Matematica finanziaria

Set domande: matematica finanziaria economia

7IX(SQERHI0$7(0$7,&$),1$1=,$5,$(&2120,$ '0(SGIRXI/D]]DULQL3DRORSet Domande: Matematica finanziaria economia (D.M. 270/04)Docente: Lazzarini Paolo

Indice

• Indice Lezioni .......................................................................................................................... p. 2
• Lezione 004 ............................................................................................................................. p. 4
• Lezione 005 ............................................................................................................................. p. 6
• Lezione 006 ............................................................................................................................. p. 7
• Lezione 007 ............................................................................................................................. p. 9
• Lezione 008 ............................................................................................................................. p. 10
• Lezione 009 ............................................................................................................................. p. 11
• Lezione 010 ............................................................................................................................. p. 12
• Lezione 011 ............................................................................................................................. p. 13
• Lezione 012 ............................................................................................................................. p. 15
• Lezione 013 ............................................................................................................................. p. 18
• Lezione 014 ............................................................................................................................. p. 19
• Lezione 015 ............................................................................................................................. p. 20
• Lezione 016 ............................................................................................................................. p. 21
• Lezione 017 ............................................................................................................................. p. 24
• Lezione 018 ............................................................................................................................. p. 25
• Lezione 019 ............................................................................................................................. p. 26
• Lezione 021 ............................................................................................................................. p. 27
• Lezione 022 ............................................................................................................................. p. 28
• Lezione 024 ............................................................................................................................. p. 31
• Lezione 025 ............................................................................................................................. p. 33
• Lezione 026 ............................................................................................................................. p. 35
• Lezione 027 ............................................................................................................................. p. 36
• Lezione 028 ............................................................................................................................. p. 38
• Lezione 030 ............................................................................................................................. p. 39
• Lezione 031 ............................................................................................................................. p. 40
• Lezione 032 ............................................................................................................................. p. 43
• Lezione 033 ............................................................................................................................. p. 45
• Lezione 034 ............................................................................................................................. p. 47
• Lezione 035 ............................................................................................................................. p. 48
• Lezione 038 ............................................................................................................................. p. 50
• Lezione 039 ............................................................................................................................. p. 51
• Lezione 040 ............................................................................................................................. p. 52
• Lezione 043 ............................................................................................................................. p. 53
• Lezione 044 ............................................................................................................................. p. 55
• Lezione 045 ............................................................................................................................. p. 57
• Lezione 047 ............................................................................................................................. p. 58
• Lezione 048 ............................................................................................................................. p. 59

Paniere completo di matematica finanziaria 26 - 2/78Set Domande: Matematica finanziaria economia (D.M. 270/04)Docente: Lazzarini Paolo

