The Mathematics of Money

476 Chapter 11 International Business

Of course, the answer to this is no. As a buyer of Canadian dollars, the bank will most

likely once again offer you an exchange rate that is less attractive than the published rates.

For retail foreign currency exchanges, there are usually two separate rates. The bid rate

(also called the offered or buying rate) is the rate that the exchanger will give you to

exchange your foreign currency for U.S. dollars (i.e., when it buys your foreign currency

from you). The asked rate (also called the selling rate) is the rate it will give you when you

exchange your U.S. dollars for foreign currency (i.e., when it sells you foreign currency).

This may seem unfair, but in fact it is no different from a retail store buying merchandise

for less than it sells it for. The difference between the two rates is sometimes referred to as

the spread.

The table below is an example of a retail currency rate table:

TRANSNATIONAL NATIONAL CURRENCY EXCHANGE

RETAIL RATES AS OF 8/25/06

Country/Currency Sell Buy

Euro 1.2954 1.2575

Japan/yen 0.008645 0.008414

Canada/dollar 0.9250 0.8650

Mexico/peso 0.0917 0.0912

South Korea/won 0.001105 0.001025

Switzerland/franc 0.8255 0.7945

UK/pound 1.9221 1.8567

Of course, we can still use the same mathematics to convert currencies. The difference

between the published rates and retail rates means we use a different rate, but we don’t

need different mathematical tools to do the conversion.

There is, however, one complication that sometimes arises. For both its buy and sell

rates, Transnational National Currency Exchange is giving the price for one unit of each

currency in US$, or in other words the “US$ Equivalent” form of the rate. When the

company is selling you euros, each euro will cost US$1.2954. But when it is buying euros,

it will only pay US$1.2575 for each. The difference between these two rates is how the

currency exchange business makes its profit.

Since this table gives the US$ equivalent rate, converting from the foreign currency

into dollars is no problem. For example, if you have €250 to exchange for U.S. dollars, we

would use the buy rate from the table to find how much Transnational National would pay:

€ 1 
 $1.2575

€ 250 
 $314.38

On the other hand, if you want to exchange U.S. dollars for euros, the rate is not presented

in the form we would want it to be. The following exercise will demonstrate how we can

calculate this conversion.

Example 11.1.7 Suppose you want to exchange $200 for euros. Calculate the

amount you would receive in euros from the retail table given above.

Transnational National would be selling you euros, so we use the selling rate:

€ 1 
 $1.2954

We want this rate in a form that gives us the value of $1 in euros. We can get this by dividing

both sides of the equation by 1.2954, to make the right side $1. When we do this, we get:

€0.771962328 
 $1

Once we have this, we can multiply both sides by 200 to get:

€154.39 
 $200

You would receive €154.39.