GEEM - Skills and Knowledge

F1.1 Identify and compare exchange rates, and convert foreign currencies to Canadian dollars and vice versa.

Skill: Identifying and Comparing Exchange Rates and Converting Foreign Currencies to Canadian Dollars and Vice Versa

The exchange rate is the number of units of a foreign currency that can be purchased with one unit of your home currency. In order to determine an exchange rate, one must understand the concept that countries have their own currency.

Foreign currency is obtained by converting it according to the exchange rate and then purchasing it with Canadian dollars. The price or value of the Canadian dollar is set by the international market and is determined by the demand for Canadian goods and services. The exchange rate fluctuates on a daily basis and banking tools are available online, such as the Bank of Canada's website.

The mechanism of exchange rates is an abstract concept, which can be difficult to learn, so it is useful to present several examples using current currency conversion rates and discuss the daily fluctuation in currency values.

In order to determine exchange rates, students must be able to understand that for some currencies where the Canadian dollar has a greater value, it will convert to a greater amount, but conversely, when the value of another currency is greater, our conversion of the Canadian dollar into that currency will be to a smaller amount.

Examples of Exchange Rates

Country	Currency Value in Canadian Dollars	Value of the Canadian Dollar in the Currency	Explanation
Canada (dollar, $, CAD)	1.00 CAD	1.00 CAD	N/A
United States (dollar, $, USD)	1.38 CAD	0.72 USD	The USD is worth more than the CAD, so you have to spend more than 1 CAD to get 1 USD.
Japan (Yen, ¥, JPY)	0.0094 CAD	106.37 ¥	The yen is worth less than the CAD. You have to spend less than 1 CAD to get 1 ¥.
European Union (Euro, €, EUR)	1.34 CAD	0.75 €	The Euro is worth more than the CAD, so you have to spend more than 1 CAD to get 1 €.
India (Rupee, ₹, RS)	0.016 CAD	62.50 ₹	The Rupee has a lower value than the CAD, so you have to spend less than 1 CAD to get 1 ₹

*Please note that the rates used in these examples are arbitrary; actual rates vary in real time.

Banks provide information on daily exchange rates. Students can consult charts such as the one below to find out how many Canadian dollars they will need to buy another currency.

Here is an example of a financial institution, showing the country, the currency and the prices at which the bank buys and sells the currency.

Exchange Rates for the Most Popular Currencies

Country	Currency	We Buy	We Sell
United States	dollar (USD)	1.2520	1.3215
Euro (zone)^[1]	euro (EUR)	1.2633	1.3721
Mexico	peso (MXN)	0.05931	0.06715
England	pound (GBP)	1.4944	1.6128
Switzerland	franc (CHF)	1.2924	1.3796

Source: Desjardins.

In the Number strand, students represent multiplicative relationships involving rates with whole numbers. A rate describes a multiplicative relationship between two quantities that are expressed in different units.

As students begin to compare Canadian money with money from other countries using an online currency converter or using rates, they gain a greater understanding of the value of the Canadian dollar internationally. To make this comparison, it is important to use the concept of unit rate to compare the two currency values. In the Number strand, junior students have represented equivalent ratios and rates, including unit rate. As they begin to compare the value of one Canadian dollar (CAD) with the value of international currencies, students will use multiplication or division to calculate the amount of Canadian money required to purchase a different currency.

In the Intermediate Division, students use proportional reasoning in the Number strand. Currency conversion can be said to be a proportional relationship.

Students should note the cost, in Canadian dollars, of purchasing different currencies. Currencies from other countries are not worth the same as the Canadian dollar. Students will note that it will cost more to purchase some currencies than others. There are many reasons why currencies from other countries are worth more or less than the Canadian dollar, such as the economies of the countries, political stability, employment rates and interest rates.

To begin identifying and comparing currencies, students can use the Bank of Canada's currency converter shown below. Please note that exchange rates fluctuate daily.

The Bank of Canada website allows you to search for historical data for various currencies and the conversion rate in relation to the Canadian dollar.

This image shows the result of a search for the conversion rate from CAD to USD for one week. The maximum, minimum and average for this period is shown.

Source: Bank of Canada.

Students must first determine the quantity of the currency and then its relationship to other quantities.

Example: Currency Conversion

On September 7, 2022, if I have $100 Canadian to convert to U.S. currency, how much U.S. currency would I have?

