Respuesta :
Given:
Expect to receive = $10000
Rate = 8%
Final amount = $95000
Find-:
How long will you wait
Explanation-:
Value after some time is:
[tex]A=P(1+\frac{r}{100})^t[/tex]Where,
[tex]\begin{gathered} A=\text{ Future value} \\ \\ P=\text{ Present value} \\ \\ r\text{ = Rate of interest} \\ \\ t=\text{ Time period} \end{gathered}[/tex]So, the value is:
[tex]\begin{gathered} A=95000 \\ \\ P=10000 \\ \\ r=8 \\ \\ \end{gathered}[/tex][tex]\begin{gathered} A=P(1+\frac{r}{100})^t \\ \\ 95000=1000(1+\frac{8}{100})^t \\ \\ \frac{95000}{10000}=(1+0.08)^t \\ \\ 9.5=1.08^t \end{gathered}[/tex]For time taking log both sides.
[tex]\begin{gathered} \ln9.5=\ln1.08^t \\ \\ \frac{\ln9.5}{\ln1.08}=t \\ \\ t=29.25 \\ \end{gathered}[/tex]Hence time wait from now:
[tex]=t+2[/tex][tex]\begin{gathered} =29.25+2 \\ \\ =31.25 \end{gathered}[/tex]So the total time is 31.25 years.
