Banks lending resrves

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Focusing on banks lending reserves to other banks who need to meet the reserve requirement, are the interest on fed fund rates given directly to the lending bank? Or to the fed? Also wouldn’t it be disadvantageous for the lending bank to lend reserves to another if the fed fund rate was not higher than the interest that could be otherwise earned from the principal of the lending bank’s excess reserves, or is the rate always higher?
I may have completely misunderstood the process but any explanations would help, thank you!

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Interest rates are “use of my money” fees, so it goes to whoever provides their money.

No bank is going to make another bank pay extra for balancing their books, because when they need a loan to balance theirs, they don’t want to pay extra either. They’re not doing it (just) to make money, but because they also have to have that money on hand themselves.

And if they have money beyond the daily need, a straightforward loan to another bank will give a speedy return on investment, unlike a mortgage or credit card that is only repaid in pieces over time. Money just sitting there actually loses value, so any kind of activity is better than nothing.

There would be a sweet spot where it’s profitable, but you’re right in that loaning to other banks at prime can’t be the bulk of their income.

I’m not sure how much they’re allowed to invest in other banks – that feels like the kind of risky trading that could be prohibited by the reserve, so maybe they’re not allowed to charge more than prime.