日本語 Japanese Ask Questions Thread 6

If you have a question about the language, ask it and fellow 4channers might see it and answer it for you.

Japanese - Ask questions thread
http://dis.4chan.org/read/lang/1174719097/1-40

日語 Japanese Ask Questions Thread2 質問
http://dis.4chan.org/read/lang/1206158123/1-40

日本語 Japanese Ask Questions Thread 3
http://dis.4chan.org/read/lang/1267485093/1-40

日本語 Japanese Ask Questions Thread 4
http://dis.4chan.org/read/lang/1302350850/1-40

日本語 Japanese Ask Questions Thread 5
http://dis.4chan.org/read/lang/1330050873/1-40

I came across these lines in a manga (same page, different panels).

「住環境は問題ないかと」

「概算ですが養育費として毎月この程度お支払いできるかと」

I'm confused about the かと bit. My best guess would be that か makes the statement somehow more polite by expressing doubt, and the と would be short for と思います, but I'm not sure if that's an accurate interpretation (if at all). The speaker is a lawyer informing his late client's relative the situations, so wouldn't he be a bit more… firm?

Thanks in advance.