Respuesta :
Step 1
GIven;
[tex]\begin{gathered} A(t)=P(1+\frac{r}{n})^{nt} \\ P=25000 \\ r=8.2\text{\%} \\ \end{gathered}[/tex][tex]\begin{gathered} r=\frac{8.2}{100}=0.082 \\ n=4 \\ A(t)=200000 \end{gathered}[/tex]Required; To find t, the time
Step 2
Find t
[tex]200000=25000(1+\frac{0.082}{4})^{4t}[/tex][tex]\begin{gathered} \frac{200000}{25000}=\frac{25000(1+\frac{0.082}{4})^{4t}}{25000} \\ \left(1+\frac{0.082}{4}\right)^{4t}=8 \\ 4t\ln \left(1+\frac{0.082}{4}\right)=\ln \left(8\right) \\ t=\frac{3\ln\left(2\right)}{4\ln\left(\frac{4.082}{4}\right)}=25.61809 \end{gathered}[/tex]Hence, the time it will take will be;
[tex]25.62\text{ years a}pproximately\text{ to 2 decimal places}[/tex]