The redevelopment that's been ongoing for a while in this town has finally been completed.
I’ll call you back when my cellphone battery has finished charging, okay?
A perfect finish is when everything is at total completion. Nothing is left over and all is done.
This is a jukugo word, which usually means on'yomi readings from the kanji. If you know the readings of your kanji you'll know how to read this as well.