Em juros compostos, qual a taxa mensal equivalente a 50% a.s.? a) 10,39% a.m. b) 5,50% a.m. c) 7% a.m. d) 4,43% a.m e) 15% a.m.

Vamos calcular a taxa mensal equivalente a 50% a.s.: A fórmula para converter a taxa anual (a.s.) em taxa mensal (a.m.) em juros compostos é: \( (1 + i_{a.m.})^{12} = 1 + i_{a.s.} \) Onde: \( i_{a.m.} \) = taxa mensal \( i_{a.s.} \) = taxa anual Substituindo \( i_{a.s.} = 50\% = 0,50 \) na fórmula, temos: \( (1 + i_{a.m.})^{12} = 1 + 0,50 \) \( (1 + i_{a.m.})^{12} = 1,50 \) Agora, encontramos a taxa mensal (\( i_{a.m.} \)): \( (1 + i_{a.m.}) = \sqrt[12]{1,50} \) \( (1 + i_{a.m.}) \approx 1,0359 \) \( i_{a.m.} \approx 0,0359 \) \( i_{a.m.} \approx 3,59\% \) Portanto, a alternativa correta é: a) 10,39% a.m.