"Unless you're literally storing notes under your bed, your bank is lending out your money to someone."

Banks don't lend deposits. It seems that it's one of those fallacies that never die. Maybe, because it's in the textbooks.

"[..]reserve requirement does not act as a binding constraint on banks’ ability to lend and consequently their ability to create money. The reality is that banks first extend loans and then look for the required reserves later."

From: http://www.investopedia.com/articles/investing/022416/why-ba...

From your quote: "..and then look for the required reserves later."

Banks are required to have certain reserves. It's true that they can already lend money while they are still looking for the required money to refill their reserve. But they will have to fill up their reserve at some point, and for that they need money, otherwise they will have to stop lending.

So it is not a fallacy that banks are lending deposits and it's not so strange that this is in the textbooks.

Banks can get reserves three ways:

-From deposits. -In the interbank market, where banks with excess reserves lean to bank that need reserves. -From the Central Bank.

The Central Bank always lend the necessary reserves. A different issue is if that would be a good business for the bank.

The point is that the quantity a bank can lend it's not limited by deposits as the normal narrative imply.

That might have been true long ago but with fractional reserve lending this linkage is effectively severed. The bank usually isn't lending out your money. The total amount a bank can lend out is constrained more by regulatory requirements and its invested capital than by the balance of customer savings/checking/CD accounts.

It's true that the lending amount of a bank is heavily constrained by regulatory requirements. But that doesn't mean that banks are not lending your deposited money to someone else.

Consider two banks in the same country, so having to comply with the same reserve requirements. The reserve requirements are defined as a percentage of the amount on the banks's deposit account at the central bank. So the bank which can transfer an extra deposit to this acount is the one which is able to lend more money.

And what, would you say, is the current legally mandated "reserve requirement" in the US?

Even putting your money under the mattress doesn't make a difference: as long it's a stable amount economy-wide, the central bank can just print enough cash to make up for that amount under mattresses. Cash is free to make.

Sure, the bank benefits, but with near zero interest rates on saving accounts (in the US at least) the wealth isn’t productive for you. You are actually losing money to inflationso it’s not a good idea to keep all of your wealth in cash.

True in the larger economic sense. But on an individual level, even the best savings accounts which typically get a bit above 1% interest will not keep up with the 2-3% inflation that we see (and the fed targets).