Just to throw this out there...
Fed M2 is >$11t right now and has been increasing at an insane rate in the past few years, ~9% annually. Assuming 11m spendable coins now, we get to - wait for it - $1m/btc on the nose if BTC matches USD (without factoring in displacement)!

-- but what's interesting is that we're right around a 9% annual rate of inflation with BTC right now -- basically, any increase in nominal $price right now has to come from an increase in "real" investment money, but this will be changing. Before the next halving, the rate will dip well below the M2 inflation rate. Assuming M2 maintains its current course, BTC should be increasing 4-6% annually from USD inflation after the next halving, then ~7%/yr in the next halving. That's without factoring any kind of real growth in.
Anyway -- just looking at the effects of compounding inflation 10 years down the line, 11t @ 9% growth annually gets us to $26t M2. We'll have around 16-17M spendable coins at that point (I'll say 16.5M), I think, so we get ~$1.58M/BTC if it meets USD usage (and assuming that usage results in the same price effect).
What really underlines Bitcoin's awesomeness as a savings vehicle comes after that point, though, because inflation will be pretty much gone from BTC at that point. Assuming the USG keeps pumping M2 @ 9% for ANOTHER 10 years after, we get to ~$62t M2. Bitcoin, however, will only inflate to having maybe 18M spendable coins (and at this point, coin losses may actually match target inflation rate). 20 years down the road, then, the number we're referencing becomes ~$3.44M/BTC.
That brings us to 2034, yeah? (yeah.) Anyway, we have another 66 years in this century, so let's just figure the numbers out for the end product. 66 years of M2 inflation @ 9% gets us to 18.2Q (quadrillion, in case that's your first time seeing it!

). Assuming 19M spendable coins (after this point and probably somewhere in this range of time, BTC is deflating due to "coin loss leakage"), we get to ~$958M/BTC. I think, by the end of this century, either BTC goes over $1b/coin or it dies.