Question

How long will it take for $2000 to double if it is invested at 6.25% interest compounded continuously?

Answer 1

solve
\[2=e^{.0625t}\] for t

Answer 2

doesn't matter what you start with, if it doubles you end up with twice your initial investment. you solve via
\[\ln(2)=.0625t\]
\[t=\frac{\ln(2)}{.0625}\]

Answer 3

i get 11.09 rounded. unfortunately no one is giving 6.25% interest, and no one is compounding interest continuously

Answer 4

so what your saying is it would take 11.09 years?

Answer 5

yes

Answer 6

i would say "11" because no one says 11.09 years.

Answer 7

what did you do to get 11.09?

Answer 8

i used a calculator and computed
\[t=\frac{\ln(2)}{.0625}\]

Answer 9

I need to show my work

Answer 10

steps are
\[4000=2000e^{.0625t}\]
divide by 2000
\[2=e^{.0625t}\]take the log (write in equivalent logarithmic form
\[\ln(2)=.0625t\] solve for t get
\[t=\frac{\ln(2)}{.0625}\] use a calculator get
\[11.09\]