I find it helpful to convert debt interest rates to real money. My student loans are down to the point where I could drain my savings and pay for them, and while they are low interest they're still above inflation. (Probably. It's kind of getting close.) But if I actually calculate in real money what's left, it's about $125 in interest left to pay over three years. I'd rather hold on to the cash; at this point in my life, that's a rounding error. A largish one, but still a rounding error. Whereas losing all my savings could really hurt; we dipped into them quite deeply recently when I had both my cars break down in the same week and also a moderate house issue.

Keeping cash on hand instead of paying off cheap debt can prevent you from having to incur expensive debt, which functions as a non-obvious term in deciding how much cash to keep around.