) Uma televisão pode ser adquirida por R$ 1.500,00 de entrada mais 5 prestações de R$ 657,38. Sabendo que a loja cobra 0,9% a.m. de juros para pagamentos parcelados, qual é o valor à vista da televisão? Se, com a mesma entrada, a primeira das 5 prestações só ocorrer no início do terceiro mês, de quanto devem ser as prestações?
Respostas
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Boa noite!
Calculando o valor à vista da TV:
![PV=E+PMT\cdot\left[\dfrac{1-\left(1+i\right)^{-n}}{i}\right]\\PV=1\,500,00+657,38\cdot\left[\dfrac{1-\left(1+0,9\%\right)^{-5}}{0,9\%}\right]\\PV=1\,500,00+657,38\cdot\left(\dfrac{1-1,009^{-5}}{0,009}\right)\\\boxed{PV\approx 4\,700,00}](https://tex.z-dn.net/?f=PV%3DE%2BPMT%5Ccdot%5Cleft%5B%5Cdfrac%7B1-%5Cleft%281%2Bi%5Cright%29%5E%7B-n%7D%7D%7Bi%7D%5Cright%5D%5C%5CPV%3D1%5C%2C500%2C00%2B657%2C38%5Ccdot%5Cleft%5B%5Cdfrac%7B1-%5Cleft%281%2B0%2C9%5C%25%5Cright%29%5E%7B-5%7D%7D%7B0%2C9%5C%25%7D%5Cright%5D%5C%5CPV%3D1%5C%2C500%2C00%2B657%2C38%5Ccdot%5Cleft%28%5Cdfrac%7B1-1%2C009%5E%7B-5%7D%7D%7B0%2C009%7D%5Cright%29%5C%5C%5Cboxed%7BPV%5Capprox+4%5C%2C700%2C00%7D "PV=E+PMT\cdot\left[\dfrac{1-\left(1+i\right)^{-n}}{i}\right]\\PV=1\,500,00+657,38\cdot\left[\dfrac{1-\left(1+0,9\%\right)^{-5}}{0,9\%}\right]\\PV=1\,500,00+657,38\cdot\left(\dfrac{1-1,009^{-5}}{0,009}\right)\\\boxed{PV\approx 4\,700,00}")
Dando a mesma entrada, R$ 1.500,00, e começando a pagar só no início do terceiro mês, teremos:
![PV\cdot\left(1+i\right)^k=PMT\cdot\left[\dfrac{1-\left(1+i\right)^{-n}}{i}\right]\\<br />(4\,700-1\,500)\cdot\left(1+0,9\%\right)^2=PMT\cdot\left[\dfrac{1-\left(1+0,9\%\right)^{-5}}{0,9\%}\right]\\3\,200\cdot 1,009^2=PMT\left(\dfrac{1-1,009^{-5}}{0,009}\right)\\<br />PMT=\dfrac{3\,200\cdot 1,009^2\cdot 0,009}{1-1,009^{-5}}\\<br />\boxed{PMT\approx 669,27}](https://tex.z-dn.net/?f=PV%5Ccdot%5Cleft%281%2Bi%5Cright%29%5Ek%3DPMT%5Ccdot%5Cleft%5B%5Cdfrac%7B1-%5Cleft%281%2Bi%5Cright%29%5E%7B-n%7D%7D%7Bi%7D%5Cright%5D%5C%5C%3Cbr+%2F%3E%284%5C%2C700-1%5C%2C500%29%5Ccdot%5Cleft%281%2B0%2C9%5C%25%5Cright%29%5E2%3DPMT%5Ccdot%5Cleft%5B%5Cdfrac%7B1-%5Cleft%281%2B0%2C9%5C%25%5Cright%29%5E%7B-5%7D%7D%7B0%2C9%5C%25%7D%5Cright%5D%5C%5C3%5C%2C200%5Ccdot+1%2C009%5E2%3DPMT%5Cleft%28%5Cdfrac%7B1-1%2C009%5E%7B-5%7D%7D%7B0%2C009%7D%5Cright%29%5C%5C%3Cbr+%2F%3EPMT%3D%5Cdfrac%7B3%5C%2C200%5Ccdot+1%2C009%5E2%5Ccdot+0%2C009%7D%7B1-1%2C009%5E%7B-5%7D%7D%5C%5C%3Cbr+%2F%3E%5Cboxed%7BPMT%5Capprox+669%2C27%7D "PV\cdot\left(1+i\right)^k=PMT\cdot\left[\dfrac{1-\left(1+i\right)^{-n}}{i}\right]\\<br />(4\,700-1\,500)\cdot\left(1+0,9\%\right)^2=PMT\cdot\left[\dfrac{1-\left(1+0,9\%\right)^{-5}}{0,9\%}\right]\\3\,200\cdot 1,009^2=PMT\left(\dfrac{1-1,009^{-5}}{0,009}\right)\\<br />PMT=\dfrac{3\,200\cdot 1,009^2\cdot 0,009}{1-1,009^{-5}}\\<br />\boxed{PMT\approx 669,27}")
Espero ter aj
Calculando o valor à vista da TV:
Dando a mesma entrada, R$ 1.500,00, e começando a pagar só no início do terceiro mês, teremos:
Espero ter aj
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