Question

Matemática:
Uma poupança será feita em 12 depositos mensais de Rs 1500,00...sabendo.se que a correção mensal é de 0,6% ao mes. Qual o montante no final de um ano?​

Answer 1

n = Nº de Meses

j = Taxa de Juros Mensal

p = Valor do Depósito Regular

Sn = Valor Obtido ao Final

$Sn = ( 1 + 0,006) \frac{(1 + 0,006)^{12}-1 }{0,006} 1500\\\\1,006 * \frac{1,006^{12}-1 }{\frac{3}{500} }1500\\\\\frac{503}{500} *\frac{(\frac{503}{500} )^{12} -1}{\frac{3}{500} } *1500\\\\\frac{503}{500} *\frac{\frac{503^{12} }{500^{12} } -1}{\frac{3}{500} } *1500\\\\503*\frac{\frac{503^{12} }{500^{12} }-1 }{\frac{3}{500} } *3\\\\\\503*\frac{\frac{503^{12-500^{12} } }{500^{12} } }{\frac{3}{500} } *3\\\\503*\frac{503^{12}-500^{12} }{3*500^{11} } *3$$503*\frac{503^{12}-500^{12} }{500^{11} } \\\\\frac{503(500^{12}-500^{12}) }{500^{11} }\\\\\frac{503^{13}-503*500^{12} }{500^{11} } \\\\= 18.717,67818$

Answer 2

FV = PMT × [(1 + i)^n - 1]/i

FV = 1500 × [(1 + 0,006)¹² - 1]/0,006

FV = 1500 × [1,006¹² - 1]/0,006

FV = 1500 × [1,07442417 - 1]/0,006

FV = 1500 × 0,7442417/0,006

FV = 1500 × 12,4040283

FV ≈ 18.606,04

Resposta: R$ 18.606,04