According to my research, the average sum a person would invest in bitcoins is $1000. Therefore, 4 million new users are needed in addition to the 1 million current ones to reach $7000.
That seems like a lot to ask for the next 7 months. I think chances are some bigger investment funds are going to have a big impact though.
That is only 25.8% monthly growth in userbase. Which happens to coincide with the long-term slope of the price appreciation curve.
With this adoption growth, without the logistic slowing, we would be at 2 billion people in March, 2017.
My suspicion is before we get anywhere near 2 billion people using bitcoins that there will be factors at play that will dwarf the impact on price arising out of adoption and its use in day-to-day transactions.
My fear is as the realisation dawns on the bigger players that Bitcoin is 'the one' that it will be pumped by banks and central banks who can magic large sums of fiat into existence with which to buy bitcoin (and who may even dump gold temporarily), creating the ultimate bitcoin megabubble so that billions of latecomer ordinary people and businesses buying their first bitcoins will be shafted as the great bitcoin dump starts, into pms, into land, artwork etc. into a 'better' crypto - assets that had been neglected for the period bitcoin was so attractive, even back into fiat (they could use this point to launch more 'stable' 'new crypto-dollar or new crypto-pound etc.) until bitcoin finds a stable long-term pricepoint well below (even orders of magnitude below) the hyped price the masses bought at. Problem is of course nobody beforehand can know what this price will be. We would still be in a much better world than today because with bitcoin established fiats (old or new) will not be that attractive but if central banks are deliberately hyperinflating forcing people into crypto on their pump stage people could end up with 1000th of what they had before.
Btw, I'm only just exploring this idea so please point out if there's an obvious reason this is not how the future looks!
If that happens we might not end up with the assets / bitcoin and all the stuff in the most desirable hands, true. However what makes me have a positive long-term outlook (for humanity, I personally might be gone by the time we see the fruits of this) is the fact that we will then have transitioned to a sound money regime, which should have the effect of a fairer, more level playing-field and much a more efficient economy that puts much less strain on our human and natural resources than what we currently have (the fiat-fuelled continuous growth paradigm that keeps producing these cancerous escapades and keeps hurting us).
So even if entities that don't "deserve" it end up with the most wealth initially (by the way you described), after the transition is complete that wealth will dissipate from them if they make bad decisions towards the people that make good decisions. If they make "good" decisions on the other hand, they get to keep and grow their wealth, and rightly so. Noone will be bailed out by the taxpayer as is the case now (no more inflation tax) and everybody will suffer or enjoy the consequences of their actions, as should be.
I hope it'll work out and I hope I'll be able to see and live it, too. Crypto is our best shot at this.
This view may be simplistic or even naive, but for lack of better options I hold it (and bitcoin, too ;-) )