Should I drain my savings or finance to replace my furnace/AC/water heater

I’ve been getting some quotes on replacing these items in my home since I have been having trouble with them. One of the better options I have gotten was from a local HVAC company. They quoted me just shy of $11k to replace my furnace, AC and water heater.

The furnace is about ~30 years old and the water heater is about ~15-18 years old. I am not sure about the AC unit, it is definitely not new by any means and is probably just as old.

My questions is that I have $13k in my savings. Should I use that and have about $2k left over and pray that I don’t have an emergency any time soon. Or should I go about getting financing and possibly pay some interest, but still keep the majority of my savings?