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:
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
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.