carry adjustment for currencies

Sheroda is considering international securities but does not want to be exposed to foreign currency risk. She asks Parisi if there are derivative contracts to address this risk. Parisi comments, “there is a large market for foreign exchange forward contracts that are used to hedge this risk. Let’s assume you want to hedge a EUR investment back to USD. The carry adjustment in a currency derivative contract is very similar to other carry models such as equity derivatives. In this case, if the USD/EUR forward exchange rate is higher than the current spot rate, then the Eurozone interest rate must be lower than the US interest rate.”

can someone explain why the eurozone interest rate should be lower than the us interest rate. i understand the general idea of carry but i am struggling to conceptualize this for currencies.

It is easy to grasp with the formula between spot rate, forward rate and interest rates.

F0(USD/EUR) = S0(USD/EUR) * (1 + iUSD)t / (1 + iEUR)t

if forward rate is higher than the current spot rate, then (1 + iUSD)t / (1 + iEUR)t is greater than 1, which means US interest rate is higher than Eurozone interest rate.