Question

if $4000 is invested in an account that pays interest compounded continuously, how long will it take to grow to $8000 at 7%?

Answer 1

So, since it is continuously, we need to think of PERT

$A=P\times e^{rt}$

So, we just plug our numbers in to solve for T

$8000=4000e^{.07t}\\\ln(8000)=\ln(4000e^{.07t})\\\ln(8000) = \ln(4000) + \ln(e^{.07t})\\\ln(8000)=\ln(4000)+.07t\ln(e)\\\ln(8000)=\ln(4000)+.07t\\\frac{\ln(8000)}{\ln(4000)}=.07t\\\frac{\ln(8000)}{.07\ln(4000)}=t\\ 15.479=t$

It will take 15.479 years