we use the following formula for interest compounded continuously:

T = P*e^(rt)

where 'T' is the total amount accumulated

'P' is the principal amount

'r' is the rate

't' is the time, in years, over which interest is accrued

...and 'e' is the exponential constant approximated by 2.718

we want to solve for T=3500 when r=0.09 and P=1000

3500=1000*e^(0.09t)

solving for t, we have:

t=13.9196

it will take approximately 13.92 years for the $1000 to be worth $3500