I was wondering if the expression “I thank you for your answer” isn’t nicer than ” Thank you for your answer”.
For comparison, saying “I thank you” in French is nicer because the person who says it is more involved than when he/she simply says “Thank you for …”.
Is it the same thing in English?
In English, there’s minimal difference. It really depends on the formality of the context.
I thank you for…
would be better suited under Dear…. in a letter (or nowadays, an email).
Thank you for…
usually belongs in more casual speech. There’s no real difference in how ‘involved’ either one is. It depends on the context.