Question

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24. If you invest $4000 in an account that gains 7% interest each year, how long will it take for there
to be $9000 in the account?
(5 Points)

Answer 1

Answer: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

Explanation: