd\ufffdWHPSR\ufffd\ufffdLJXDO\ufffdD\ufffd]HUR\ufffd
3RGH\ufffdWDPEpP\ufffdVHU\ufffdFKDPDGD\ufffdGH\ufffd3ULQFLSDO\ufffd\ufffd3\ufffd\ufffd\ufffd9DORU\ufffd\$WXDO\ufffdRX\ufffdCapital\ufffd\ufffd&\ufffd\ufffd\ufffd3HUFHEDP\ufffdTXH\ufffdH[LVWHP\ufffdYiULDV\ufffdWHUPLQRORJLDV\ufffdH\ufffdTXH\ufffd
WRGDV\ufffdSRGHP\ufffdVHU\ufffdXWLOL]DGDV\ufffdQRV\ufffdHQXQFLDGRV\ufffdGRV\ufffdH[HUFtFLRV\ufffd\ufffd3RU\ufffdLVVR\ufffdp\ufffdPXLWR\ufffdLPSRUWDQWH\ufffdFRQKHFHU\ufffdWRGDV\ufffdDV\ufffdWHUPLQRORJLDV\ufffd
)9\ufffd\ufffd)XWXUH\ufffd9DOXH\ufffd\ufffd\ufffdVLJQL¿\ufffdFD\ufffd9DORU\ufffd)XWXUR\ufffd\ufffdRX\ufffdVHMD\ufffd\ufffdp\ufffdR\ufffdYDORU\ufffdGD\ufffdRSHUDomR\ufffdDSyV\ufffdD\ufffdLQFLGrQFLD\ufffdGH\ufffdMXURV\ufffd\ufffdYDORU\ufffdD\ufffdVHU\ufffdUHVJDWDGR\ufffd
3RGH\ufffdVHU\ufffdFKDPDGR\ufffdWDPEpP\ufffdMontante (M) RX\ufffd6DOGR\ufffd)XWXUR\ufffd6\ufffd\ufffd\ufffd'HVWD\ufffdPDQHLUD\ufffdWHPRV\ufffdD\ufffdSULPHLUD\ufffdIyUPXOD\ufffd\ufffdFV = PV + J
\ufffd9DORU\ufffd)XWXUR\ufffdp\ufffdD\ufffdVRPD\ufffdGR\ufffd9DORU\ufffd3UHVHQWH\ufffdFRP\ufffdRV\ufffd-XURV\ufffd\ufffd
J \u2013 Juros\ufffd\ufffdUHSUHVHQWDP\ufffdD\ufffdUHPXQHUDomR\ufffdGR\ufffd9DORU\ufffd3UHVHQWH\ufffd\ufffd39\ufffd\ufffdHPSUHJDGR\ufffdHP\ufffdDOJXPD\ufffdDWLYLGDGH\ufffdSURGXWLYD\ufffd R\$\ufffd
L\ufffd\ufffdLQWHUHVW\ufffdUDWH\ufffd\ufffd\ufffdVLJQL¿\ufffdFD\ufffd7D[D\ufffdGH\ufffdMXURV\ufffd \$\ufffdWD[D\ufffdGH\ufffdMXURV\ufffdLQGLFD\ufffdTXDO\ufffdUHPXQHUDomR\ufffdVHUi\ufffdSDJD\ufffdDR\ufffdGLQKHLUR\ufffdHPSUHVWDGR\ufffd\ufffdSDUD\ufffd
XP\ufffdGHWHUPLQDGR\ufffdSHUtRGR\ufffd\ufffd([\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffdDR\ufffdPrV\ufffd
Q\ufffd\ufffd\ufffdQ~PHUR GH\ufffdSHUtRGRV\ufffdQD\ufffdRSHUDomR\ufffd\ufffde\ufffdR\ufffdSUD]R\ufffd\ufffdR\ufffdWHPSR\ufffd
PORDENTRODOTEMA
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HP\ufffdIRUPD\ufffdGH\ufffddiagrama\ufffd\ufffd)OX[R\ufffdGH\ufffd&DL[D\ufffd\ufffd\ufffd\ufffd*,0(1(6\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffdS\ufffd\ufffd\ufffd\ufffd
([HPSOR\ufffd\ufffdXPD\ufffdSHVVRD\ufffdWRPRX\ufffdHPSUHVWDGR\ufffdR\ufffdYDORU\ufffdGH\ufffd5\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffdSDJDQGR\ufffdXPD\ufffdWD[D\ufffdGH\ufffdMXURV\ufffdVLPSOHV\ufffdGH\ufffd\ufffd\ufffd\ufffd\ufffdDR\ufffdPrV\ufffd\ufffd
3DJRX\ufffd5\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffdDSyV\ufffdWUrV\ufffdPHVHV\ufffd
