200 years.
Here's an example:
Let's say the population is 1000. 0.5% of 1000 would be 5. That means every year the population would increase by 5.
Now, the double of 1000 is 2000. That means we need 1000 more people to double the current size.
1000 people needed / 5 people every year = 200 years.
Message me if you need further explanation. No problem.
:D