Lezione 004

/H]LRQH 4XDOªLOIDWWRUHGLPRQWDQWHFKHFDUDWWHUL]]DODFDSLWDOL]]D]LRQHDLQWHUHVVHVHPSOLFH"9 /DIXQ]LRQH GHILQLVFHXQDOHJJHGLFDSLWDOL]]D]LRQH4XDOH"'ETMXEPM^^E^MSRIEMRXIVIWWIERXMGMTEXS'ETMXEPM^^E^MSRIGSQTSWXE'ETMXEPM^^E^MSRIGSRXMRYE'ETMXEPM^^E^MSRIWIQTPMGI'ETMXEPM^^E^MSRIWIQTPMGI /DIXQ]LRQH GHILQLVFHXQDOHJJHGLFDSLWDOL]]D]LRQH4XDOH"'ETMXEPM^^E^MSRIEMRXIVIWWIERXMGMTEXS'ETMXEPM^^E^MSRIWIQTPMGI'ETMXEPM^^E^MSRIGSQTSWXE'ETMXEPM^^E^MSRIGSQTSWXE'ETMXEPM^^E^MSRIGSRXMRYE &DOFRODUHQHOUHJLPHGHOO୩LQWHUHVVHVHPSOLFHO୩LQWHUHVVHGLHXURLPSLHJDWLSHUDQQLDOWDVVRDQQXRL &DOFRODUHQHOUHJLPHGHOO୩LQWHUHVVHVHPSOLFHO୩LQWHUHVVHGLHXURLPSLHJDWLSHUDQQLHPHVLDOWDVVRDQQXRL &DOFRODUHQHOUHJLPHGHOO୩LQWHUHVVHVHPSOLFHO୩LQWHUHVVHGLHXURLPSLHJDWLSHUDQQLPHVLHJLRUQLDOWDVVRDQQXRL Paniere completo di matematica finanziaria 26© - 4/78Set Domande: Matematica finanziaria economia (D.M. 270/04)Docente: Lazzarini PaoloGHILQLVFHXQDOHJJHGLFDSLWDOL]]D]LRQH4XDOH" /DIXQ]LRQH'ETMXEPM^^E^MSRIEMRXIVIWWIERXMGMTEXS'ETMXEPM^^E^MSRIEMRXIVIWWIERXMGMTEXS'ETMXEPM^^E^MSRIWIQTPMGI'ETMXEPM^^E^MSRIGSQTSWXE'ETMXEPM^^E^MSRIGSRXMRYE 3HUTXDQWRWHPSRVLGHYHLPSLHJDUHODVRPPD& HXURSHUSURGXUUHXQPRQWDQWH0SDULDHXURQHOO୩LSRWHVLGLXQWDVVRDQQXRGLLQWHUHVVHVHPSOLFHL "ERRMIQIWMERRMIQIWMERRMIQIWMERRMIQIWMERRMIQIWMࡵ(࢚) = ࡯ כ ࢏ כ ࢚ ՜ ࡵ(࢚) = ૜૟૞૙ כ ૙, ૙૛૜ כ ૢ = ૠ૞૞, ૞૞ ࡵ(࢚) = ࡯ כ ࢏ כ ࢚7XWWDYLD SRLFKp W q HVSUHVVR LQ DQQL RFFRUUH WUDVIRUPDUH W LQ DQQL WHQHQGR SUHVHQWH FKH ૞ ૞= ૠ + .PHVLFRUULVSRQGRQRD GLDQQR'LFRQVHJXHQ]D࢚૚૛ ૚૛૞ࡵ(࢚) = ૜૟૞૙ כ ቀૠ + ቁ כ ૙, ૙૛૜ = ૟૛૛, ૟૜3HUWDQWR ૚૛ࡵ(࢚) = ࡯ כ ࢏ כ ࢚7XWWDYLD SRLFKp W q HVSUHVVR LQ DQQL RFFRUUH WUDVIRUPDUH W LQ DQQL WHQHQGR SUHVHQWH FKH ૞ ૛૙GLDQQLHFKHJLRUQLFRUULVSRQGRQRD GLDQQR±SUHQGHQGRLQPHVLFRUULVSRQGRQRD ૚૛ ૜૟૙૞ ૛૙࢚ = ૠ + + .FRQVLGHUD]LRQHO¶DQQRFRPPHUFLDOH'LFRQVHJXHQ]D ૚૛ ૜૟૙૞ ૛૙+ ቁ כ ૙, ૙૛૜ = ૟૛ૠ, ૛ૢࡵ(࢚) = ૜૟૞૙ כ ቀૠ +3HUWDQWR ૚૛ ૜૟૙ 3RVWRFKH ࡹെ࡯ ૛࡯ െ ࡯ ૟૙૙ െ ૜૙૙࢚ = = = = ૚૛, ૞࡯כ࢏ ࡯כ࢏ ૟૙૙ כ ૙, ૙ૡ2YYHURDQQLHPHVLPaniere completo di matematica finanziaria 26 - 5/78Set Domande: Matematica finanziaria economia (D.M. 270/04)Docente: Lazzarini Paolo

