NO, it is not finished.
The anime finished before the manga:
Anime finished: April 16, 2006
Manga finished: November 01, 2008
MangaUpdates contains information about the anime adaptation and indicates that it is incomplete.
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Binchou-tan tells the gentle story of a young girl living a solitary life in a rural, mountainous setting.
The anime offers a slice-of-life glimpse into her daily routines, focusing on the simple tasks that fill her days: preparing meals, foraging for resources, and maintaining her home.
Each episode showcases the beauty of her quiet existence and the subtle joys she finds in her connection to nature.
While she lives a modest life, she is not entirely alone, as a cast of friends and acquaintances occasionally visit and offer support, adding warmth and companionship to her world.
The overall narrative emphasizes the importance of finding happiness in simplicity and appreciating the small moments of everyday life.