I have the same question. I learned that по-моему means "in my opinion", which to me is slightly different from "I think". The first means this is how I feel about something, and the other means I'm not sure if this statement is correct. Are по-моему and я думаю что interchangeable in Russian?
No, по моему and я думаю are not interchangeable in Russian.
Я думаю - i think, i guess..
По моему - in my opinion, it seems to me…
But unfortunately "It seems to me that the entrance is under the bridge" is not accepted :(
There is one more meaning of "по моему" - всё будет по-моему - Everything will be as i wish.
It means something like "according to my way". In my experience it is used when speaking about something you're not sure of,or disagreeing on,presenting your own opinion. -Где Россия? -В Азии. -По моему в Европе. But I'm not a native speaker so if someone could validate it I'd be thankful.