Q. Is a depreciation of the dollar/euro exchange rate correlated with a decrease in the dollar return on U.S. deposits?

Answer: No, suppose that the Interest Parity is maintained. Embracing the foreign interest rate constant one would expect a depreciation of the dollar/euro exchange rate that is an increase in E to be correlated with a decrease in the U.S interest rate and dollar returns on euro deposits. Though the higher expected inflation in the U.S imply an increase in the expected future dollar to euro exchange rate. Therefore expected depreciation increases despite a depreciation in the current dollar to euro exchange rate.