Lezione 005

/H]LRQH ,QTXDQWRWHPSRUDGGRSSLDXQFDSLWDOHSDULDLPSLHJDWRLQFDSLWDOL]]D]LRQHVHPSOLFHVHLOWDVVRDQQXRG୩LQWHUHVVHDSSOLFDWRªGHO"ERRMERRMERRM'MVGEERRMERRM 4XDOªODIRUPXODSHULOWHPSRWLQIXQ]LRQHGL0&LULFDYDELOHGDOODIRUPXODSHULOPRQWDQWHLQFDSLWDOL]]D]LRQHDLQWHUHVVHVHPSOLFH" 4XDOªODIRUPXODSHULOWHPSRWLQIXQ]LRQHGL0&LULFDYDELOHGDOODIRUPXODSHULOPRQWDQWHLQFDSLWDOL]]D]LRQHDLQWHUHVVHFRPSRVWR" ,QTXDQWRWHPSRUDGGRSSLDXQFDSLWDOHSDULDLPSLHJDWRLQFDSLWDOL]]D]LRQHVHPSOLFHVHLOWDVVRDQQXRG୩LQWHUHVVHDSSOLFDWRªGHO"6FULYLO HTXD]LRQHFKHFRQGXFHDOODVROX]LRQHࡹି࡯ ૛ࡹି࡯ ૛כ૚૙૙ି૚૙૙࢚ = = = = ૚૙ ࡯כ࢏ ࡯כ࢏ ૚૙૙כ૙,૚૙ 3RVWRFKH ࡹ (࢚) = ࡯ ( ૚ + ࢏ כ ࢚)ࡹି࡯W = ࡯כ࢏ 3RVWRFKH ࢚ 0 W = ࡯ (૚ + ࢏)ࡹ ࡹ࢚ ࢚= (૚ + ࢏) GDFXLDSSOLFDQGRLORJDULWPL HDSSOLFDQGRODSURSULHWjGHLORJDULWPL՜ ࢒࢔ = ࢒࢔ (૚ + ࢏)࡯ ࡯VHFRQGRFXLLOORJDULWPRGLXQDSRWHQ]DqXJXDOHDOO¶HVSRQHQWHSHULOORJGHOODEDVHHFKHLOORJGLXQUDSSRUWRqSDULDOODGLIIHUHQ]DGHLORJ՜ (ࡹ) (࡯) (૚࢒࢔ െ ࢒࢔ = ࢚ ࢒࢔ + ࢏), ࢊࢇ ࢉ࢛࢏:࢒࢔ ࡹି࢒࢔ ࡯W = ࢒࢔ (૚ା࢏) 3RVWRFKH ࡹെ࡯ ૛࡯ െ ࡯ ૛ כ ૚૛૙ െ ૚૛૙࢚ = = = = ૛૙࡯כ࢏ ࡯כ࢏ ૚૛૙ כ ૙, ૙૞Paniere completo di matematica finanziaria 27 - 6/78Set Domande: Matematica finanziaria economia (D.M. 270/04)Docente: Lazzarini Paolo

Lezione 006

/H]LRQH ,QYHVWHQGRHXURSHUDQQLRWWHQJRHXUR4XDOHWDVVRDQQXRGLLQWHUHVVHFRPSRVWRªVWDWRSUDWLFDWR" &DOFRODUHQHOUHJLPHGHOO୩LQWHUHVVHFRPSRVWRO୩LQWHUHVVHGLHXURLPSLHJDWLSHUDQQLPHVLHJLRUQLDOWDVVRDQQXRL 4XDOªODIRUPXODLQFDSLWDOL]]D]LRQHFRPSRVWDSHULOPRQWDQWH0DPHVLGLXQFDSLWDOH&DOWDVVRDQQXRL"9 4XDOªLOYDORUHRJJLGLHXURGLVSRQLELOHWUDPHVLQHOUHJLPHGHOORVFRQWRVHPSOLFHDOWDVVRDQQXRG୩LQWHUHVVHL " 4XDOªODIRUPXODSHULOWHPSRWLQIXQ]LRQHGL0&LULFDYDELOHGDOODIRUPXODSHULOPRQWDQWHLQFDSLWDOL]]D]LRQHDLQWHUHVVHFRPSRVWR"92IWWYREHIPPITVIGIHIRXM Paniere completo di matematica finanziaria 28 - 7/78Set Domande: Matematica finanziaria economia (D.M. 270/04)Docente: Lazzarini Paolo

