A sudden Rise in the EU Interest Rate would likely Increase Interest Rate in the USA and Depreciates its Currency.(Global Economics)

I agree with the statement stated above. As per the equation depicting the link between the foreign exchange and financial markets we have; (ieu-ius) > xa, where ieu is the interest rate in the EU and ius is the interest rate in the USA.

Firstly, under the condition of perfect capital mobility, the sudden increase in the interest rate in EU will attract the investor of U.S. to make the capital investment in E.U. conditioning that they should get a certain amount of premium to cover their risk for cross-border investment. This soon creates the scarcity of the loanable fund in the U.S. economy which then creates an upward pressure in the U.S interest rates. Further, the excessive supply of the U.S dollars in the foreign exchange markets to convert it to the foreign currency for the investment in EU will depreciate its values.

Further, if we analyze from another angle, the increase in the EU interest rate will make foreign short-term investments attractive, here we could observe an increased outflow of short-term capitals from the USA to EU. Now for the USA, a higher domestic interest rate is required to balance the BOP at all income levels. Ultimately the BOP curve shift upwards, at this new BOP curve the existing interest rate is low for attaining BOP (domestic)and for the time being incipient deficit appears.

The domestic currency depreciates (shifting the BOP curve downwards from the increased point, i.e. to right from the initial increased position) which increases the export and decreases the imports, these shifts the IS curve to the right (due to increase in the net exports) where a new equilibrium is reached between the initial LM curve, new IS curve and new BP curve, increasing the interest rate, income as well as depreciating the US currency.