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Answer :
Final answer:
The Japanese yen is trading at an annualized forward premium of 6.49%, indicating that the yen is expected to be stronger relative to the U.S. dollar in the future compared to its current spot exchange rate. The correct option is 1) premium; 1.57.
Explanation:
The correct option is 1) premium; 1.57. The question at hand involves calculating the per annum forward premium or discount of a currency exchange rate, specifically the U.S. dollar to Japanese yen rate. To find this, we look at the spot rate and the forward rate. Given that the current spot rate is ¥125/$ and the 90-day forward rate is ¥127/$, we can determine that the Japanese yen is trading at a forward premium because the forward rate is higher than the spot rate. The annualized premium is calculated using the difference between the forward and spot rates, divided by the spot rate, and then annualized by scaling up to a full year from the 90 days.
Let's perform the calculation:
Premium = ((Forward Rate - Spot Rate) / Spot Rate) * (365 / Number of Days)
Premium = ((127 - 125) / 125) * (365 / 90)
Premium = (2 / 125) * (365 / 90) = 0.016 * 4.0556 = 0.0649 or 6.49%
Therefore, the yen is selling at a per annum premium of 6.49%, not 1.57%, nor is it selling at a discount. Accordingly, option 3) premium; 6.30 is the closest to the calculated value, albeit slightly inaccurate as the precise calculation yields a premium of 6.49%.
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