a.The euro is expected to appreciate at an annual rate of approximately ((1.005 - 1.000)/1.000)•(360/180)•100 = 1%. The expected uncovered interest differential is approximately 3% + 1% - 4% = 0, so uncovered interest parity holds (approximately).
b.If the interest rate oN180-day dollar-denominated bonds declines to 3%, then the spot exchange rate is likely to increase-the euro will appreciate, the dollar depreciate. At the initial current spot exchange rate, the initial expected future spot exchange rate, and the initial euro interest rate, the expected uncovered interest differential shifts in favor of investing in euro-denominated bonds (the expected uncovered differential is now positive, 3% + 1% - 3% = 1%, favoring uncovered investment in euro-denominated bonds. The increased demand for euros in the spot exchange market tends to appreciate the euro. If the euro interest rate and the expected future spot exchange rate remain unchanged, then the current spot rate must change immediately to be $1.005/euro, to reestablish uncovered interest parity. When the current spot rate jumps to this value, the euro's exchange rate value is not expected to change in value subsequently during the nexT180 days. The dollar has depreciated immediately, and the uncovered differential then again is zero (3% + 0% - 3% = 0).
a.For uncovered interest parity to hold, investors must expect that the rate of change in the spot exchange-rate value of the yen equals the interest rate differential, which is zero. Investors must expect that the future spot value is the same as the current spot value, $0.01/yen.
b.If investors expect that the exchange rate will be $0.0095/yen, then they expect the yen to depreciate from its initial spot value during the next 90 days. Given the other rates, investors tend to shift their investments toward dollar-denominated investments. The extra supply of yen (and demand for dollars) in the spot exchange market results in a decrease in the current spot value of the yen (the dollar appreciates). The shift to expecting that the yen will depreciate (the dollar appreciate) sometime during the next 90 days tends to cause the yen to depreciate (the dollar to appreciate) immediately in the current spot market.
Law of One Price indicates that a product which is easily and freely use for trading in a perfect competitive international market should have the similar price all around the world, once if the prices at different places are determined in terms of same currency which we called it as equilibrium international price. The law of one price proposes that the price (P) of the product measured in domestic currency will tied up to the price (P f ) that means the price product measured in terms foreign currency through the current spot exchange rate (e, Domestic currency/Foreign currency)
And The law of one price works perfectly on traded commodities, at particular point of time or in other time, as long as governments permit freedom in trade in the commodity, which is traded highly commodities include gold, other metals, crude oil etc.
So, on the basis of above discussion we can state that the Law of One Price better apply to gold.