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As far as I'm aware, the Federal Reserve has 4.5$ Billion on its balance sheet.

Where did it get the money for buying all those assets?

I understand that it makes money out of interest on the bonds it holds, but where did it get the money to buy those bonds in the first place?

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If you read Fed's balance sheet, you'll see a corresponding increase in its liabilities under various deposits. They simply credit the accounts of institutions who sold them the assets.

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