\u2022 )OX[R\ufffdGH\ufffdFDL[D\ufffdGR\ufffdSRQWR\ufffdGH\ufffdYLVWD\ufffdGR\ufffdWRPDGRU\ufffd
9RFr\ufffdHVWi\ufffdUHFHEHQGR\ufffdR\ufffdGLQKHLUR\ufffdQR\ufffdPRPHQWR\ufffdLJXDO\ufffdD\ufffd]HUR\ufffdHQWmR\ufffdD\ufffdVHWD\ufffd¿\ufffdFD\ufffdSDUD\ufffdFLPD\ufffd\ufffdSRLV\ufffdLQGLFD\ufffdTXH\ufffdentrou\ufffdGLQKHLUR\ufffdQD
VXD\ufffdFRQWD\ufffd\ufffd\$SyV\ufffdWUrV\ufffdPHVHV\ufffdYRFr\ufffdHIHWXD\ufffdR\ufffdSDJDPHQWR\ufffdGR\ufffdHPSUpVWLPR\ufffdH\ufffdD\ufffdVHWD\ufffd¿\ufffdFD\ufffdSDUD\ufffdEDL[R\ufffd\ufffdSRLV\ufffdLQGLFD\ufffdTXH\ufffdR\ufffdGLQKHLUR
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0
FV= 130
2 meses1 3
PV= 100
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\$\ufffdLQVWLWXLomR\ufffd¿\ufffdQDQFHLUD\ufffd\ufffd%DQFR\ufffd\ufffdHVWi\ufffdHPSUHVWDQGR\ufffdR\ufffdGLQKHLUR\ufffdQR\ufffdPRPHQWR\ufffdLJXDO\ufffdD\ufffd]HUR\ufffdHQWmR\ufffdD\ufffdVHWD\ufffd¿\ufffdFD\ufffdSDUD\ufffdEDL[R\ufffd\ufffdSRLV
LQGLFD\ufffdTXH saiu\ufffdGLQKHLUR\ufffdGD\ufffdFRQWD\ufffdGR\ufffdEDQFR\ufffd\ufffd\$SyV\ufffdWUrV\ufffdPHVHV\ufffdR\ufffdFOLHQWH\ufffdHIHWXD\ufffdR\ufffdSDJDPHQWR\ufffdGR\ufffdHPSUpVWLPR\ufffdH\ufffdD\ufffdVHWD\ufffd¿\ufffdFD
SDUD\ufffdFLPD\ufffd\ufffdSRLV\ufffdLQGLFD\ufffdTXH\ufffdR\ufffdGLQKHLUR entrou\ufffdQD\ufffdFRQWD\ufffdGR\ufffdEDQFR\ufffd
PORDENTRODOTEMA
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0
FV= 130
2 meses1 3
PV= 100
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Juros Simples
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PDWHPiWLFD\ufffd´\ufffd\ufffd*,0(1(6\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffdS\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd3DUD\ufffdIDFLOLWDU\ufffdD\ufffdGHPRQVWUDomR\ufffdGR\ufffdFRQFHLWR\ufffdGH\ufffd MXURV\ufffdVLPSOHV\ufffd\ufffdVHJXH\ufffdR\ufffdSULPHLUR
H[HPSOR\ufffd
([HPSOR\ufffd\ufffd\ufffd\ufffdXPD\ufffdSHVVRD\ufffdWRPRX\ufffdXP\ufffdHPSUpVWLPR\ufffdGH\ufffd5\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffdQXP\ufffd%DQFR\ufffd\ufffdSHOR\ufffdSUD]R\ufffdGH\ufffdWUrV\ufffdPHVHV\ufffd\ufffdFRP\ufffdXPD\ufffdWD[D\ufffdGH\ufffd
\ufffd\ufffd\ufffd\ufffdDR\ufffdPrV\ufffd\ufffdQR\ufffdUHJLPH\ufffdGH juros simples\ufffd\ufffd'HWHUPLQH\ufffdR\ufffdVDOGR\ufffd¿\ufffdQDO\ufffdDFXPXODGR\ufffd
\$\ufffdWDEHOD\ufffd\ufffd\ufffdLUi\ufffdDMXGDU\ufffdD\ufffdHQWHQGHU\ufffdD\ufffdPHWRGRORJLD\ufffdGH\ufffdFiOFXORV\ufffdGRV\ufffdMXURV\ufffdVLPSOHV\ufffd
