Question

Um capital aplicou a juros simples durante 2 anos , sob taxá de juros de 5% ao mês, gerou um montante de R$ 26.950,00.Detereine o valor do capitaliano aplique

Answer 1

Legenda:

๏ M: Montante
๏ C: Capital inicial
๏ i: Taxa de juros
๏ t: Tempo de aplicação
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Dados:

๏ M: R$ 26.950,00
๏ i: 5% a.m = 5/100
๏ t: 2 anos = 2×12 meses = 24 meses
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Considerando juros simples:

$\mathsf{M=C+J}\\\mathsf{M=C+\left(C\cdot i\cdot t\right)}\\\mathsf{M=C\cdot \left(1+it\right)}\\\\\mathsf{26.950=C\cdot \left(1+\dfrac{5\cdot 24}{100}\right)}\\\\\\\mathsf{26.950=C\cdot \left(1+\dfrac{24}{20}\right)}\\\\\\\mathsf{26.950=C\cdot \left(1+\dfrac{6}{5}\right)}\\\\\\\mathsf{26.950=C\cdot \dfrac{5+6}{5}}\\\\\\\mathsf{26.950=\dfrac{11C}{5}}\\\\\\\mathsf{C=\dfrac{26.950\cdot 5}{11}}\\\\\\\boxed{\mathsf{C=R\ \:12.250,00}}\: \: \checkmark$

Answer 2

C=?
t=2a
i=5%am= 60%aa
M= 26 950,00

Vou usar o artifício do Capital Falso.( serve qualquer valor)

Capital falso=500,00
 t=2a
i=60%aa
Jf= 500.2.60/100= 600,00
Mf=500+600=1100,00

500,00-------1100,00
  x-------------26950,00

x= 500.26950/1100=  12250,00
Resp:R$12250,00