The Mathematics of Money

Copyright © 2008, The McGraw-Hill Companies, Inc.

The method shown in this example is probably not what you would use if you needed to

make these conversions often. It is also correct, and quicker, to simply divide 200/1.2954

and get the same result. The same caution about shortcuts given before applies here, but

even more so. This gives the correct answer, but the mathematical reasoning behind it is

not obvious, and for that reason it is quite easy to get confused about when to multiply and

when to divide. If you worked somewhere where you needed to do these calculations often,

they would become second nature, so you would be unlikely to make a mistake by using a

shortcut. For those who need to make these conversions only occasionally, the method is a

bit more cumbersome, but is less likely to lead to an error.

Sometimes, rate quotes will instead give only the “currency per US$” rate. Rate tables

are often not particularly clear about which type or rate is being quoted. Knowing in

advance whether the currency you are looking to exchange is worth more, or less, than a

U.S. dollar can help in figuring this out.

Exchange Rates as a Percent (Optional)

There is yet another commonly used way of expressing exchange rates: as a percent. This

is especially common at businesses located in places such as restaurants and shops near

the U.S./Canadian border, where the two countries’ currencies share a common name, are

fairly close in value and are used on both sides of the border.

For example, a fast food restaurant in Canada might have a sign posted stating that “15%

exchange on U.S. funds.” What this means is that if you pay in U.S. currency, each U.S. dollar

will be worth 15% “more” in Canadian dollars. This is the same as an exchange rate of US$1 


C$1.15. On the U.S. side of the border, a sign saying “15% exchange on Canadian funds”

would be interpreted slightly differently. There, the meaning would be that each Canadian dol-

lar is worth 15% “less” in U.S. dollars, equivalent to the exchange rate C$1 
 US$0.85.

How are we supposed to know that in one case the 15% means more, and in the other

case the 15% means less? Sometimes, signs will make this clear by using the word “pre-

mium” to indicate more (“15% premium for U.S. funds”) or “discounted” to indicate “less”

(as in “Canadian funds discounted 15%”). Often, though, this will not be stated explicitly.

However, exchange rates are expressed in this way only in places where it is common

knowledge which currency has the higher value. Anyone in a restaurant near the border

would know that U.S. dollars have a higher value than Canadian dollars,^3 and so there is no

need to give that extra information.

Example 11.1.8 A sign posted in a souvenir shop in Ganonoque, Ontario, states

“U.S. exchange 25%.” If you buy a sweatshirt there costing C$52.97, how much will it

cost you if you pay in U.S. funds?

The posted exchange rate means:

US$1 
 C$1.25

Dividing both sides by 1.25 to get the value of C$1 gives us:

US$0.80 
 C$1

Multiplying both sides by 52.97 gives

C$52.97 
 US$42.38

Once again, we could also have got this by dividing 52.97/1.20 
 42.38.

Example 11.1.9 A souvenir shop in Niagara Falls, New York has posted “Canadian

exchange: 15%”. If you buy a framed poster there costing US$75.94 but pay in

Canadian funds, how much will you pay?

(^3) At least this is true at the time I am writing this. If that changes in the future, and Canadian dollars become more
valuable than U.S. dollars, the interpretation of the percentage would switch. But the relative values of the two
currencies would still be common knowledge, and so the signs would still be just as well understood.
11.1 Currency Conversion 477