\ufffd\ufffd3DVVR\ufffd\ufffdODQoDU\ufffdR\ufffdYDORU\ufffdGH\ufffd5\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffdQR\ufffd39\ufffd\ufffd9DORU\ufffd3UHVHQWH\ufffd\ufffdH\ufffdD\ufffdWD[D\ufffdGH\ufffdMXURV\ufffdGH\ufffd\ufffd\ufffd\ufffd\ufffdDR\ufffdPrV\ufffd\ufffdL\ufffd\ufffd\ufffd
Mês PV (R\$) i Juros (R\$) Saldo Final (FV)
1 100,00 10%
2
3
7DEHOD\ufffd\ufffd
PORDENTRODOTEMA
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\ufffd\ufffd3DVVR\ufffd\ufffdFDOFXODU\ufffdR\ufffdYDORU\ufffdGRV\ufffd-XURV
6H\ufffdGLYLGLUPRV\ufffdRV\ufffd\ufffd\ufffd\ufffd\ufffdSRU\ufffd\ufffd\ufffd\ufffd\ufffd\ufffdLUHPRV\ufffdHQFRQWUDU\ufffdD WD[D\ufffdXQLWiULD\ufffd\ufffdRX\ufffdVHMD\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd
(IHWXDQGR\ufffdD\ufffdPXOWLSOLFDomR\ufffdGH\ufffd\ufffd\ufffd\ufffd\ufffd[\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd-XURV\ufffd\ufffd
2\ufffd6DOGR\ufffd)LQDO\ufffdp\ufffdD\ufffdVRPD\ufffdGR\ufffd39\ufffdFRP\ufffdRV\ufffd-XURV\ufffd\ufffd)9\ufffd \ufffd39\ufffd\ufffd\ufffd-\ufffd\ufffd
Mês PV (R\$) i Juros (R\$) Saldo Final (FV)
1 100,00 10% 10,00 110,00
2
3
7DEHOD\ufffd\ufffd
\ufffd\ufffd3DVVR\ufffd\ufffdDWHQomR\ufffdDTXL\ufffdp\ufffdR\ufffdSRQWR\ufffdSULQFLSDO\ufffdGRV\ufffdMXURV\ufffdVLPSOHV\ufffd\ufffd2\ufffdVDOGR\ufffdLQLFLDO\ufffdGR\ufffdSUy[LPR\ufffdSHUtRGR\ufffdFRQWLQXD\ufffdVHQGR\ufffd5\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd
SRLV\ufffdQRV\ufffdMXURV\ufffdVLPSOHV\ufffdR\ufffdMXURV\ufffdVy\ufffdLQFLGH\ufffdVREUH\ufffdR\ufffd9DORU\ufffd3UHVHQWH\ufffd\ufffd39\ufffd\ufffd
Mês PV (R\$) i Juros (R\$) Saldo Final (FV)
1 100,00 10% 10,00 110,00
2 100,00 10%
3
7DEHOD\ufffd\ufffd
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-XURV\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd[\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd
6DOGR\ufffd)LQDO\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffdOHPEUDQGR\ufffdTXH\ufffdVH\ufffdGHYH\ufffdVRPDU\ufffdR\ufffdVDOGR\ufffd¿\ufffdQDO\ufffdGR\ufffdSHUtRGR\ufffdDQWHULRU\ufffdFRP\ufffdRV\ufffdMXURV\ufffd\ufffd
PORDENTRODOTEMA
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Mês PV (R\$) i Juros (R\$) Saldo Final (FV)
1 100,00 10% 10,00 110,00
2 100,00 10% 10,00 120,00
3
+
=
7DEHOD\ufffd\ufffd
\ufffd\ufffd3DVVR\ufffd\ufffd)LQDOL]DU\ufffdD\ufffdRSHUDomR\ufffd\ufffdUHSHWLQGR\ufffdRV\ufffdFiOFXORV\ufffd
Mês PV (R\$) i Juros (R\$) Saldo Final (FV)
1 100,00 10% 10,00 110,00
2 100,00 10% 10,00 120,00
3 100,00 10% 10,00 130,00
7DEHOD\ufffd\ufffd
9DOH\ufffdUHVVDOWDU\ufffdTXH\ufffdR\ufffdUHJLPH\ufffdGH\ufffdFDSLWDOL]DomR\ufffdVLPSOHV\ufffdp\ufffdXPD\ufffdIXQomR\ufffdOLQHDU\ufffd\ufffdRX\ufffdVHMD\ufffd\ufffdGH\ufffd\ufffd\ufffdJUDX\ufffd\ufffd2\ufffdYDORU\ufffdIXWXUR\ufffdp\ufffdIRUPDGR
SHOD\ufffdVRPDWyULD\ufffdGR\ufffdYDORU\ufffdSULQFLSDO\ufffd\ufffd39\ufffd\ufffd\ufffd\ufffd*,0(1(6\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffdS\ufffd\ufffd\ufffd\ufffd
PORDENTRODOTEMA
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'HVWD\ufffdPDQHLUD\ufffdWHUHPRV\ufffdDV\ufffdSULPHLUDV\ufffdIyUPXODV\ufffdGRV\ufffdMXURV\ufffdVLPSOHV\ufffd
)9\ufffd \ufffd39\ufffd\ufffd\ufffd\ufffd\ufffd\ufffdQ\ufffd\ufffd\ufffdL\ufffd
FV\ufffd \ufffd9DORU\ufffd)XWXUR\ufffdRX\ufffd0RQWDQWH\ufffd
PV\ufffd \ufffd9DORU\ufffd3UHVHQWH\ufffd
n \ufffdSUD]R\ufffd\ufffd\ufffdWHPSR\ufffd
i\ufffd \ufffdWD[D\ufffdGH\ufffdMXURV\ufffd\ufffd\ufffd\ufffd\ufffd
3RGHPRV\ufffdWDPEpP\ufffdGHGX]LU\ufffdXPD\ufffdVHJXQGD\ufffdIyUPXOD\ufffdTXH\ufffdp\ufffdPDLV\ufffdHVSHFt¿\ufffdFD\ufffd\ufffdQD\ufffdTXDO\ufffdSRGHPRV\ufffdFDOFXODU\ufffdR\ufffdYDORU\ufffdGRV\ufffd-XURV\ufffd\ufffd-\ufffd\ufffd
-\ufffd \ufffd39\ufffd\ufffd\ufffdL\ufffd\ufffd\ufffdQ
J\ufffd \ufffd-XURV\ufffd\ufffd5\ufffd\ufffd\ufffd
PV \ufffd&DSLWDO\ufffdRX\ufffd9DORU\ufffd3UHVHQWH\ufffd
n\ufffd \ufffdSUD]R\ufffd\ufffd\ufffdWHPSR\ufffd
i\ufffd \ufffdWD[D\ufffdGH\ufffdMXURV\ufffd\ufffd\ufffd\ufffd\ufffd
5HVROXomR\ufffdGR\ufffdH[HPSOR\ufffdSHOD\ufffdIyUPXOD\ufffd
8PD\ufffdSHVVRD\ufffdWRPRX\ufffdXP\ufffdHPSUpVWLPR\ufffdGH\ufffd5\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffdQXP\ufffdEDQFR\ufffd\ufffdSHOR\ufffdSUD]R\ufffdGH\ufffdWUrV\ufffdPHVHV\ufffd\ufffdFRP\ufffdXPD\ufffdWD[D\ufffdGH\ufffd\ufffd\ufffd\ufffd\ufffdDR\ufffdPrV\ufffd\ufffd
QR\ufffdUHJLPH\ufffdGH\ufffdjuros simples\ufffd\ufffd'HWHUPLQH\ufffdR\ufffdVDOGR\ufffd¿\ufffdQDO\ufffdDFXPXODGR\ufffd
\ufffd\ufffdSDVVR\ufffd\ufffdFROHWD\ufffdGH\ufffdGDGRV\ufffdGR\ufffdHQXQFLDGR\ufffd
39\ufffd \ufffd5\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd
Q\ufffd \ufffd\ufffd\ufffdPHVHV\ufffd
L\ufffd \ufffd\ufffd\ufffd\ufffd\ufffdDR\ufffdPrV\ufffd
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PORDENTRODOTEMA
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