Answer: It will take 4.05 years for an initial investment of $40,000 to grow to $60,000.
Step-by-step explanation:
The exponential growth equation (Compounded continuously) is given by :-
[tex]A= Pe^{rt}[/tex] (1)
, where r = rate of growth (in decimal)
t= time
P= initial amount.
As per given , we have
P= $40,000
A = $60,000
r = 10% =0.10
Put values in (1) , we get
[tex]60000= (40000)e^{(0.10)t}[/tex]
[tex]1.5=e^{(0.10)t}[/tex] [Divide both sides by 40000]
[tex]1.5=e^{0.1t}[/tex]
Taking natural log on both sides , we get
[tex]\ln(1.5)=0.1t[/tex]
[tex]0.405465=0.1t[/tex]
[tex]\Rightarrow\ t=\dfrac{0.405465}{0.1}=4.05465\approx4.05\text{ years}[/tex]
Hence, it will take 4.05 years for an initial investment of $40,000 to grow to $60,000.