4XDOªLOPRQWDQWHDGXHDQQLLQFDSLWDOL]]D]LRQHFRPSRVWDGLXQHXURDOWDVVRDQQXRG୩LQWHUHVVHL " 4XDOªLOYDORUHRJJLGLHXURGLVSRQLELOHWUDPHVLQHOUHJLPHGHOORVFRQWRFRPSRVWRDOWDVVRG୩LQWHUHVVHL " 4XDOªLOPRQWDQWHDPHVLGLHXURDOWDVVRG୩LQWHUHVVHFRPSRVWRL " &DOFRODUHSHUTXDQWRWHPSRVLGHYHLPSLHJDUHODVRPPD& HXURDOWDVVRDQQXRGLLQWHUHVVHFRPSRVWRL SHUSURGXUUHLOPRQWDQWH0 HXUR 8QFDSLWDOH& HXURLPSLHJDWRSHUDQQLLQFDSLWDOL]]D]LRQHFRPSRVWDSURGXFHXQPRQWDQWH0 HXUR'HWHUPLQDUHLOWDVVRDQQXRG୩LQWHUHVVHFRPSRVWRL 8QFDSLWDOH& HXURLPSLHJDWRSHUDQQLLQFDSLWDOL]]D]LRQHVHPSOLFHSURGXFHXQPRQWDQWH0 HXUR'HWHUPLQDUHLOWDVVRTXDGULPHVWUDOHG୩LQWHUHVVHVHPSOLFHL 8QFDSLWDOH& HXURLPSLHJDWRSHUDQQLLQFDSLWDOL]]D]LRQHVHPSOLFHSURGXFHXQPRQWDQWH0 HXUR'HWHUPLQDUHLOWDVVRVHPHVWUDOHG୩LQWHUHVVHVHPSOLFHL ࡹ ૞.૝૞૙૝࢚ ටට࢏ = െ ૚ െ ૚ == ૙, ૙૛૚ૠૡ࡯ ૞.૙૙૙ 3RVWRFKH, W 0 W ±& W VLKDFKH૞ ૛૙W + = ૠ, ૝ૠ૛૛૚૛ ૜૟૙࢚ ૠ,૝ૠ૛૛, [࡯(૚ ] [૜૟૞૙(૚ ]+ ࢏) െ ࡯ = + ૙, ૙૛૜) െ ࡯ = ૝. ૜૛૞, ૢૢ, ± ૚ 3RVWRFKH࡭ = ࡿ ૚ା࢏࢚ ૚ ૚HFKHW VLKD࡭ = ૚ = = ૙. ૢ૞ૡ૝ૠ૚ା(૙,૙૛כ ૛,૚૟૟ૠ) ૚,૙૝૜૜૜࢚ ૛ 3RVWRFKH0 W [࡯(૚ ], ࢙࢏ ࢎࢇ: ࡹ = ૚((૚ + ૙, ૙ૠ) = ૚, ૚૝ૢૢ+ ࢏) Paniere completo di matematica finanziaria 28 - 8/78࢚ ૛ 3RVWRFKH0 W [࡯(૚ ], = ૚, ૚૝ૢૢ࢙࢏ ࢎࢇ: ࡹ = ૚((૚ + ૙, ૙ૠ)+ ࢏)૚ ૚3RVWRFKH$ ࡿ , ࢙࢏ ࢎࢇ: ࡭ = ૚ = ૙, ૢ૟૟૚૚૝૚ା࢏࢚ ૚ା(૙,૙૜כ )૚૛ ૚૜ ࢚3RVWRFKH0 W [࡯(૚+࢏) ],࢙࢏ ࢎࢇ:ࡹ=૚૛૙((૚+૙,૙૝) =૚૛૞,૛૚૚૛ dĂƐƚŽlogƐƵůůĂܔܗ܏ ૛૙૙૙ି ܔܗ܏ ૚૙૙૙ܔܗ܏ࡹି ܔܗ܏࡯ = = ૜૞, ૙૙3RVWRFKH࢚= ܔܗ܏(૚ା࢏) ܔܗ܏(૚ା૙.૙૛) ĐĂůĐŽůĂƚƌŝĐĞࡹ ૚ૠ૙૙࢚ ૝ 3RVWRFKH࢏ ටට= െ ૚, ࢙࢏ ࢎࢇ ࢉࢎࢋ: ࢏ = െ ૚ = ૙. ૙૚૞૛ૠ࡯ ૚૟૙૙ ࡹି࡯ 3RVWRFKHQHOUHJLPHILQDQ]LDULRGHOO¶,QWHUHVVH6HPSOLFH࢏ = , ࢙࢏ ࢎࢇ ࢉࢎࢋ࡯࢚૚ૡ૙૙ െ ૚૟૙૙࢏ = = ૙, ૙૜૚૛૞.૚૟૙૙ כ ૝૚ ૚'DWRFKH ࢏ = ࢏ , ࢙࢏ ࢎࢇ ࢉࢎࢋ ࢏ = ૙, ૙૜૚૛૞ = ૙, ૙૚૙૝૚૜ ࢇ ૜૜ ૜ ࡹି࡯ , ࢙࢏ ࢎࢇ ࢉࢎࢋ3RVWRFKHQHOUHJLPHILQDQ]LDULRGHOO¶,QWHUHVVH6HPSOLFH࢏= ࡯࢚૚ૠ૙૙ି૚૟૙૙࢏ = ૙, ૙૚૞૟૛૞.= ૚૟૙૙כ૝૚ ૚'DWRFKH࢏ = ࢏ , ࢙࢏ ࢎࢇ ࢉࢎࢋ ࢏ = ૙, ૙૚૞૟૛૞ = ૙, ૙૙ૠૡ૚૛૞૛ ࢇ ૛૛ ૛ Set Domande: Matematica finanziaria economia (D.M. 270/04)Docente: Lazzarini Paolo

