(i) Let i
denote the US interest rate, and let i*
denote the British interest rate. Interest parity requires that i=i*+D, where D denotes the expectede
depreciation of the dollar. As i=4%
and i* = 6% (equal tot
interest rate charged by the banks minus their 2% premium), D=-2%. Thus, the dollar is expected
to appreciate by 2% against the pound or, equivalently, the pound is
expected to depreciate by 2%.
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(ii) If I borrow at 8%, and can earn 4% in
dollars, I need the pound to depreciate by at least 4% in order to
cover my costs.
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(iii) If the pound
depreciates by 7%, I can calculate how much money I make as follows. I
borrow 10 billion pounds, and convert it to $10E billion. After a year of earning
4% interest, this turns into $10.4E
billion. I then convert
enough of these dollars back into pounds at the new exchange rate E/1.07 to repay principal plus
interest equal to 10.8 billion pounds. Let y
be the number of dollars I need to repay. Then y/(E/1.07)=10.8 billion, implying that y=$10.093E billion. Subtracting the dollars
I must repay from what I earn gives a net profit of $0.3065E billion. Thus, if the exchange
rate is, say $1.80 per pound, I make $551 million.
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(iv) Because I've taken
intermediate macroeconomics.
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