I've been thinking about it and it still doesn't make sense. I'm a scientist, not an economist, so it's wildly out of my wheelhouse. Would you mind pointing me in the right direction?
Here's where I'm hung up. Let's assume a 10% fractional reserve and, for the sake of simplicity, just one bank and a dramatically simplified deposit/loan scenario, just to minimize the number of hypothetical people and transactions.
Person A deposits $1000. Bank lends $900 to person A which is sent to Person B.
Person B deposits $900. Bank lends $810 to person B which is sent to Person C.
Person C deposits $810. Bank lends $729 to person C which is sent to Person D.
Person D deposits $729. Bank lends $656 to person D which is sent to Person E.
Let's stop there. So we have one initial deposit of $1000, which has resulted in an additional $2,493 in deposits ($3,493 in total) and $3,095 in loans. The bank is now receiving payments, plus interest, on over 3x the amount of actual money it was actually given. To me, it seems like the bank is figuratively "printing money" and gaining interest on it. Nothing I've read on fractional reserve lending has suggested this is incorrect.
Halp!