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Question of the Week - Economics
The exchange rate between two currencies has decreased to 101.34. The price currency has appreciated by 7.5 percent against the base currency. The initial exchange between the two currencies was closest to:
Question of the Week - Economics 22 votes
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The exchange rate decreased to 101.34 units of the price currency per 1 unit of the base currency. For ease of explanation, let’s suppose this exchange rate is quoted in Japanese yen (¥) per United States dollar ($).
A decrease of the yen-per-dollar exchange rate to 101.34 is equal to an increase in the dollar-per-yen exchange rate to 1/101.34 dollars per yen. We are told this exchange rate appreciated by 7.5%.
That means the exchange rate was (1/101.34) / 1.075 = 0.009179 dollars per yen, which is equivalent to 108.94 yen per dollars.
Alternatively, because (1 / 1.075) – 1 = -6.98%, a 7.5% appreciation of the dollar-per-yen exchange rate is equivalent to a 6.98% depreciation of the yen-per-dollar exchange rate. If the exchange rate was X, that means X(1 - 6.98%) = 101.34. Solve for X = 108.94.