と思います vs. と思っています

Question

Consider the following sentences:

引越しをして本当に良かったと思います。

引越しをして本当に良かったと思っています。

If I use と思います, does the sentence become more formal?

Answer 1

It's not about formality, but meaning difference.

Both are translated "think", but the plain ending 思います（思う） stands for an instant judgment at that moment, reacting to an event or responding to a question; or begin to think. The stative 思っています（思っている）, on the other hand, means holding an idea or belief in one's mind for a duration.

Another explanation, if you prefer, is that 思う : 思っている is analogous to put on : wear.

私を誰だと思っているのだ。 Who do you think I am!?
× 私を誰だと思うのだ。

In the examples above, only the first one tells the meaning in English. The second is very, um... prosopagnostic (if grammatical in any way).

この映画を見たら、人生も捨てたものじゃないと思いました。 When I watched the movie, I thought the life is not as bad as it seems.
× この映画を見たら、人生も捨てたものじゃないと思っていました。

In these examples, たら indicates immediate trigger, so only the first sentence is grammatical.

Related

• Difference between volitional +と思う and volitional+ と思っている
• Vようと思います／Vようと思っています

Answer 2

Neither is particularly more formal.

The difference is that both 思う and 思っている can be used for the 1st person while you can't use 思う for present indicative by the 2nd and the 3rd person (except historical present or such in narratives).

Answer 3

They’re both equally polite but the tenses are different. The non-past tense 思います(思う) is and action that is done in the present or future. In this case having a thought or holding an opinion. The present continuous tense 思っています(思っている) is an ongoing action. In this case having an opinion at the current time (implying that you could change your mind). You can’t use this form of 思う for someone else’s thoughts such asking a question.

Using either form of 思う is regarded as less assertive than saying a direct statement as you’re admitting it’s your opinion (limited by your perception) and could be wrong. It’s similar to say “I think”, “probably”, or “it could be” in English. Either of these can still be used in plain dictionary form in conversation.

Note that 考えます or 考えています has a similar meaning but is different. The act of thinking or “considering” but does not follow a quote or statement with the と particle. You can say 考えます (I’ll think about it) without specifying your thoughts.