De acordo com o estudado em RENDAS OU SÉRIES UNIFORMES, utilizando a Renda Antecipada estudada demonstre o cálculo que determina o problema abaixo: Desejo possuir R$ 40.000,00 daqui a dois anos. Quanto devo aplicar mensalmente, a uma taxa de 2% a.m.
Soluções para a tarefa
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• Valor futuro: 
• Taxa:
• Prazo da aplicação:
• Prestação mensal:
![\mathtt{VF=PMT\cdot \dfrac{(1+i)^n-1}{i}\cdot (1+i)}\\\\\\ \mathtt{VF\cdot \dfrac{i}{1+i}=PMT\cdot \left[(1+i)^n-1\right ]}\\\\\\ \mathtt{PMT=VF\cdot \dfrac{i}{(1+i)\cdot \left[(1+i)^n-1\right]}} \mathtt{VF=PMT\cdot \dfrac{(1+i)^n-1}{i}\cdot (1+i)}\\\\\\ \mathtt{VF\cdot \dfrac{i}{1+i}=PMT\cdot \left[(1+i)^n-1\right ]}\\\\\\ \mathtt{PMT=VF\cdot \dfrac{i}{(1+i)\cdot \left[(1+i)^n-1\right]}}](https://tex.z-dn.net/?f=%5Cmathtt%7BVF%3DPMT%5Ccdot+%5Cdfrac%7B%281%2Bi%29%5En-1%7D%7Bi%7D%5Ccdot+%281%2Bi%29%7D%5C%5C%5C%5C%5C%5C+%5Cmathtt%7BVF%5Ccdot+%5Cdfrac%7Bi%7D%7B1%2Bi%7D%3DPMT%5Ccdot+%5Cleft%5B%281%2Bi%29%5En-1%5Cright+%5D%7D%5C%5C%5C%5C%5C%5C+%5Cmathtt%7BPMT%3DVF%5Ccdot+%5Cdfrac%7Bi%7D%7B%281%2Bi%29%5Ccdot+%5Cleft%5B%281%2Bi%29%5En-1%5Cright%5D%7D%7D)
Substituindo os valores conhecidos na fórmula,
![\mathtt{PMT=40\,000\cdot \dfrac{0,\!02}{(1+0,\!02)\cdot \left[(1+0,\!02)^{24}-1\right]}}\\\\\\ \mathtt{PMT=40\,000\cdot \dfrac{0,\!02}{(1,\!02)\cdot \left[(1,\!02)^{24}-1\right]}}\\\\\\ \mathtt{PMT=40\,000\cdot \dfrac{0,\!02}{1,\!02\cdot (1,\!608437-1)}}\\\\\\ \mathtt{PMT=40\,000\cdot \dfrac{0,\!02}{1,\!02\cdot 0,\!608437}}\\\\\\ \mathtt{PMT=40\,000\cdot \dfrac{0,\!02}{0,620606}}\\\\\\ \mathtt{PMT=40\,000\cdot 0,0322266} \mathtt{PMT=40\,000\cdot \dfrac{0,\!02}{(1+0,\!02)\cdot \left[(1+0,\!02)^{24}-1\right]}}\\\\\\ \mathtt{PMT=40\,000\cdot \dfrac{0,\!02}{(1,\!02)\cdot \left[(1,\!02)^{24}-1\right]}}\\\\\\ \mathtt{PMT=40\,000\cdot \dfrac{0,\!02}{1,\!02\cdot (1,\!608437-1)}}\\\\\\ \mathtt{PMT=40\,000\cdot \dfrac{0,\!02}{1,\!02\cdot 0,\!608437}}\\\\\\ \mathtt{PMT=40\,000\cdot \dfrac{0,\!02}{0,620606}}\\\\\\ \mathtt{PMT=40\,000\cdot 0,0322266}](https://tex.z-dn.net/?f=%5Cmathtt%7BPMT%3D40%5C%2C000%5Ccdot+%5Cdfrac%7B0%2C%5C%2102%7D%7B%281%2B0%2C%5C%2102%29%5Ccdot+%5Cleft%5B%281%2B0%2C%5C%2102%29%5E%7B24%7D-1%5Cright%5D%7D%7D%5C%5C%5C%5C%5C%5C+%5Cmathtt%7BPMT%3D40%5C%2C000%5Ccdot+%5Cdfrac%7B0%2C%5C%2102%7D%7B%281%2C%5C%2102%29%5Ccdot+%5Cleft%5B%281%2C%5C%2102%29%5E%7B24%7D-1%5Cright%5D%7D%7D%5C%5C%5C%5C%5C%5C+%5Cmathtt%7BPMT%3D40%5C%2C000%5Ccdot+%5Cdfrac%7B0%2C%5C%2102%7D%7B1%2C%5C%2102%5Ccdot+%281%2C%5C%21608437-1%29%7D%7D%5C%5C%5C%5C%5C%5C+%5Cmathtt%7BPMT%3D40%5C%2C000%5Ccdot+%5Cdfrac%7B0%2C%5C%2102%7D%7B1%2C%5C%2102%5Ccdot+0%2C%5C%21608437%7D%7D%5C%5C%5C%5C%5C%5C+%5Cmathtt%7BPMT%3D40%5C%2C000%5Ccdot+%5Cdfrac%7B0%2C%5C%2102%7D%7B0%2C620606%7D%7D%5C%5C%5C%5C%5C%5C+%5Cmathtt%7BPMT%3D40%5C%2C000%5Ccdot+0%2C0322266%7D)
<——— esta é a resposta.
Dúvidas? Comente.
Bons estudos! :-)
• Taxa:
• Prazo da aplicação:
• Prestação mensal:
Substituindo os valores conhecidos na fórmula,
Dúvidas? Comente.
Bons estudos! :-)
Lukyo:
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