Exchange Rates and Currency Exchange

Exchange Rates

An exchange rate between two currencies is defined as the number of units of a foreign currency that are bought with one unit of the domestic currency, or vice versa. Since two currencies are involved in every transaction, two published exchange rates are available. Let's use Canada and the United States to illustrate this concept.

The first exchange rate indicates what one dollar of Canada's currency becomes in US currency.
The second exchange rate indicates what one dollar of US currency becomes in Canadian currency.

These two exchange rates allow Canadians to determine how many US dollars their money can buy and vice versa. These currency rates have an inverse relationship to one another: if 1 Canadian dollar equals 0.80 US dollars, then 1 US dollar equals $\frac{1}{$0.80}=1.25$ Canadian dollars.

Most Canadian daily and business newspapers publish exchange rates in their financial sections. Although exchange rates are published in a variety of ways, a currency cross-rate table, like the table below, is most common. Note that exchange rates fluctuate all of the time as currencies are actively traded in exchange markets. Therefore, any published table needs to indicate the date and time at which the rates were determined. Also note that the cells where the same currency appears show no published rate as you never need to convert from Canadian dollars to Canadian dollars!

	Per C$	Per US$	Per €	Per ¥	Per MXN$	Per AU$
Canadian Dollar (C$)	╲	0.9787	1.4012	0.0122	0.0823	1.0360
US Dollar (US$)	1.0218	╲	1.4317	0.0125	0.0841	1.0585
Euro (€)	0.7137	0.6985	╲	0.0087	0.0588	0.7394
Japanese Yen (¥)	82.0233	80.2765	114.9287	╲	6.7540	84.9747
Mexican Peso (MXN$)	12.1445	11.8859	17.0165	0.1481	╲	12.5814
Australian Dollar (AU$)	0.9652	0.9447	1.3525	0.0118	0.0795	╲

In the table, all exchange rates have been rounded to four decimals. In true exchange markets, most exchange rates are expressed in 10 decimals or more such that currency exchanges in larger denominations are precisely performed. For the purposes of this textbook, we will use a four decimal standard to simplify the calculations while still illustrating the principles of currency exchange.

Technically, only half of the table is needed, since one side of the diagonal line is nothing more than the inverse of the other. For example, the euro is $0.7137$ per $C$$ on the bottom of the diagonal. The inverse, or $\frac{1}{0.7137}=1.4011$ per €, is what is listed on top of the diagonal (the difference of 0.0001 is due to rounding to four decimals).