Respuesta :
1) In this problem, let's consider that there was no other investment after the initial investment of $30,000. Since the interest rate of this investment will be compounded annually, we can write the following below:
[tex]\begin{gathered} F=P(1+\frac{r}{n})^{nt} \\ \\ 70,000=30,000(1+\frac{0.075}{1})^{1t} \\ \\ 70000=30000(1.075)^t \end{gathered}[/tex]2) Now, we can solve for "t" applying logarithms:
[tex]\begin{gathered} 30000\cdot \:1.075^t=70000 \\ \\ \frac{30000\cdot \:1.075^t}{30000}=\frac{70000}{30000} \\ \\ 1.075^t=\frac{7}{3} \\ \\ t\ln \left(1.075\right)=\ln \left(\frac{7}{3}\right) \\ \\ \frac{t\ln \left(1.075\right)}{\ln \left(1.075\right)}=\frac{\ln \left(\frac{7}{3}\right)}{\ln \left(1.075\right)} \\ \\ t=\frac{\ln\left(\frac{7}{3}\right)}{\ln\left(1.075\right)}\approx11.71 \end{gathered}[/tex]3) So, you have to wait almost 12 years (11.7) so that the investmente reaches
