To double a 1k bank in 4 mos you'd need to make >0.8% net profit a day (>25% monthly return). Not unrealistic (the "£100 into £120" before threw me a bit) and I think most traders would be delighted with that performance as it would lead well into 6 figures by the end of the second year (after fee). However, if instead you end up making say 0.5% profit per day (which is more in line with my estimates), you're reaching <25k in the same time period. In that case a £500 monthly contribution would boost your growth close to the 100k mark.
The good news I think is that, while lower profit margins can significantly dampen prospects with a small bank, there's only around a 1-year "delay" in the above example for achieving a living wage level. And if you manage to increase your deposit limit after getting that far (I'm assuming that's how BF look at it) then you can always boost going forward for that 1M
It's all very speculative of course, just sharing for curiosity's sake. (You can use any compounding calculator, I used this one following a post in another thread.)