Another person living in Japan. Sounds about right. A unit from a good brand (daikin, mitsubishi) costs ~$800? More or less depending on the room size. We had them installed when we built the house, installation price included. Two are enough to keep our house cool or warm in any season (it's a well insulated house). We have another in the guest room, use it only for when guests stay.
Our renovation company had rip-off pricing on years-old models, so we just asked a few electronics stores for quotes. First looked up the cheapest online options as baseline pricing, and then used the in-store sale deals to stay at the same total price but get the units in the bigger rooms upgraded to fancier/higher grade options.