Lezione 007

/H]LRQH &RVDSXRLGLUHFRQIURQWDQGR LOPRQWDQWH0 W UHODWLYRDOODFDSLWDOL]]D]LRQHVHPSOLFH W UHODWLYRDOODFDSLWDOL]]D]LRQHFRPSRVWD LOPRQWDQWH0 0 W !0 W SHUW! 00 W 00 W SHUW! 0 W PDJJLRUHRSSXUHXJXDOHD0 W TIVSKRMW 0 W PLQRUHRSSXUHXJXDOHD0 W TIVSKRMW 8QFDSLWDOH&LPSLHJDWRSHUGXHDQQLIRUQLVFHORVWHVVRPRQWDQWH0VLDVHLQYHVWLWRLQFDSLWDOL]]D]LRQHVHPSOLFHVLDVHLQYHVWLWRLQFDSLWDOL]]D]LRQHFRPSRVWD,QGLFDQGRULVSHWWLYDPHQWHFRQL HFRQL LOWDVVRVHPSOLFHHTXHOORFRPSRVWRTXDOHGHOOHVHJXHQWLDIIHUPD]LRQLªYHUD"V F9 Paniere completo di matematica finanziaria 28 - 9/78Set Domande: Matematica finanziaria economia (D.M. 270/04)Docente: Lazzarini Paolo

Lezione 008

/H]LRQH /DVRPPDQRPLQDOH6 HXURªGLVSRQLELOHWUDXQDQQR FLRªLQW HGLOVXRYDORUHDWWXDOHª$ HXUR4XDOªLOWDVVRGLVFRQWRDSSOLFDWRLQFV" ,OYDORUHDWWXDOHGLHXURGLVSRQLELOLWUDDQQLPHVLHJLRUQLªHXUR4XDOªLOWDVVRG୩LQWHUHVVHFKHªVWDWRDSSOLFDWRLQFV" &RVDVLJQLILFDFKHXQIDWWRUHGLPRQWDQWHI W HXQIDWWRUHGLVFRQWRJ W VRQRFRQLXJDWL"9 4JHOJGJDBDIFVOPÒJMSFDJQSPDPEFMMhBMUSPࡿ ࡿ ࡿ ࡿି࡭ ૚૙૙ିૡૠ 3RVWRFKH࡭ (૚՜ + ࢏࢚) = ՜ ࢏࢚ = െ ૚ ՜ ࢏ = ՜࢏ = = ૙, ૚૝ૢ૝૜= ࡭࢚ ૡૠכ૚૚ା࢏࢚ ࡭ ࡭࢏ ૙,૚૝ૢ૝૜HGDWRFKHG = ࢙࢏ ࢎࢇ: ࢊ = = ૙, ૚૜૙૙૚ା࢏ ૚ା૙,૚૝ૢ૝૜ࡿ ࡿ ࡿ ࡿି࡭ ૚૙૙૙૙ିૠ૛૙૙ 3RVWRFKH࡭ (૚= ՜ + ࢏࢚) = ՜ ࢏࢚ = െ ૚ ՜ ࢏ = ՜࢏ =૚ା࢏࢚ ࡭ ࡭ ࡭࢚ ૠ૛૙૙כ࢚૜ ૛૙'DWRFKH࢚ = ૜ + + = ૜, ૜૙૞૞, ࢙࢏ ࢎࢇ:૚૛ ૜૟૙ ૚૙૙૙૙ െ ૠ૛૙૙࢏ = = ૙, ૚૚ૠ૟૞ૠ૛૙૙ כ ૜, ૜૙૞૞ Paniere completo di matematica finanziaria 28© - 10/78Set Domande: Matematica finanziaria economia (D.M. 270/04)Docente: Lazzarini Paolo

