QUESTÃO CERTA: O diagrama abaixo apresenta as entradas e saídas referentes a um determinado projeto de investimento. Observe-o e identifique, na sequência de alternativas, aquela que permite, com base no sistema de juros compostos, o cálculo do valor equivalente a esse fluxo no tempo zero.
Série uniforme de prestações periódicas antecipadas. Esta série caracteriza-se pelo fato de que os pagamentos (ou recebimentos) sempre irão ocorrer no início do intervalo de tempo. Outro conceito importante é o de VPL (valor presente líquido), que é aquele calculado com relação à data zero. Para se obter o VPL devemos descapitalizar as parcelas lançadas em períodos futuros. Isso é feito usando-se o fator:
1/(1+i)^t [ i : taxa aplicada; t: período de capitalização ]
Assim, para o que se pede nesta questão, devemos aplicar o fator adequado à cada parcela e somar para se obter o VPL.
Logo:
t = 0 → -10000
t = 1 → 1000 / (1+i)¹
t = 2 → (1000-1500) / (1+i)¹ = -500 / (1+i)²
t = 3 → 1000 – 1000 = 0 / (1+i)³ = 0
t = 4 → 30000 / (1+i)⁴
∑ = -10000 + 1000 / (1+i)¹ – 500 / (1+i)² + 0 + 30000 / (1+i)⁴
Resposta: – $10.000 + $1.000/(1 + i) 1 – $500/(1 + i) 2 + $30.000/(1 + i) 4
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