Uma compra foi financiada em 15 parcelas mensais e iguais de R$433,50, sob regime de taxa de juros compostos de 3,3% a.m. com entrada de R$250,00. Determine o valor à vista deste financiamento.
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![\displaystyle{PV=E+PMT\cdot\left[\frac{1-\left(1+i\right)^{-n}}{i}\right]}\\\displaystyle{PV=250+433,50\cdot\left[\frac{1-\left(1+3,3\%\right)^{-15}}{3,3\%}\right]}\\\displaystyle{PV=250+433,50\cdot\left[\frac{1-\left(1+0,033\right)^{-15}}{0,033}\right]}\\\displaystyle{PV=250+433,50\cdot\left(\frac{1-1,033^{-15}}{0,033}\right)}\\\displaystyle{\boxed{PV\approx{5\,314,56}}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%7BPV%3DE%2BPMT%5Ccdot%5Cleft%5B%5Cfrac%7B1-%5Cleft%281%2Bi%5Cright%29%5E%7B-n%7D%7D%7Bi%7D%5Cright%5D%7D%5C%5C%5Cdisplaystyle%7BPV%3D250%2B433%2C50%5Ccdot%5Cleft%5B%5Cfrac%7B1-%5Cleft%281%2B3%2C3%5C%25%5Cright%29%5E%7B-15%7D%7D%7B3%2C3%5C%25%7D%5Cright%5D%7D%5C%5C%5Cdisplaystyle%7BPV%3D250%2B433%2C50%5Ccdot%5Cleft%5B%5Cfrac%7B1-%5Cleft%281%2B0%2C033%5Cright%29%5E%7B-15%7D%7D%7B0%2C033%7D%5Cright%5D%7D%5C%5C%5Cdisplaystyle%7BPV%3D250%2B433%2C50%5Ccdot%5Cleft%28%5Cfrac%7B1-1%2C033%5E%7B-15%7D%7D%7B0%2C033%7D%5Cright%29%7D%5C%5C%5Cdisplaystyle%7B%5Cboxed%7BPV%5Capprox%7B5%5C%2C314%2C56%7D%7D%7D "\displaystyle{PV=E+PMT\cdot\left[\frac{1-\left(1+i\right)^{-n}}{i}\right]}\\\displaystyle{PV=250+433,50\cdot\left[\frac{1-\left(1+3,3\%\right)^{-15}}{3,3\%}\right]}\\\displaystyle{PV=250+433,50\cdot\left[\frac{1-\left(1+0,033\right)^{-15}}{0,033}\right]}\\\displaystyle{PV=250+433,50\cdot\left(\frac{1-1,033^{-15}}{0,033}\right)}\\\displaystyle{\boxed{PV\approx{5\,314,56}}}")
Espero ter ajudado!
Espero ter ajudado!
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