Question

Urgente! Sobre Juros compostos, preciso ajuda para solucionar esses exercícios o 21,22,23,24 e o 25.

Answer 1

Explicação passo-a-passo:

21)

$\sf M=C\cdot(1+i)^t$

$\sf M=200000\cdot(1+0,05)^2$

$\sf M=200000\cdot(1,05)^2$

$\sf M=200000\cdot1,1025$

$\sf \red{M=220500}$

22)

=> Montante

• $\sf 3~trimestres=9~meses$

$\sf M=C\cdot(1+i)^t$

$\sf M=65000\cdot(1+0,02)^9$

$\sf M=65000\cdot1,195$

$\sf \red{M=77675}$

=> Juros

$\sf M=C+J$

$\sf 77675=65000+J$

$\sf J=77675-65000$

$\sf \red{J=12675}$

23)

$\sf M=C\cdot(1+i)^t$

$\sf 76930,81=C\cdot(1+0,075)^{15}$

$\sf 76930,81=C\cdot(1,075)^{15}$

$\sf log~76930,81=log~[C\cdot(1,075)^{15}]$

$\sf log~76930,81=log~C+log~(1,075)^{15}$

$\sf log~76930,81=log~C+15\cdot log~(1,075)$

$\sf 4,8861=log~C+15\cdot0,0314$

$\sf 4,8861=log~C+0,471$

$\sf log~C=4,8861-0,471$

$\sf log~C=4,4151$

$\sf C=10^{4,4151}$

$\sf \red{C=26000}$

24)

$\sf M=C\cdot(1+i)^t$

$\sf 18249,79=15000\cdot(1+0,04)^t$

$\sf 18249,79=15000\cdot(1,04)^t$

$\sf (1,04)^t=\dfrac{18249,79}{15000}$

$\sf (1,04)^t=1,22$

$\sf log~[(1,04)^t]=log~1,22$

$\sf t\cdot log~(1,04)=log~1,22$

$\sf t\cdot0,0170=0,0852$

$\sf t=\dfrac{0,0852}{0,0170}$

$\sf t=\dfrac{852}{170}$

$\sf \red{t=5~meses}$

25)

$\sf M=C\cdot(1+i)^t$

$\sf M=5000\cdot(1+0,25)^{18}$

$\sf M=5000\cdot(1,25)^{18}$

$\sf M=5000\cdot55,51$

$\sf \red{M=277550}$