Can someone who knows how that works do the math for us?

It's an arbitrage issue. If you can borrow EUR for 1% and it costs %1 to get a USD/EUR hedge, you can turn around and loan USD for 2% and be guaranteed to not lose money. The market eliminates arbitrage opportunities whenever they appear; so if the cost of borrowing EUR is less than the cost of borrowing USD, you'll have to pay at least the difference in order to get someone to guarantee a rate for converting USD back to EUR later.

There could in theory be other risks in EUR which prevent the arbitrage (legal? liquidity? cost of initial transaction being high?) which is why I'd prefer to see actual numbers bearing that out instead of just a derivation from first principles.

In general the price of a futures contract is that which avoids arbitrage opportunities.

If the interest rate in EUR is 2% and the interest rate in USD is 4% and the cost to maintain a EUR/USD hedge is less than 2% then you can make free risk-free money by borrowing EUR at 2%, exchanging it to USD, and lending it out at 4%.

Such a situation is unstable as more and more capital would pour in to take advantage of it and the cost to hedge would rise or the interest rates would move closer together until the gap disappeared.