Initially, currency conversion lends itself well to estimation. By checking an online currency converter, I know that 1 CAD is worth 0.76 USD.

Knowing that 0.76 is about $\frac{3}{4}$, we can estimate that the value in USD will be about $\frac{3}{4}$ of 100 CAD, or 75 USD.

Using a multiplicative relationship, the estimate can then be verified.

Multiplied by 100 a « C » « A » « D » equals zero point 76 « U » « S » « D ».!00 « C » « A » « D » equals 76 « U » « S » « D ».

I would have 76 USD to spend in the United States.

Or, if I want $100, how much will it cost me in Canadian dollars?

By checking an online currency converter, I know that 1 USD is worth 1.31 CAD. This is close to 1 and $\frac{1}{3}$. I can then estimate that I will need to exchange 133.33 CAD to get 100 USD. I can verify my answer by using a multiplicative relationship.

Multiplied by 100.A « U » « S » « D » equals a 31 point « C » « A » « D ».100 « U » « S » « D » equals 131 « C » « A » « D ».

It will cost me 131 CAD to get 100 USD.

Example: Currency Comparison

A group of students are planning a humanitarian trip to two different countries, the Philippines and Vietnam.

What are the currencies of the two countries and what is the value of 500 Canadian dollars for each?
Which of the currencies will cost more and which will cost less?

To find the current exchange rate of the different countries, an online currency converter was used. Here are the exchange rates as of September 7, 2022.

For 1 Canadian dollar, one would get 43.46 Philippine pesos, which is about 50 pesos. So an estimation can be made that for 500 Canadian dollars, one would get 500 x 50, which is about 25 000 Philippine pesos.

Philippines - Philippine Peso (PHP, ₱)

Multiplied by 500.A « C » « A » « D » equals 43 point 46 « P » « H » « P ».500 « C » « A » « D » equals 21730 « P » « H » « P ».

For 1 Canadian dollar, one would get about 18 000 Vietnamese dongs. An estimation can be made that, for 500 Canadian dollars, one would get 500 x 18 000, so about 9 000 000 Vietnamese dongs.

Vietnam - Vietnamese Dong (VND, ₫)

Multiplied by 500.A « C » « A » « D » equals 18000 point 09 « V » « N » « D ».500 « C » « A » « D » equals 9000045 « V » « N » « D ».

Now I need to determine which of the currencies will cost the most and which will cost the least.

Philippines - Philippine Peso (PHP, ₱)

$\displaylines{\begin{align} 1 \ \mathrm{CAD} & = 43.46 \ \mathrm{PHP} \\ ? \ \mathrm{CAD} & = 1 \ \mathrm{PHP} \\ 1 \ ÷ \ 43.46 & = 1 \ \mathrm{PHP} \\ 1 \ \mathrm{PHP} & = 0,02 \ \mathrm{CAD}\end{align}}$

Vietnam - Vietnamese Dong (VND, ₫)

$\displaylines{\begin{align} 1 \ \mathrm{CAD} & = 18 000.09 \ \mathrm{VND} \\ ? \ \mathrm{CAD} & = 1 \ \mathrm{VND} \\ 1 \ ÷ \ 18 000.09 & = 1 \ \mathrm{VND} \\ 1 \ \mathrm{VND} & = 0.00056 \ \mathrm{CAD}\end{align}}$

The Philippine peso is the most expensive currency and the Vietnamese dong is the least expensive.

Knowledge: Currencies

All countries use a system of currency (money) which typically includes coins and bills.

Note: The currencies of other countries are not equal in value to the Canadian dollar.

For the sake of simplicity and to establish an international standard where all currencies can be talked about anywhere in the world without language barriers, each currency has a three-letter acronym. Usually, but not as a general rule, the first two letters refer to the country and the third to the name of the currency.

For example, here are the abbreviations for the currencies of Canada, the United States, China and Peru:

Canada: Canadian dollar, CAD
United States: US dollar, USD
China: yuan (¥), CNY
Peru: new soil, PEN

Knowledge: Currency Converters

Students can use the Bank of Canada's currency converter to convert currencies from other countries to Canadian dollars and vice versa by entering an amount of money in one country's currency to obtain the corresponding amount in another country's currency.

Source: Bank of Canada.

Knowledge: Exchange Rate

An exchange rate shows how much it costs to buy units of one currency using another, and shows the relationship between the value of one country's currency to another.