Encontre a taxa de juros para que um investimento de R$ 10000,00 cresça até R$18000,00 em cinco anos, sendo os juros compostos mensalmente.
Eu tentei resolver e meu resultado foi i=11,81% a.m.
Fiz desta forma:
1800=10000(1+i/12)^60
1,8=(1+i/12)^60
raiz sexágésima de 1,8=1+i/12
1,009844587=1+i/12
0,009844587=i/12
0,1181=i
i=11,81% a.m
Gostaria de saber se está certo?
![\\ \boxed{S = P(i + 1)^n} \\\\ 18000 = 10000(i + 1)^5 \\\\ (i + 1)^5 = 1,8 \\\\ i + 1 = \sqrt[5]{1,8} \\\\ i + 1 = 1,124 \\\\ \boxed{i = 0,124}](/latexrender/pictures/163e8ebca9f69fe5b339008192d58077.png "\\ \boxed{S = P(i + 1)^n} \\\\ 18000 = 10000(i + 1)^5 \\\\ (i + 1)^5 = 1,8 \\\\ i + 1 = \sqrt[5]{1,8} \\\\ i + 1 = 1,124 \\\\ \boxed{i = 0,124}")
![\\ \boxed{(i_a + 1) = (i_m + 1)^{12}} \\\\ 1,124 = (i_m + 1)^{12} \\\\ i_m + 1 = \sqrt[12]{1,124} \\\\ i_m + 1 = 1,009 \\\\ i_m = 0,009 \\\\ \boxed{\boxed{i_m = 0,9}}](/latexrender/pictures/4955d284d1582af260e1471c0f2046ec.png "\\ \boxed{(i_a + 1) = (i_m + 1)^{12}} \\\\ 1,124 = (i_m + 1)^{12} \\\\ i_m + 1 = \sqrt[12]{1,124} \\\\ i_m + 1 = 1,009 \\\\ i_m = 0,009 \\\\ \boxed{\boxed{i_m = 0,9}}")
![\frac{\sqrt[]{\sqrt[4]{8}+\sqrt[]{\sqrt[]{2}-1}}-\sqrt[]{\sqrt[4]{8}-\sqrt[]{\sqrt[]{2}-1}}}{\sqrt[]{\sqrt[4]{8}-\sqrt[]{\sqrt[]{2}+1}}}](/latexrender/pictures/981987c7bcdf9f8f498ca4605785636a.png "\frac{\sqrt[]{\sqrt[4]{8}+\sqrt[]{\sqrt[]{2}-1}}-\sqrt[]{\sqrt[4]{8}-\sqrt[]{\sqrt[]{2}-1}}}{\sqrt[]{\sqrt[4]{8}-\sqrt[]{\sqrt[]{2}+1}}}")
![\sqrt[]{2}](/latexrender/pictures/f21662d1cabab6e8b273a4b6f1cd663a.png "\sqrt[]{2}")
e elevar ao quadrado os dois lados)