14.03 Exchange rates

Different countries throughout the world have their own currency.

• Canada has the Canadian Dollar which is represented by the three letter code CAD.
• Australia has the Australian Dollar, which is represented by the three letter code AUD.
• The United States of America has the United States Dollar, and their code is USD.
• The United Kingdom has the pound sterling, with code GBP.
• Countries in Europe who are part of the eurozone, have the Euro, and their code is EUR.

When you travel overseas, you will be purchasing products and services in the currency of that country.

For example, if you are travelling to France and you wish to take cash, you will exchange some CAD for some EUR. You can do this at a bank or at a Foreign Exchange outlet either here, or once you arrive at your destination.

If instead, you will mainly use a credit card, then your bank will convert your CAD to EUR, and charge you a transaction fee for doing so. This is also a common occurrence when purchasing goods online from international vendors.

Exchange rates

When you want to exchange one currency for another, it is very rarely a one-to-one swap. Instead, there is a relationship between the two currencies which can be expressed as a rate.

If  $1$1 CAD was worth $0.68$0.68 EUR. Your one Canadian dollar would only receive $0.68$0.68 euros in return. If we wanted to, we could write this as the rate $0.68$0.68 EUR/CAD, although this is not common practice.

These rates change daily as the circumstance of each economy fluctuate and influence each other. These changes are often very unpredictable.

Some implications of the change in the value of a currency are as follows:

• A drop in the value of the CAD, compared with other currencies, means that more Canadians will be encouraged to buy products in Canada, rather than from an online overseas outlet, because items are cheaper.
• Also, a drop in the value of the CAD will encourage Canadian exports, because our products will appear cheaper to other countries.
• An increase in the value of the CAD might mean Canadians can better afford an overseas holiday because the high exchange rate allows you to purchase more goods and services while on holiday.
• Similarly, an increase in the value of the CAD might mean Canada can afford to import more from overseas.

 

Buying currency

When you wish to exchange your country's currency for the currency of another country, you are considered to be buying that currency.

As with anything you buy, the purchase price of that currency will be different, depending on where you purchase.

Let's look at an example.

This first image shows you the official exchange rate for exchanging $1$1 AUD for Euros at a point in time.

This next table shows you how many Euros the ANZ bank would give buy and sell to you for every $1$1 AUD on the same day.

			Bank buys			Bank Sells
Country	Currency	Currency code	IMT/TT	Travel card/Chq	Notes	IMT/TT	Travel Card/Chq	Notes
USA	Dollars	USD	$0.7127$0.7127	$0.7166$0.7166	$0.7216$0.7216	$0.6540$0.6540	$0.6540$0.6540	$0.6540$0.6540
EURO MONETARY UNION	Euro	EUR	$0.6559$0.6559	$0.6664$0.6664	$0.6786$0.6786	$0.5966$0.5966	$0.5966$0.5966	$0.5966$0.5966

And finally, this image shows you how many euros a Foreign Exchange centre would give you for every $1$1 AUD, again on the same day.

As you can see, when buying another currency, you'll receive less than the official rate. These various outlets make money on the sale.

Worked examples

example 1

If we had $\$500$$500 CAD, how many euros could we buy at RBC?

Think: At RBC today,  $1$1 CAD is exchanged for $0.67$0.67 EUR. Since we have $500$500 CAD, we need to multiply $500$500 by $0.67$0.67.

Do:

$1$1 CAD	$=$=	$0.67$0.67 EUR	Write the exchange rate as an equation.
$500\times1$500×1 CAD	$=$=	$500\times0.67$500×0.67	Multiply both sides by $500$500 to keep balanced.
$500$500 CAD	$=$=	$335$335 EUR

 

Example 2

If we just bought $600$600 EUR from RBC bank, how much CAD did we spend?

Think: Using the same rate as in the first example, we will this time need to divide $600$600 by $0.67$0.67.

Do: $\frac{600}{0.67}=895.52$6000.67​=895.52 CAD

This can also be calculated using a balanced equation to follow the process and be clear when to divide and when to multiply.

$0.67$0.67 EUR	$=$=	$1$1 CAD	Divide both sides by $0.67$0.67 to find the cost of $1$1 Euro.
$1$1 EUR	$=$=	$\frac{1}{0.67}$10.67​ CAD	This is approximately $1.49$1.49 CAD but don't round until your final answer.
$600$600 EUR	$=$=	$\frac{600}{0.67}$6000.67​ CAD	Multiply both sides by $600$600 to find the cost of $600$600 Euro.
$600$600 EUR	$=$=	$895.52$895.52 CAD

 

Selling currency

When you exchange another currency for your own, you are selling, instead of buying.

Worked example

Example 3

Let's say you've come back from your wonderful holiday in France and you have $50$50 EUR left over in cash. You can't spend euros in Canada, so you return to the RBC bank to exchange it back to CAD.

Think: If we use the same RBC table given above (although realistically the rates would likely have changed), we can see that the bank buys from you (or you sell to them) $0.67$0.67 EUR and gives you $1$1 CAD in return. In other words, for every $0.67$0.67 EUR you have, you'll get $1$1 CAD. 

We'll divide our $50$50 EUR by $0.67$0.67 to see how many CAD we'll get.

Do: $\frac{50}{0.67}=\$74.63$500.67​=$74.63 CAD.

When travelling overseas or purchasing items online be aware of exchange rates and fees your bank may charge so you don't accidentally overspend your budget or pay too much for an item.

 

Practice questions

QUESTION 1

QUESTION 2