Question

Calcular o capital que, investido a juros compostos de 4% ao mês, durante 4 meses, produziu um montante de R$ 7.000,00. *

a) R$ 5983,63

b) R$ 6000,03

c) R$ 6102,58

d) R$ 6277,99

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Answer 1

Juros compostos

$\sf{m = c(1 + i)^{n} } \\ \\ \sf{7000 = c(1 + 4\%)^{4} } \\ \\ \sf{7000 = c {\left(1 + \frac{4}{100} \right)}^{4} } \\ \\ \sf{7000 = c {\left( 1 + \frac{1}{25} \right)}^{4} } \\ \\ \sf{7000 = c {\left( \frac{25 + 1}{25} \right)}^{4} } \\ \\ \sf{7000 = c {\left( \frac{26}{25} \right)}^{4} } \\ \\ \sf{7000 = c \times \frac{ {26}^{4} }{ {25}^{4} } } \\ \\ \sf{7000 = \frac{ {26}^{4}c }{ {25}^{4} } } \\ \\ \sf{ \frac{7000 \times {25}^{4} }{ {26}^{4} } = c } \\ \\ \sf{c = \frac{7000 \times {25}^{4} }{ {26}^{4} } } \\ \\ \sf{c = \frac{7000 \times 390625}{456976} } \\ \\ \sf{c = \frac{2734375000}{456976} } \\ \\ \boxed{ \sf{c \approx 5983,62 }}$

Resposta

Item (a)

Att: José Armando