The Mathematics of Money

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

Of course, a cross rate table is only practical for a limited number of currencies; a table that

included many more would quickly become ridiculously large. We can closely approximate

the conversion with our original table by using the U.S. dollar as an imaginary intermediate

step. For example, to convert Russian rubles to Thai baht, we could first find the value of

the rubles in dollars, and then convert those dollars to baht. (Of course, the intermediate

step of converting to dollars need not actually take place. We simply pretend that it does to

be able to calculate the values.)

Example 11.1.6 Convert 40,000 Russian rubles into Thai baht. Use the Thursday

rates.

First convert from rubles to U.S. dollars:

R1 
 US$0.03731

R40,000 
 US$1,492.40

Then convert from dollars to baht:

$1 
 B37.693

$1,492.40 
 B56,253

So we conclude that 40,000 Russian rubles equals 56,253 Thai baht.

Retail Foreign Currency Exchanges

Exchange rate tables such as the one we have been using above give a good indication of

the values of different currencies, but there is no guarantee that you will be able to get those

rates when making a foreign currency exchange. The rates published in the financial pages

are used for very large exchanges between large financial institutions. Tables published in

The Wall Street Journal and other financial publications note that the rates quoted “apply

to trading among banks in amounts of $1 million and more.” You may be able to get these

rates, or rates close to them, when you pay for something by using a credit card or with-

draw cash from an ATM in a foreign country.^2 They are not, though, the rates that you will

be offered to exchange cash at a bank branch, a hotel front desk, or at an airport foreign

exchange counter.

Suppose that you return home to Cleveland after a business trip to Vancouver and

discover that you still have C$120 in Canadian currency in your wallet. You want to

convert that money back into U.S. dollars. According to the tables that we used above, this

would be worth $108.04. However, when you take this money to your local bank, you are

disappointed to find that the bank offers you only $98.50 for it. What gives?

The fact of the matter is that, as we discussed at the start of this chapter, for most curren-

cies the exchange rate is determined by the market: what a willing buyer will give a willing

seller. The published exchange rates are not written in stone. The rate your bank offers will

reflect its costs of processing the exchange and need to make a profit. A bank may also

not be particularly excited about making a small, retail foreign currency exchange and the

rates it offers may reflect this fact. In fact, your local bank branch may not even offer this

service at all. If you don’t like the rate offered, you don’t have to accept it. You can keep

your Canadian currency, or shop around for a better deal. You aren’t forced to take the less

attractive rate, but by the same token it really is not realistic to expect the bank to offer you

the published rate.

Bitterly sulking home, grumbling about the rotten exchange rate, you might notice that

there is a flip side to this rate. The bank’s rate treated the Canadian dollar as “cheaper”

versus U.S. dollars than it should have been. This worked against you as a seller of Canadian

currency—but what if you instead went there to buy Canadian dollars? Could you then take

advantage of the exchange rate to buy “cheap” Canadian dollars?

(^2) You can’t assume this, though, and may want to check with your credit card company or bank about what sort of
exchange rates you can expect if you do this. There may be a fee charged for foreign currency transactions as well.
11.1 Currency Conversion 475