I do have an emergency fund. Actually, I have two of them.
Keep six months living expensese in an on-line savings account. This money is not to be touched except in the direst of circumstances. It is augmented monthly by automatic funds transfer, and I'd like to see it climb to a full year's expenses.
Locally, I have two savings accounts that I also fund monthly. One is used for annual and semi-annual expenses (insurance, tags, taxes); the other is used for -- emergencies.
Unbudgeted expenses that would disrupt my cash flow. I like the term "slush fund" used earlier. There's a difference between an emergency and an inconvenience, and I like to be ready for both.
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