The Mathematics of Money

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

Few countries have fixed currencies today, though there are some notable

exceptions. The most significant example is China, which fixes the value of

its currency against the U.S. dollar, though China appears to be gradually

moving toward a more flexible exchange rate. China is likely to eventually

switch to a floating currency, and in fact by the time you are reading this it

may already have done so. Fixed rates can still vary over time, as the gov-

ernment adjusts the rates, but will not normally vary much, if at all, from

day to day. In the table, you can see that there was actually a slight change

in the Chinese exchange rate between Wednesday and Thursday.

Most of the foreign currencies are listed by the name of their country.

One important exception appears at the bottom of the table. The euro

is a currency that has been adopted for common use by many Europe-

an countries, including France, Germany, Italy, Spain and many others.

These countries are not listed in the table. Not every European country

uses the euro, however. The United Kingdom, Switzerland, and many

Scandinavian and Eastern European nations do not at this time. It is likely, though by no

means certain, that these other European countries will eventually adopt the euro. The euro

is a particularly important currency to be familiar with, not only because of its use in major

European nations, but also because it is seen by many as a significant rival to the U.S. dol-

lar as an “international currency.”

Converting from US$ to a Foreign Currency

When you want to convert an amount of money from US$ into a foreign currency, the most

helpful form of the exchange rate is that given in the “Currency per US$” column of the

table. Suppose that we want to know how much US$500 would be worth in New Zealand

dollars. From the table, using the more recent Thursday rate, we found that US$1 was

worth NZ$1.5751, which we can express by the equation

US$1 
 NZ$1.5751

Common sense tells us that US$500 would be worth $500 times as much. Using this

common sense together with the rules of mathematics, we can multiply both sides of this

equation by 500 to get:

US$500 
 NZ$787.55

which gives us the answer we were looking for.

Example 11.1.1 Convert US $3,724.59 into euros, using the Thursday rate.

From the table, we fi nd that on Thursday the exchange rate was

US$1 
 €0.7838

Multiplying both sides of the equation by 3,724.59 we get

US$3,724.59 
 €2,919.33

In this example, we made use of the symbol “€” for the euro, analogous to the symbol “$”

used for the U.S. dollar. Knowing the symbols for major foreign currencies is not a bad thing.

We will use them in this text at least for particularly widely used currencies, specifically:

Country Currency Symbol

United States Dollar $

European Union Euro €

United Kingdom Pound £

Japan Yen ¥

China Yuan

A sign advertises exchange rates in downtown

Montreal. Timothy J. Biehler

11.1 Currency Conversion 471