Question

"Um capital foi colocado a juro composto a uma taxa semestral de 5%. A taxa anual equivalente a essa taxa semestral corresponde a;"

Answer 1

$\large\boxed{1 + ia = (1 + ip)^n}\\\\\\ ia=taxa~~anual\\\\ ip=taxa~~do~~periodo\\\\ n=n\°~~de~~periodos\\\\ 5\%~~ao~~semestre\to~~ 5:100\to~~0,05~as\\\\\\1~~ano~~tem~~2~~semestres, ~~ent\~ao:\\\\ n=2\\ip=0,05\\ia=?\\\\\\ 1+ia=(1+0,05)^2\to\\1+ia=1,05^2\to \\1+ia=1,1025\to\\ ia=1,1025-1\to\\ ia=0,1025 \\\\0,1025\times 100=10,25~\%\\\\\\\\ A~~taxa~~anual~~que~~equivale~~a~~taxa~~semestral~~e\´~10,25\%$