I've been sub-20 for 6 months and am only now in the 17-18 range. I agree with a number of these cubers that it may take me 1.5 years to go from sub-20 to sub-15. Plus, I'm 29 and my hands don't work the same as a teenager!
I don't even remember this happening, but that's probably because I didn't consider sub15 as a thing at all.
According to WCA, it looks like a year, but I improve slowly so you can probably do it faster.