Interest rate parity

The 1 year forward rate for the pound is USD1.567 and the spot is USD1.553. The real rate of interest is 2% in all world economies. If expected inflation equals 3% in the US and interest rate parity holds, the nominal interest rate in the UK must be A. 2% B. 4.06% C. 5.95% D. 5% I keep flogging myself for setting up these problems wrong. C is correct. Any advice …

interest rate parity, (1.567 US/L )/ (1.553 US/L) =(1+ 5%)/x+1 so x=4.06% B

Are you sure the answer is C? I would have thought B is the correct answer. Note that the pound is appreciating against the dollar (since it gets 1.567 in a year and only 1.553 today). So you get a bonus by holding pounds instead of the dollar, simply by the changing currency exchange rate. That bonus should be offset by a lower UK nominal interest rate. The nominal rate in the US is about 5% (~2% + 3%). So the UK rate should be below 5%. Thus, I don’t see how C is correct without giving rise to an arbitrage opportunity. That’s the intuition. In terms of calculation, I agree with the preceding post.

Sorry, B is correct.

I get C (1+Rd US) = (1+R GB)*Forward US/Spot US (1+0.02+0.03)=(1+RGB)*(1/1.553)/(1/1.567) R GB = 5.95%

The reason the prior calculation yielded the wrong answer is that the rates were inverted to be FC/DC without a corresponding change to the interest rates. The equation is either: Forward (DC/FC)/Spot (DC/FC) = (1+domestic interest)/(1+foreign interest) or Forward (FC/DC)/Spot(FC/DC) = (1+foreign interest)/(1+domestic interest) It doesn’t matter which currency is given which label, so long as there is consistency.

you know 1 pound buys now 1.553 us and will buy 1.567 in the future. therefore us will depreciate. that means uk interest rate needs to be lower. So you know it’s A or B the above calc are correct

i actually calculated the nominal rate as (1.02)(1.03) and B worked out to be the “closest answer”