From IB website: “Accounts with a Net Asset Value (NAV) of USD 100,000 (or equivalent) or more are paid interest at the full rate for which they are eligible. Accounts with NAV of less than USD 100,000 (or equivalent) receive interest at rates proportional to the size of the account. There will be no interest paid on the first USD 10,000 of cash. Please note that interest is earned on positive settled cash balances held in the securities segment of an account but not on cash held in the commodities segment.” Does that mean, if NAV > USD 100,000, you earn interest on a EUR 10,000 balance or not? https://www.interactivebrokers.com/en/accounts/fees/pricing-interest-rates.php
I believe the answer is "yes", if that EUR cash balance is larger than 10k (the current interest rate for the first 10k is 0%). Why do you doubt this? Have you experienced otherwise?
I do not understand the difference between having a NAV > USD 100.000 and NAV < USD 100.000, if it does not mean that you earn interest below USD 10.000 when NAV > USD 100.000. In other words, what does this mean: "Accounts with a Net Asset Value (NAV) of USD 100,000 (or equivalent) or more are paid interest at the full rate for which they are eligible?"
If your account value is less than 100k USD they'll give you a lower interest percentage. Let's give an example, assuming a flat 1% interest rate for EUR: Account value 100k USD or more: you receive 1 EUR for each 100 EUR cash in your account. Account value 80k USD: you receive 0.8 EUR for each 100 EUR cash in your account (80% of 1%).