> Yes, it's a juggling act: Person A still has $1000 on the ledger in their deposit even if the bank lends $800 of that to Person B
Fractional reserve banking isn't up-to-date with the modern banking system, where in many cases, like in the UK, and in the US as of 2020, there are no reserve requirements. [1]
> But they aren't just adding numbers to a cell in a spreadsheet without having the money to back it
I disagree; this is the reality. Banks don't have to wait for deposits to extend loans. When creating a loan involves novel financial instruments to hide or offload the loan's risk, this has caused massive bubbles, as in the 2008 mortgage crisis.
This credit they extend to customers is "broad money" that, while not being created by the central bank, is effectively the same, as it is the deposit for someone else, which can be withdrawn.
[1] https://en.m.wikipedia.org/wiki/Reserve_requirement