Uma financeira remunera os valores investidos à base de 4% de juros simples. Quanto conseguirá resgatar nesse investimento uma pessoa que depositar, mensalmente, 500 reais durante 10 meses?
luizhenriquealves:
me ajudem por favor
Respostas
respondido por:
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Olá, Luiz Henrique.
Observe que 4% = 0,04. Assim:
![C=500+(500+500\cdot0,04)+(500+2\cdot500\cdot0,04)+...\\+...+(500+9\cdot500\cdot0,04)=\\\\
=10\cdot500+500\cdot0,04\cdot[\underbrace{1+2+...+9}_{\text{soma de PA}}]=\\\\\\
=5.000+500\cdot0,04\cdot[9\cdot(\frac{1+9}{2})]=\\\\
=5.000+500\cdot0,04\cdot45=\\\\
=\boxed{\text{R\$ }5.900}](https://tex.z-dn.net/?f=C%3D500%2B%28500%2B500%5Ccdot0%2C04%29%2B%28500%2B2%5Ccdot500%5Ccdot0%2C04%29%2B...%5C%5C%2B...%2B%28500%2B9%5Ccdot500%5Ccdot0%2C04%29%3D%5C%5C%5C%5C%0A%3D10%5Ccdot500%2B500%5Ccdot0%2C04%5Ccdot%5B%5Cunderbrace%7B1%2B2%2B...%2B9%7D_%7B%5Ctext%7Bsoma+de+PA%7D%7D%5D%3D%5C%5C%5C%5C%5C%5C%0A%3D5.000%2B500%5Ccdot0%2C04%5Ccdot%5B9%5Ccdot%28%5Cfrac%7B1%2B9%7D%7B2%7D%29%5D%3D%5C%5C%5C%5C%0A%3D5.000%2B500%5Ccdot0%2C04%5Ccdot45%3D%5C%5C%5C%5C%0A%3D%5Cboxed%7B%5Ctext%7BR%5C%24+%7D5.900%7D "C=500+(500+500\cdot0,04)+(500+2\cdot500\cdot0,04)+...\\+...+(500+9\cdot500\cdot0,04)=\\\\
=10\cdot500+500\cdot0,04\cdot[\underbrace{1+2+...+9}_{\text{soma de PA}}]=\\\\\\
=5.000+500\cdot0,04\cdot[9\cdot(\frac{1+9}{2})]=\\\\
=5.000+500\cdot0,04\cdot45=\\\\
=\boxed{\text{R\$ }5.900}")
Observe que 4% = 0,04. Assim:
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