Dr. Hess wrote: You're comparing no fund and no emergency with 3K fund and an emergency. You're missing a couple of options. No fund with 3K emergency and 3K fund with no emergency. Then there's cost of not having a fund. The math/probability starts to get tricky in the analysis, but you are always better off having the 3K fund, even if you just drained it. The cards you cut up, never allowing yourself to fall into that trap again.
Pretty sure I covered all four basic options. Both fund and no fund were meant to be addressed in each scenario, but it was somewhat implicit.
Let's try it again, more explicitly in case I missed something. Feel free to demonstrate my idiocy. I'm good at being dense sometimes.
Case 1: No fund/No emergency. This one's easy. It gets you out of debt the fastest, and since nothing went wrong, the lack of a fund doesn't hurt.
Case 2: 3k fund/no emergency: Still not too bad, because you didn't have an emergency. But you paid extra interest on the $3k you didn't use to pay off the CC.
Result for 1&2: No fund comes out ahead.
Case 3: $3k Fund with $3k emergency: This is the type of thing you have the fund for. Fund pays off the emergency, and you keep on going. However, you've still been paying interest on that $3k you used to make the fund between when you started and when the emergency occurs.
Case 4: No fund with $3k emergency You get stuck putting $#k back on the card. A depressing occurrence to say the least. However, it's the same $3k that you would have left on the car earlier to build up the fund, so your total balance on the card is in the same ballpark as in Case 3. In fact, since you've not been paying interest on that $3k in the meantime, your balance is still somewhat better than in case 3.
Results for 3&4. No fund still comes out ahead.
Keep the card for just long enough to build up a fund after thee CC has been paid off. Then cut it up.
This is predicated on a realistic grasp of what does or doesn't constitute an emergency. If you don't have that, the fund makes it harder to fall back into bad habits.