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Question:

# Assume that one year ago, the exchange rate between the Japanese yen and the euro was 100 JPY/EUR, and the exchange rate between the Japanese yen and the U.S. dollar was 80 JPY/USD. Current exchange rates are 104.2 JPY/EUR and 76.6 JPY/USD. Which of the following statements is most accurate1

A The USD has depreciated relative to the EUR.
explanation

We can calculate the current USD/EUR cross rate as 104.2 / 76.6 = 1.3603 USD/ ELJR. The original USD/EUR cross rate was 100 / 80 = 1.2500 USD/EUR. Thus, the USD has depreciated relative to the EUR. While it is correct to say that the EUR has appreciated 4.2% relative to the JPY (104.2 / 100 - 1) = 4.2%, it is not correct to say that the JPY has depreciated by the same percentage. To calculate the percentage change in the JPY relative to the EUR, we need to invert the quotes. One year ago, the quote was 0.0100 EUR/JPY and now the quote is 0.0096 EUR/JPY. (0.0096 I 0.0100 — 1) = 0.0403 or 4.0% depreciation in the JPY relative to the EUR.