Question

determine o periodo de uma aplicaçao a juros compostos , cujo o capital é de 32 mil reais e o montante de 96 mil a taxa de 8% de a.d. considere log2=0,30 e log3=0,48

Answer 1

$M=C(1+i)^t\implies$

$\implies 96000=32000(1+8\%)^t\implies$

$\implies \frac{96000}{32000}=(1+\frac{8}{100})^t\implies$

$\implies 3=(\frac{108}{100})^t\implies$

$\implies log\,(3)=log\,[(\frac{108}{100})^t]\implies$

$\implies 0,\!48=log\,(\frac{108}{100})\cdot t\implies$

$\implies 0,\!48=[log\,(108)-log\,(100)]\cdot t\implies$

$\implies 0,\!48=[log\,(2^2\cdot3^3)-log\,(10^2)]\cdot t\implies$

$\implies 0,\!48=[log\,(2^2)+log\,(3^3)-log\,(10)\cdot2]\cdot t\implies$

$\implies 0,\!48=[log\,(2)\cdot2+log\,(3)\cdot3-1\cdot2]\cdot t\implies$

$\implies 0,\!48=[0,\!3\cdot2+0,\!48\cdot3-2]\cdot t\implies$

$\implies 0,\!48=[0,\!6+1,\!44-2]\cdot t\implies$

$\implies 0,\!48=0,\!04\cdot t\implies$

$\implies t=\frac{0,\!48}{0,\!04}\implies$

$\implies \underline{\boxed{t=12}}\leftarrow \text{12 dias, pois a taxa \rm\acute{e} a.d. (ao dia).}$