Module 8
1. Module 8
1.16. Page 5
Module 8: Daily Living
Using Conversion Factors
If you look at the foreign-exchange table, you will notice that both the conversion factors for changing Canadian dollars into a foreign currency and the conversion factor for changing a foreign currency into Canadian dollars are given. This is very convenient. If you were converting between Chinese Yuan and Canadian dollars, you would simply refer to the following line in the table.
|
Units per C$1.00 |
Number of CAD per Unit |
||
|
CNY |
China Yuan Renminbi |
6.431 307 657 4 |
0.155 489 373 7 |
To convert C$100.00 to Chinese Yuan, you would use the first conversion factor and multiply.
To convert CNY 100.00 to Canadian dollars, you would use the second conversion factor and multiply.
However, what would you do if you only knew one conversion factor? This is where knowing how to set up proportions becomes very useful.
Study the following example.
Example 3
Marcel is reviewing his financial records. On January 22, 2003, he transferred C$500.00 into a US-dollar savings account. If, on that date, US$1.00 = C$1.532, what was Marcel’s deposit in US dollars? Disregard fees and commissions.
Solution
Method 1
Set up a proportion. Let x be the deposit in US dollars. On the other side of the equal sign is the conversion rate. The numerators of the ratios in the proportion must be in one currency, and the denominators in the other currency. Since the unknown is in US dollars, it may be preferable to put US dollars on top, since this creates fewer steps to solve and no cross-multiplying is necessary.
On January 22, 2003, Marcel deposited US$326.37.
Method 2
Divide by the conversion factor. Since US$1.00 = C$1.532, if you were given a sum in American dollars, you would multiply by 1.532 to convert the sum into Canadian dollars. To reverse the process in order to change Canadian dollars into American dollars, you would divide.
On January 22, 2003, Marcel deposited US$326.37.
Self-Check
In each of the following questions, apply both methods shown in Example 3.
© Jgz/4678816/Fotolia
SC 7. On March 20, 2009, Victor was in Peru on his way to the Inca city of Machu Picchu. He was going to witness the sun on the Intihuatana stone at noon during the equinox. On March 20, he spent PEN 450.00. That day, C$1.00 was equal to PEN 2.5189. What did Victor spend in Canadian dollars?
SC 8. On October 1, 2009, the Cardinal family stayed at a motel in Sydney, Australia. The charge for the room was A$150.00. If on that date, C$1.00 was equal to A$1.0632, what was the room charge in Canadian dollars?
Buy and Sell Exchange Rates
Up to this point in the lesson you have worked with nominal currency exchange rates. There were no transaction fees. However, nothing in life is free. Banks and other financial institutions charge a percentage of the currency exchange as their commission. This commission is often 4%.
These fees may vary depending on whether the transaction is in cash, involves a cheque, is a credit card transaction,
or is an investment. The fees also depend on the amount of the exchange, and the fees may be negotiable.
buy and sell exchange rates: exchange rates reflecting transaction fees
For customers wishing to exchange currency, banks will advertise their buy and sell exchange rates based on whether they are selling the foreign currency to the customer or buying the foreign currency from the customer. The exchange rates for selling and buying are different from one another, and they both differ from the nominal exchange rates because they include fees.
Consider the Royal Bank of Canada’s Buying and Selling Rates from February 3, 2010. You may wish to print this document.
Study the following examples to see the effects of built-in fees.
Example 4
Yolanda walks into the bank and asks to exchange C$100.00 for US dollars. The teller consults the “Sell to You” column, because the bank is selling US dollars to Yolanda. The rate is US$1.00 = C$1.0855.
- What will the amount be in US dollars?
- If Yolanda changes her mind shortly afterwards, and returns to the bank to exchange the US dollars back into Canadian dollars, the teller will consult the “Buy from You” column. The rate is US$1.00 = C$1.0303. How much money will Yolanda receive in Canadian dollars?
- What were the total fees for the two transactions?
Solution
- Let x be the amount in US dollars. Since US$1.00 = C$1.0855, you will end up with less than US$100.00. Divide C$100.00 by the conversion rate.
Yolanda will receive US$92.12 for her C$100.00.
- US$1.00 = C$1.0303
Yolanda receives C$94.91.
Self-Check
Use the Royal Bank of Canada’s Buying and Selling Rates from February 3, 2010, to answer these questions.
SC 9. Xena has been on a holiday in Germany. On her return to Canada, she has €350.12 in cash. She exchanges the euros for Canadian dollars. How much does she receive in Canadian money?
SC 10. Wilma is planning a trip to Sweden. She goes to the bank to exchange C$500.00 for Swedish Kronas. How much will she receive in Swedish Kronas?
SC 11. Quincy has turned 17. He received a cheque for £50.00 from his uncle in Scotland. How much will Quincy receive in Canadian dollars from the bank?
Mastering Concepts
On Thursday, the exchange rate for the Australian dollar was C$1.00 = A$1.0692. On the same day, the exchange rate for the euro was C$1.00 = €0.6678. Complete the following conversions. Round to four decimal places.
- €1.00 = A$?
- A1.00 = €?