Lezione 009

/H]LRQH 4XDOªODIXQ]LRQHJ W FKHGHILQLVFHLOIDWWRUHGHOORVFRQWRFRPSRVWR"9 ,OYDORUHDWWXDOHGLHXURGLVSRQLELOLWUDDQQLPHVLHJLRUQLªHXUR4XDOªLOWDVVRGLVFRQWRFKHªVWDWRDSSOLFDWRLQFF" ,OYDORUHDWWXDOHGLHXURGLVSRQLELOLWUDDQQLPHVLHJLRUQLªHXUR4XDOªLOWDVVRG୩LQWHUHVVHFKHªVWDWRDSSOLFDWRLQFF" ,QTXDQWRWHPSRUDGGRSSLDXQFDSLWDOHSDULDLPSLHJDWRLQFDSLWDOL]]D]LRQHFRPSRVWDVHLOWDVVRDQQXRG୩LQWHUHVVHDSSOLFDWRªGHO"ERRMERRMGMVGEERRMGMVGEERRMGMVGEERRM ,QTXDQWRWHPSRUDGGRSSLDXQFDSLWDOHSDULDLPSLHJDWRLQFDSLWDOL]]D]LRQHFRPSRVWDVHLOWDVVRDQQXRG୩LQWHUHVVHDSSOLFDWRªGHO"6FULYLHULVROYLMhFRVB[JPOFDIFDPOEVDFBMMBTPMV[JPOFࡿ ࡿ ࡿ ࡿ࢚࢚ ࢚ 3RVWRFKH࡭ (૚ ට= ՜ + ࢏) = ՜ ࢏ = െ ૚ ՜ ࢏ = െ ૚, ࢙࢏ ࢎࢇ:࢚(૚ା࢏) ࡭ ࡭ ࡭૜,૜૙૞૞ ૚૙૙૙૙ ࢏ ૙,૚૙૝૝ૢHVDSHQGRFKHLQFFࢊ VLKDFKHࢊට࢏ = െ ૚ = ૙, ૚૙૝૝ૢ = = = ૙, ૙ૢ૝૟૙ૠ૛૙૙ ૚ା࢏ ૚ା૙,૚૙૝૝ૢܔܗ܏ ࡹି ܔܗ܏ ࡯ ܔܗ܏ ૛૙૙ି ܔܗ܏ ૚૙૙ 3RVWRFKH࢚ , ࢙࢏ ࢎࢇ: = ૠ, ૛ૠ૛૞= ܔܗ܏(૚ା࢏) ܔܗ܏(૚ା૙.૚)࢒࢕ࢍ ࡹି ࢒࢕ࢍ ࡯ ࢒࢕ࢍ ૛૝૙ି ࢒࢕ࢍ ૚૛૙ 3RVWRFKH࢚ = , ࢙࢏ ࢎࢇ: = ૚૝, ૛૙૟ૠ࢒࢕ࢍ(૚ା࢏) ࢒࢕ࢍ(૚ା૙.૙૞) ࢇ࢔࢔࢏ ࢇ࢔࢔࢏ ࢓ࢋ࢙࢏2YYHUR࢚ (૙, (૙,+ ૛૙૟ૠ) כ ૚૛ = ૚૝ + ૛ + ૝ૡ) כࢇ࢔࢔࢏ + ࢟ כ ૚૛࢓ࢋ࢙࢏ + ࢟ כ ૜૙ࢍ࢏࢕࢘࢔࢏ = ૚૝ࢇ࢔࢔࢏ ࢓ࢋ࢙࢏ ࢍ࢏࢕࢘࢔࢏ ૜૙ = ૚૝ + ૛ + ૚૝ Paniere completo di matematica finanziaria 29 - 11/78Set Domande: Matematica finanziaria economia (D.M. 270/04)Docente: Lazzarini Paolo

Lezione 010

/H]LRQH &RVDVLSX´GLUHGHOJUDILFRGHOIDWWRUHGLPRQWDQWHI W UHODWLYRDOODFDSLWDOL]]D]LRQHDLQWHUHVVHVHPSOLFH"«YRKVEJMGSMTIVFSPMGS«YRETEVEFSPE«YREVIXXE«YREWIQMVIXXE«YREWIQMVIXXE Paniere completo di matematica finanziaria 29 - 12/78Set Domande: Matematica finanziaria economia (D.M. 270/04)Docente: Lazzarini P