If I mistakenly give the bank two different amounts, does that change the offer I get?

Yes, it does. The amount is not just a figure on the form; it decides the rate tier, whether the amount is above the minimum of the product or of a variant of it, and the return you get. So if two different figures were said in the same conversation, any calculation on one of them may not describe your money. What to do: confirm the right amount and state it clearly, and if you are correcting, say so plainly ('no, I meant…') so the old figure is dropped. Then ask for the calculation again on the right amount, and do not rely on any offer made on the other figure. Note that the amount actually locked can differ from the one in your head if the product is sold in set multiples. Before signing, check the amount written on the application and in the key-facts statement, the minimum and its multiples, and the rate tier that amount falls in.