(Apologies to Bill Watterson)
Where have the billions gone? Not vanished in a poof of smoke...
Sometimes it does vanish in a poof of smoke.
Maynard, Karl, Ayn, and Alan each have 100 g.p. (that's gold pieces for you non-dungeons&dragons economists). Maynard and Karl put their gold in First Bank, while Ayn and Alan put their gold in National Bank.
Maynard: 100 gp
Karl: 100 gp
Ayn: 100 gp
Alan: 100 gp
First Bank can now give a 50 g.p. loan to Alan. Alan now has 150 g.p. in his bank account. When Maynard and Karl check their bank accounts, they still say 100 g.p. each.
Maynard: 100 gp
Karl: 100 gp
Ayn: 100 gp
Alan: 150 gp
National Bank now has 250 g.p. and makes a 100 g.p. loan to Maynard, who (according to his bank) now has 200 g.p. in his bank account.
Maynard: 200 gp
Karl: 100 gp
Ayn: 100 gp
Alan: 150 gp
Back and forth it goes. Money magically appears without a single paper bill being printed.
Now if everyone suddenly decides to withdraw their money at the same time, what happens? The two banks have "real" g.p. to cover the first 400 g.p. of withdrawals. After that, the banks collapse and all the "wealth" went poof.
It's not real wealth of course - what can you really do with g.p. other than trade it for what you really want, like food to eat, a place to live, energy, heat, clothing, video games, +1 backscratchers, AK-47s, gas masks, printing presses, tractors, assembly lines, or whatever.