Introdu o a Matem tica Financeira

■♥tr♦❞✉çã♦ à ♠❛t❡♠át✐❝❛ ✜♥❛♥❝❡✐r❛
❊st❡❧❛ ▼❛r❛ ❞❡ ❖❧✐✈❡✐r❛ ✶ ❡
❙ô♥✐❛ ❘❡❣✐♥❛ ▲❡✐t❡ ●❛r❝✐❛ ✭❖r✐❡♥t❛❞♦r❛✮✷

◆♦ r❡❣✐♠❡ ❞❡ ❥✉r♦s s✐♠♣❧❡s✱ s❡ i é ❛ t❛①❛ ❞❡ ❥✉r♦s
♣♦r ✉♥✐❞❛❞❡ ❞❡ t❡♠♣♦ ✭♣♦r ❡①❡♠♣❧♦✱ ♣♦r ❞✐❛✱ ♦✉ ♣♦r
♠ês✱ ♦✉ ♣♦r ❛♥♦✮ ❡ t é ♦ ♥ú♠❡r♦ ❞❡ ✉♥✐❞❛❞❡s ❞❡ t❡♠♣♦ q✉❡ ❞✉r♦✉ ❛ ❛♣❧✐❝❛çã♦✱ ❡♥tã♦✿

✶ ■♥st✐t✉t♦ ❞❡ ▼❛t❡♠át✐❝❛ ❡ ❊st❛tíst✐❝❛ ❞❛ ❯♥✐✈❡rs✐❞❛❞❡ ❞❡
❙ã♦ P❛✉❧♦ ✭■▼❊✲❯❙P✮✱ ❇r❛③✐❧

❡st❡❧❛✐♠❡❅❤♦t♠❛✐❧✳❝♦♠

✷ ■♥st✐t✉t♦ ❞❡ ▼❛t❡♠át✐❝❛ ❡ ❊st❛tíst✐❝❛ ❞❛ ❯♥✐✈❡rs✐❞❛❞❡ ❞❡

J
VF

❙ã♦ P❛✉❧♦ ✭■▼❊✲❯❙P✮✱ ❇r❛③✐❧

s♦♥✐❛❅✐♠❡✳✉s♣✳❜r

✏❙❛✐❜❛ q✉❡ sã♦ s✉❛s ❞❡❝✐sõ❡s ❡ ♥ã♦ s✉❛s ❝♦♥❞✐çõ❡s q✉❡ ❞❡t❡r♠✐♥❛♠ s❡✉ ❞❡st✐♥♦✑

❆♥t❤♦♥② ❘♦❜❜✐♥s
❞♦ ❧✐✈r♦ ❉❡s♣❡rt❡ ♦ ❣✐❣❛♥t❡ ✐♥t❡r✐♦r
✶✳

✭❏✉r♦s✮
✭❱❛❧♦r ❋✐♥❛❧✮✳

✷✳ ❆♣❧✐❝♦✉✲s❡ R$ 200, 00 ❛ ❥✉r♦s s✐♠♣❧❡s
♣♦r ✉♠ ♣❡rí♦❞♦ ❞❡ ✸ ♠❡s❡s✱ ❝♦♠ t❛①❛ ❞❡ ❥✉r♦s ❞❡ 2%
❛s ♠ês✳ ◗✉❛❧ ♦ ✈❛❧♦r q✉❡ ❢♦✐ r❡s❣❛t❛❞♦ ♥♦ ✜♥❛❧ ❞♦
♣❡rí♦❞♦ ❞❡ ❛♣❧✐❝❛çã♦❄

