Question

qual a taxa de juros composto bimestral de 10% ao ano?

Answer 1

Queremos que as duas taxas sejam equivalentes, logo, dado um mesmo período de tempo, o montante gerado por ambas deve ser também equivalente.

$Montante_1~=~Capital~.~\left(1~+~^{~~Taxa}_{Bimestral}}\right)^{Periodo}\\\\\\Montante_2~=~Capital~.~\left(1~+~^{\,Taxa}_{Anual}}\right)^{Periodo}$

$Montante_1~=~Montante_2\\\\\\Capital~.~\left(1~+~^{~~Taxa}_{Bimestral}}\right)^{Periodo}~=~Capital~.~\left(1~+~^{\,Taxa}_{Anual}}\right)^{Periodo}\\\\\\\left(1~+~^{~~Taxa}_{Bimestral}}\right)^{Periodo}~=~\left(1~+~^{\,Taxa}_{Anual}}\right)^{Periodo}\\\\\\Considerando,~um~periodo~de~1~ano~(6~bimestres),~temos:\\\\\\\left(1~+~^{~~Taxa}_{Bimestral}}\right)^{6}~=~\left(1~+~0,1\right)^{1}$

$\left(1~+~^{~~Taxa}_{Bimestral}\right)^{6}~=~1,1\\\\\\\left(1~+~^{~~Taxa}_{Bimestral}\right)~=~\sqrt[6]{1,1}\\\\\\\left(1~+~^{~~Taxa}_{Bimestral}\right)~\approx~1,0160\\\\\\^{~~Taxa}_{Bimestral}~\approx~1,0160-1\\\\\\\boxed{^{~~Taxa}_{Bimestral}~\approx~0,0160~~ou~~1,60\%~a.b.}$