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Is there an advantage to keeping a liquid emergency fund if one also has an untapped line of credit?
Stop trying to make money with your emergency fund. It's purpose is to sit there idly waiting for a bad day. A day when you need that cash (liquid) not in a bank or a line-of-credit. The few dollars you might make trying to chase interest/investments with your emergency fund aren't worth it if a true emergency came up and you couldn't get to your cash in time. Once you have a fully funded EF then start investing heavily. That's your future game plan. Not the EF.