Question of the Week – Economics

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.