Типа мне конец да

Elena, you make it sound like there's only one rate of exchange - they change daily.

Olivia, but the offer was based on some concrete old rate of exchange. Is this wrong??

If I don't know at what rate of exchange it is calculated I will use "a", and if I know it - "the". It depends on the situation and in this phrase it's not clear what is meant so both variants are correct. Do you agree?

One company made an offer to another company. And the other company comes back in 3 months and say ok, that they want to buy their products. And the first company explains that their offer was based on the rate of exchange which is no longer valid.

Elena, if I can step in - even in those situations you use A rate of exchange, because there are several. To give you an analogy, if someone tried to call you using a previous telephone number, you would say "I didn't get the call because he called me on an old number." I think the fact that you use THE OUTDATED is especially marked, because it makes it sound like there is only one. Also, remember the the "exclusive" interpretation of THE assumes that the listener also knows which rate of exchange.

In the example with the phone call, if you said THE OLD NUMBER, the listener would have to know what that number was.

Hi, Uly! Thank you. Coming back to the rates of exchange - do you think there can't be a situation when this old rate of exchange is known to both parties?

Yes, but it wouldn't necessarily be the rate of exchange itself, because by their nature, rates of exchange fluctuate. A more reasonable scenario would be one where there were two contracts - one with one rate of exchange and one with another. If you made reference to the rate of exchange in the first contract, you could say THE OLD RATE OF EXCHANGE, because then it's not about the fluctuating rates per se, but about the rate in second contract superseding that of the rate "frozen" in the first contract. I hope that makes sense to you - I know it's hard to grasp. Understanding the intricacies of the definite article is a tricky business. But this is just one of those cases that illustrates just how pivotal it is in the anglophones psyche.