Quantos depósitos mensais de R$ 850,00 (cada) um cliente deverá fazer a fim de resgatar no final R$ 103 327,46 se o banco paga uma taxa de juros de 2,1% ao mês?
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Bom dia!
Fórmula:
![<br />FV=PMT\cdot\left[\frac{\left(1+i\right)^{n}-1}{i}\right]\\<br />103327,46=850\cdot\left[\frac{\left(1+2,1\%\right)^{n}-1}{2,1\%}\right]\\<br />\frac{103327,46}{850}=\frac{1,021^n-1}{0,021}\\<br />1,021^n-1=\frac{0,021\cdot{103327,46}}{850}\\<br />1,021^n=\frac{0,021\cdot{103327,46}}{850}+1\\<br />n=\frac{\log\left(\frac{0,021\cdot{103327,46}}{850}+1\right)}{\log{1,021}}\\<br />n=61<br />](https://tex.z-dn.net/?f=%3Cbr+%2F%3EFV%3DPMT%5Ccdot%5Cleft%5B%5Cfrac%7B%5Cleft%281%2Bi%5Cright%29%5E%7Bn%7D-1%7D%7Bi%7D%5Cright%5D%5C%5C%3Cbr+%2F%3E103327%2C46%3D850%5Ccdot%5Cleft%5B%5Cfrac%7B%5Cleft%281%2B2%2C1%5C%25%5Cright%29%5E%7Bn%7D-1%7D%7B2%2C1%5C%25%7D%5Cright%5D%5C%5C%3Cbr+%2F%3E%5Cfrac%7B103327%2C46%7D%7B850%7D%3D%5Cfrac%7B1%2C021%5En-1%7D%7B0%2C021%7D%5C%5C%3Cbr+%2F%3E1%2C021%5En-1%3D%5Cfrac%7B0%2C021%5Ccdot%7B103327%2C46%7D%7D%7B850%7D%5C%5C%3Cbr+%2F%3E1%2C021%5En%3D%5Cfrac%7B0%2C021%5Ccdot%7B103327%2C46%7D%7D%7B850%7D%2B1%5C%5C%3Cbr+%2F%3En%3D%5Cfrac%7B%5Clog%5Cleft%28%5Cfrac%7B0%2C021%5Ccdot%7B103327%2C46%7D%7D%7B850%7D%2B1%5Cright%29%7D%7B%5Clog%7B1%2C021%7D%7D%5C%5C%3Cbr+%2F%3En%3D61%3Cbr+%2F%3E "<br />FV=PMT\cdot\left[\frac{\left(1+i\right)^{n}-1}{i}\right]\\<br />103327,46=850\cdot\left[\frac{\left(1+2,1\%\right)^{n}-1}{2,1\%}\right]\\<br />\frac{103327,46}{850}=\frac{1,021^n-1}{0,021}\\<br />1,021^n-1=\frac{0,021\cdot{103327,46}}{850}\\<br />1,021^n=\frac{0,021\cdot{103327,46}}{850}+1\\<br />n=\frac{\log\left(\frac{0,021\cdot{103327,46}}{850}+1\right)}{\log{1,021}}\\<br />n=61<br />")
Espero ter ajudado!
Fórmula:
Espero ter ajudado!
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