y' = 0.11y, where y' is the amount you get per year, y is the amount you have, and t is time (in years)

dy/y = 0.11dt

ln(|y|) = 0.11t + C

y = C*e^(0.11t)

y(0) = 3,415,569

y(0) = C*e^0

C = 3,415,569

y = 3,415,569*e^(0.11t) --> This is the equation you're looking for

y = 5,000,000

5,000,000 = 3,415,569*e^(0.11t)

e^(0.11t) = 1.464

0.11t = 0.381

t = 3.464

If you don't know calculus, don't worry about the above. If you do, just ask and I'll explain all the steps.

Edit:

Or are you saying that the interest rate is compounded daily? I'm having a little trouble understanding your wording.