This is related to a question [on the Interpersonal Skills
site](https://interpersonal.stackexchange.com/q/2951) about refusing free
goods from shopkeepers, etc., and paying for them instead. (Note: I'm not the
OP of that question, I'm not blind or in Germany.) The most popular answer now
suggests a polite but firm "I insist!", and that is what I'd probably use if
the conversation was in English. But in Japanese, I'm not so sure how to say
this. Would something like「失礼{しつれい}します、お支払{しはら}いたいです」be fine?

It's not uncommon to get something for free as サービス in Japanese stores,
especially if the shopkeeper made a mistake in something. In such instances,
I'd still like to pay for whatever it is they are offering me, especially so
if that's what I wanted in the first place.
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politeness word-requests
How can I say "I insist on paying" (for a free item) to a shopkeeper?
I think that it's fine.

I just add "thank you so much and I'd really appreciate it" into your phrase.

「おそれ入ります。おもてなしには感謝しますけれども、ちゃんとお支払いいたします。」

Thank you so much. I'd really appreciate your hospitality. Since I can afford
it, I would like to pay for it.
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Japanese can be offended if you are trying to pay for free stuff or if you are
trying to leave tips. Probably in your case, it's better to accept a gift and
buy something else that isn't free as gratitude.

Something like this also should work: 「お支払いさせてください」, 「お支払いを[受け取って]{うけとって}ください」
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The other answers I feel are OK, but I wanted to point out that I think your
attempt "お支払いたい" is not grammatically correct.

As far as I know the honorific お is attached to nouns (or well, する-verbs) but
not to verbs directly. Therefore if you say お支払い, here 支払い is a **noun** hence
you cannot conjugate it in the たい-form. You have two options:

  1. Use する to turn the noun into a verb and say something like: お支払いしたい. 
  2. Drop the お and just say 支払いたい using the **verb** 支払う.

This being said, I think something more natural for what you want to say could
be:

  1. お願いします！是非{ぜひ}お支払いさせてください。
  2. お願いします！是非払わせてください。

Adding お願いします makes it a polite request, and I think that 是非 adds the feeling
that you really would like to pay.
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As for polite form, everybody else has already answered it, but for me, I
would say:

> どうしても支払いたいです！

どうしても have a meaning like "no matter what" or "at any cost."
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