How long, to the nearest year, will it take me to become a millionaire if I invest $1000 at 8% interest compounded continuously?

In you are dealing with interest compounded continuously, use the formula:  A = Pe^(rt)  where:

A  =  final amount = 1,000,000        P = initial amount = 1,000     e = 2.718...

r = rate (as a decimal) = .08            t = number of years

1 000 000  =  1000 · e ^(.08 · t)                   divide by 1000          --->      1000 = e ^(.08 · t) 

Since your variable is an exponent, find the  ln  of both sides:       ln(1000)  =  ln( e ^(.08 · t) ) 

An exponent within a log comes out as a multiplier:                      ln(1000)  =  (.08 · t) · ln(e)

ln(e)  =  1                                                                                 ln(1000)  =  .08t

Divide by .08:                                                                                       t  =  86.3 yrs.  (approx)

1000x1.08

=1080

1000000/1000=926

it wold take 926 years,

to check do

1000x1.08^925

hope this helps (and hope it is right!)