❊①❡♠♣❧♦

❙♦❧✉çã♦✿

V P = 200, 00

■♥tr♦❞✉çã♦

P❡rí♦❞♦ ❞❡ ❛♣❧✐❝❛çã♦ = t = 3 ♠❡s❡s
❚❛①❛ ❞❡ ❥✉r♦s = i = 2% ❛♦ ♠ês

◆❡st❡ tr❛❜❛❧❤♦ ✈❛♠♦s ❞✐s❝✉t✐r ❛❧❣✉♥s ♣♦♥t♦s ❞❡ ♠❛✲ t❡♠át✐❝❛ ✜♥❛♥❝❡✐r❛✱ t❛✐s ❝♦♠♦ ❛ ❞✐❢❡r❡♥ç❛ ❡♥tr❡ ❥✉r♦s s✐♠♣❧❡s ❡ ❥✉r♦s ❝♦♠♣♦st♦s ✭✐♥❝❧✉s✐✈❡ ❝♦♥tí♥✉♦s✮✱ ❞❡s✲
❝♦♥t♦s ❡ ✢✉①♦ ❞❡ ❝❛✐①❛✳ ❊♠ ♣❛rt✐❝✉❧❛r✱ ❛♣r❡s❡♥t❛♠♦s
❛q✉✐ ❞✐❝❛s ❞❡ ❝♦♠♦ ❢❛③❡r ✉♠ ✢✉①♦ ❞❡ ❝❛✐①❛ ♣❛r❛ ✉♠❛
♣❡ss♦❛ ❢ís✐❝❛✳ ❋♦r❛♠ ❝♦♥s✉❧t❛❞♦s ❬✺❪✱ ❬✶❪✱ ❬✷❪✱ ❬✸❪ ❡ ❬✹❪✳
✷✳

= V P.i.t
= VP +J

2% = 2/100 = 0, 02
J
J
VF
VF

❏✉r♦s

✶✳ ❏✉r♦
➱ ♦ ❣❛♥❤♦ q✉❡ ♦❜t❡♠♦s ❛♦ ❢❛③❡r♠♦s ✉♠❛ ❛♣❧✐❝❛çã♦
❞❡ ♠♦❞♦ ♣r♦❞✉t✐✈♦✱ ❡ s❡✉ ❝á❧❝✉❧♦ é ❢❡✐t♦ ❛tr❛✈és ❞❛
❞✐❢❡r❡♥ç❛ ❡♥tr❡ ♦ ✈❛❧♦r ❢✉t✉r♦ ❡ ♦ ✈❛❧♦r ♣r❡s❡♥t❡ ❞♦
❝❛♣✐t❛❧ ❛♣❧✐❝❛❞♦✳
❱❛❧♦r ♣r❡s❡♥t❡ ❂ ❝❛♣✐t❛❧ ✐♥✐❝✐❛❧ ✭q✉❛♥t✐❛ q✉❡ s❡rá
❛♣❧✐❝❛❞❛✮
❱❛❧♦r ❢✉t✉r♦ ❂ ✈❛❧♦r ❛ s❡r r❡s❣❛t❛❞♦ ❛♣ós ♦ ♣❡✲ rí♦❞♦ ❞❡ t❡♠♣♦ ❡♠ q✉❡ ♦ ✈❛❧♦r ♣r❡s❡♥t❡ ❢♦✐ ❛♣❧✐❝❛❞♦
✭❝❤❛♠❛❞♦ ♣❡rí♦❞♦ ❞❛ ❛♣❧✐❝❛çã♦✮✳
❉❡✜♥✐çã♦ ✷✳ ❚❛①❛ ❞❡ ❏✉r♦s
➱ ❛ r❡❧❛çã♦ ❡♥tr❡ ❥✉r♦s ❡ ❝❛♣✐t❛❧ ❛♣❧✐❝❛❞♦ ♥✉♠❛
✉♥✐❞❛❞❡ ❞❡ t❡♠♣♦ ✭♣♦r ❡①❡♠♣❧♦✱ ♥✉♠ ❞✐❛✱ ♦✉ ♥✉♠
♠ês✱ ♦✉ ♥✉♠ ❛♥♦✮✳
❊①❡♠♣❧♦ ✶✳ ❙❡ ❛♦ ❛♣❧✐❝❛r♠♦s ✉♠❛ q✉❛♥t✐❛ x ♣♦r ✉♠
❛♥♦ ♦❜t✐✈❡r♠♦s 0, 12x ❞❡ ❥✉r♦s ❛♣ós ❡ss❡ ♣❡rí♦❞♦ ❞❡ t❡♠♣♦✱ ❛ t❛①❛ ❞❡ ❥✉r♦s ❝♦rr❡s♣♦♥❞❡♥t❡ ♣♦r ❛♥♦ é ❞❡
(0,