Question

Uncovered Interest Parity (UIP) theory question on a quiz which I don't understand fully the answer...

Uncovered Interest Parity (UIP) theory question on a quiz which I don't understand fully the answer to:

Question:
Suppose the ECB is expected to keep interest rates constant at the next meeting. If they lower rates, by UIP (and holding all else equal), should the euro:
(a) Appreciate
(b) Depreciate
(c) Stay the Same

Answer: Depreciate. Lower interest rates in Europe imply that the euro should appreciate over the subsequent time period. For that to happen, the euro should depreciate on the announcement.

My confusion: I understand that when interest rates lower, people will desire to invest in that currency less in the future and so there is an immediate depreciation. Why do we believe it will appreciate though over a subsequent time period?
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