Foreign Exchange Rates

Foreign currency exchange rates (“forex” in Wall Street lingo) are prices. They represent the price of trading currency X for currevncy Y. These prices can always be reported two ways. We could express the price as “how many X’s does it take to buy 1 Y”, or we could reverse it and express the price as “how many Y’s does it take to buy 1 X”. These two prices must be the mathematical reciprocal of each other.
Let’s use an example. Let’s suppose that one Canadian dollar will buy 1.05 U.S. dollars. In other words, the exchange rate is:
$1.00 CAD = $1.05 USD
if we express this as a ratio of USD per CAD, we have:
But suppose we want to know how many Canadian dollars can be purchased with one US dollar? In other words we want to know how many CAD per 1.00USD. We already know that 1.00CAD = 1.05USD, so it has to be the same ratio. It’s just that we want a 1.00 in the numerator instead of the denominator. So we can set up:
If we sole this we find the reverse exchange rate: $ 0.9524 CAD per $1.00 USD
LESSON: always pay close attention to which way the exchange rate is expressed – is it CAD per USD, or is it USD per CAD?

Let’s use an example. Let’s suppose that one Canadian dollar will buy 1.05 U.S. dollars. In other words, the exchange rate is: