189
43. Dianne is paid a commission of 4.5% on all sales in a month. Determine her sales for the month in which she earned
$2,317.50 in commission.
44. Joana receives a commission of 6.5% on all sales during that period. Last week she earned $1,935.05. What were her
sales for last week?
45. Bill is paid on a fixed commission rate basis and his gross pay in September was $2,730 on sales totalling $42,000.
Calculate his rate of commission.
46. Jennifer is paid on a fixed commission rate based on her sales. Calculate the rate of commission if she earned $3,696
in a month when her sales were $67,200.
6.4 Currency Conversion
Currency Conversion
Exchange rates are used
to convert currencies
between countries.
The exchange rate, also called the foreign exchange rate or forex rate, is used for converting currencies
between countries. The exchange rate allows you to calculate the amount of a currency required to
purchase one unit of another currency.
For example, to convert Canadian currency to US currency, it is important to know how many
Canadian dollars are equivalent to one US dollar, or vice versa.
The value of a currency may fluctuate constantly during the day and the exchange rate may vary
accordingly. For example, on March 31, 2015, US$1 was equal to C$1.2684 and C$1 was equal to US$
0.7883 at 20:00 hours EST. Thus, the exchange rate on that date and time was US$1 = C$1.2684 and
C$1 = US$0.7883.
Currency Cross-Rate Table
Currency exchange rates are generally displayed in a table called the Currency Cross-Rate Table for
quick reference. Below, is a currency cross-rate table from March 31, 2015.
Currency Cross-Rate Table as of March 31, 2015
One Unit of
Currency
Canadian dollar
US dollar
Euro
British pound
Australian dollar
Symbol
Equivalent to
Table 6.4-a
C$
US$
€
£
A$
C$
-
1.2684
1.3638
1.8822
0.9666
US$
0.7883
-
1.0749
1.4837
0.7621
€
0.7333
0.9302
-
1.3801
0.7089
£
0.5312
0.6740
0.7246
-
0.5137
A$
1.0343
1.3123
1.4107
1.9468
-
The vertical columns of the table represent one unit of the currency to be converted and the horizontal
rows represent its equivalent value in another currency.
For example, US$1 = A$1.3123 and £1 = US$1.4837.
Based on the exchange rates provided in Table 6.4-a, the exchange rates of foreign currency per
Canadian dollars (C$) and vice versa are provided in Table 6.4-b for easy reference.
6.4 Currency Conversion
190
Table 6.4-b
Exchange Rates of Foreign Currency per C$ and C$ per Unit of Foreign Currency
Currency
Symbol
Unit per C$
C$ per unit
US dollar
US$
0.7883
1.2684
Euro
€
0.7333
1.3638
British pound
£
0.5312
1.8822
Australian dollar
A$
1.0343
0.9666
For calculations involving conversion from one currency to another, we will either use the cross-rate
table or the exchange rates provided in the question. We will be using the method of proportions to
solve examples that follow.
Example 6.4-a
Converting Currency from C$ to US$
Based on the exchange rates provided in Table 6.4-a (Currency Cross-Rate Table), how many US
dollars will you receive when you convert C$400?
Solution
From the cross-rate table,
US$1 = C$1.2684
US$ : C$ = US$ : C$
1: 1.2684 = x : 400.00
In fractional form,
US$
C$
1
1.2684
x
400.00
1.2684
1
x
1
=
or
=
400.00
1.2684
400.00
x
Cross-multiplying and solving for x,
1.2684x = 400.00
400.00
x=
1.2684
= 315.357931... = US$315.36
Therefore, you will receive US$315.36 when you convert C$400.00.
Example 6.4-b
Converting Currency from C$ to US$ and from US$ to C$
If US$1 = C$1.2684, calculate:
Solution
(i)
The amount you will receive if you convert US$1,000 to Canadian dollars.
(ii)
The amount you will receive if you convert C$1,000 to US dollars.
(i)
US$ : C$ = US$ : C$
1 : 1.2684 = 1,000.00 : x
US$
C$
1
1.2684
1,000.00
x
In fractional form,
1
1.2684
1
1,000.00
=
or
=
1,000.00
x
1.2684
x
Cross-multiplying and solving for x,
x = 1,000.00 × 1.2684
= C$1,268.40
Therefore, you will receive C$1,268.40 when you convert US$1,000.00.
(ii)
US$ : C$ = US$ : C$
1 : 1.2684 = x : 1,000.00
Chapter 6 | Applications of Ratios and Percents
191
Solution
US$
continued
C$
1
1.2684
x
1,000.00
In fractional form,
x
1
1 1.2684
=
or
=
1.2684 1,000.00
x 1,000.00
Cross-multiplying and solving for x,
1.2684x = 1,000.00
1,000.00
x=
1.2684
= 788.394828... = US$788.39
Therefore, you will receive US$788.39 when you convert C$1,000.00.
Example 6.4-c
Converting from One Currency to Another Currency, Given Exchange Rates
Samantha is travelling from Canada to London for vacation. If £1 = C$1.8822, how much will she
receive if she converts C$1,000 to British pounds?
Solution
£ : C$ = £ : C$
1 : 1.8822 = x : 1,000.00
£
C$
1
1.8822
x
1,000.00
In fractional form,
x
1.8822
1
1
=
or
=
1.8822 1,000.00
x 1,000.00
Cross-multiplying and solving for x,
1.8822x = 1,000.00
1,000.00
x=
1.8822
= 531.293167... = £531.29
Therefore, she will receive £531.29 when she converts C$1,000.00.
Example 6.4-d
Series of Currency Conversions
If US$1 = C$1.2684 and C$1 = A$1.0343, calculate the amount of US dollars you will receive with
A$100.
Solution
First, find out how many Canadian dollars you will receive with A$100.
C$ : A$ = C$ : A$
1 : 1.0343 = x : 100.00
C$
A$
1
1.0343
x
100.00
In fractional form,
1.0343
1
=
x 100.00
or
1
x
=
1.0343
100.00
Cross-multiplying and solving for x,
1.0343x = 100.00
100.00
x=
1.0343
= C$96.683747...
Now, determine how many US dollars you will receive with C$96.683747...
US$ : C$ = US$ : C$
1 : 1.2684 = x : 96.683747...
6.4 Currency Conversions
192
Solution
continued
US$
In fractional form,
C$
1.2684
1
x
1
=
or
=
1.2684
96.683747...
x 96.683747...
Cross-multiplying and solving for x,
1
1.2684
x
96.683747...
1.2684x = 96.683747...
96.683747...
x=
1.2684
= 76.224966... = US$76.22
Therefore, you will receive US$76.22 when you convert A$100.00.
Buying and Selling Currencies
If you would like to convert currencies, you should go to a bank or another financial institution that
is authorized to buy and sell currencies. These financial institutions usually have different exchange
rates for buying and selling currencies, which is their stated buying rate and selling rate. They use the
actual currency exchange rates and their rate of commission to create their own buying and selling
rates for each currency. Commission is charged for their services on these transactions.
■■ Buying rate (buy rate) is the rate at which the financial institution buys a particular foreign
currency from the customers.
■■ Selling rate (sell rate) is the rate at which the financial institution sells a particular foreign
currency to the customers.
Example 6.4-e
Currency Conversion Including Commission in Buying or Selling Currencies
Sarah plans to travel to the US from Canada and approaches a local bank to purchase US$1,000.
Assume US$1 = C$1.2684 and that the bank charges a commission of 0.75% to sell or buy US dollars.
Calculate:
Solution
(i)
The amount in Canadian dollars that Sarah would have to pay for US$1,000.
(ii)
If Sarah changes her plan and wishes to convert US$1,000 back to Canadian dollars, how
much will she receive from the same bank, assuming the same exchange rate and the same
commission rate?
(i)
US$ : C$ = US$ : C$
1 : 1.2684 = 1,000.00 : x
When calculating the buying
or selling rate, it does not
matter if you calculate
the commission first and
then convert the value, or
vice-versa. You will always
obtain the same answer.
US$
C$
1
1.2684
1,000.00
x
In fractional form,
1
1.2684
1
1,000.00
=
or
=
1,000.00
x
1.2684
x
Cross-multiplying and solving for x,
x = 1.2684 × 1,000.00
= 1,268.40
Amount in C$ before the bank’s commission = C$1,268.40.
Bank’s commission:
0.0075 × 1,268.40 = C$9.513
When you buy currencies,
you will pay the converted
amount and the financial
institution’s commission.
Adding the bank’s 0.75% commission,
Total = 1,268.40 + 9.513
= 1,277.913 = C$1,277.91
Amount that Sarah will pay the bank.
Or
1,268.40 (1 + 0.0075) = 1,277.913 = C$1,277.91
Therefore, Sarah would have to pay C$1,277.91 for US$1,000.00.
Chapter 6 | Applications of Ratios and Percents
193
Solution
continued
When you sell currencies,
you will receive the
converted currency less
the financial institution’s
commission.
(ii)
US$1,000 = C$1,268.40 As calculated in (i).
0.0075 × 1,268.40 = C$ 9.513
Subtracting the bank’s 0.75% commission,
Total = 1,268.40 – 9.513
Total = 1,258.887 = C$1,258.89
Amount the bank will pay Sarah.
Or
C$1,268.40 (1 – 0.0075) = 1,258.887 = C$1,258.89
Therefore, Sarah will receive C$1,258.89 from the bank.
Example 6.4-f
Calculating Bank’s Rate of Commision to Buy and Sell Foreign Currency
When the exchange rate is US$1 = C$1.2684, a bank has the following buy rate and sell rate for US dollars:
Buy rate: US$1 = C$1.2589
Sell rate: US$ = C$1.2843
Calculate the following:
Solution
(i)
Bank’s rate of commision to buy US$
(ii)
Bank’s rate of commision to sell US$
(i)
Assume you want to sell US$1,000 to the bank. (i.e., the bank is buying from you: use buy rate).
Using bank’s buy rate, you will receive: 1,000.00 × 1.2589 = C$1,258.90.
Using exchange rate US$1.00 = C$1.2684,
US$
1
1.2684
=
1,000.00
x
C$
1
1.2684
1,000.00
x
x = C$1,268.40
Therefore, the bank’s commision = C$(1,268.40 – 1,258.90)
= C$9.50
Amount of commision
× 100%
Bank’s rate of commision to buy =
Amount based on exchange rate
C$9.50
× 100%
=
C$1,268.40
= 0.748975...%
= 0.75%
Therefore, the bank’s rate of commision to buy US$ is 0.75%.
(ii)
Assume you want to buy US$1000 from the bank (i.e., the bank is selling to you: use sell rate)
Using bank’s sell rate, you will pay: 1,000.00 × 1.2843 = C$1,284.30
Using exchange rate US$ = C$1.2684,
US$
1
1,000.00
C$
1.2684
x
1
1.2684
=
1,000.00
x
x = C$1,268.40
6.4 Currency Conversions
194
Solution
continued
Therefore, bank’s commision = C$(1,284.30 – 1,268.40)
= C$15.90
Amount of commision
Amount based on exchange rate
C$15.90
× 100%
=
C$1,268.40
Bank’s rate of commision to sell =
= 1.253547...%
= 1.25%
Therefore, the bank’s rate of commison to sell US$ is 1.25%.
6.4 Exercises
Answers to odd-numbered problems are available at the end of the textbook.
Based on the following exchange rates, answer Problems 1 to 4:
£1 = A$1.9468, US$1 = C$1.2684, €1 = US$1.0749, C$1 = £0.5312
1. Convert A$200 to British pounds (£).
2. Convert C$3,000 to US dollars (US$).
3. Convert US$5,000 to Euros (€).
4. Convert £10 to Canadian dollars (C$).
Based on the following exchange rates, answer Problems 5 to 8:
€1 = C$1.3638, A$1 = US$0.7621, US$1 = £0.6740, C$1 = A$1.0343
5. Convert C$2,500 to Euros (€).
6. Convert US$2,850 to Australian dollars (A$).
7. Convert £18 to US dollars (US$).
8. Convert A$300 to Canadian dollars (C$).
9. A bank in Ottawa charges 2.5% commission to buy and sell currencies. Assume the exchange rate is US$1 = C$1.2684.
a. How many Canadian dollars will you have to pay to purchase US$1,500?
b.How much commission in Canadian dollars (C$) will you pay the bank for the above transaction?
10. A bank in Montreal charges 2.25% commission to buy and sell currencies. Assume the exchange rate is US$1 = C$1.2684.
a. How many Canadian dollars will you receive from the bank if you sell US$1,375?
b. How much commission will you pay the bank for this transaction?
11. Mark converted US$4,500 into Canadian dollars at a bank that charged him a commission of 0.25%. How much did
he receive from the bank? Assume that the exchange rate was C$1 = US$0.7883.
12. Carmin converted £2,000 into Canadian dollars. If the commission the bank was charging was 0.90%, calculate how
many Canadian dollars she received. Assume that the exchange rate was C$1 = £0.5312.
13. If C$1 = A$1.0343 and A$1 = US$0.7621, how many Canadian dollars will you receive with US$1,000?
14. If C$1 = £0.5312 and £1 = US$1.4837, how many Canadian dollars will you receive with US$1,000?
15. David planned to travel to Australia from Canada and purchased A$5,000. A week later, he decided to cancel his trip
and wanted to convert his Australian dollars back into Canadian dollars at the same bank. How much money did he
lose or gain? Assume that the bank charged a commission of 0.5% to buy and sell currencies, and that the exchange
rate was C$1 = A$1.0343.
16. Lisa purchased US$10,000 from a bank in America, which charged her a commission of 0.80%, and sold the US
dollars to a bank in Canada, which charged her 0.80% commission. How much money did she lose or gain? Assume
that the exchange rate was C$1 = US$0.7883.
Chapter 6 | Applications of Ratios and Percents
195
17. Dell left Canada for the UK with C$8,000. When he reached the UK, he converted all his cash into British pounds.
The conversion rate was £1 = C$1.8822. After spending £1,000 in the UK, he returned to Canada. Calculate the
number of Canadian dollars he received when he converted the remaining British pounds into Canadian dollars at
an exchange rate of C$1 = £1.9000.
18. Jason travelled from Toronto to Australia, where he converted C$3,000 to Australian dollars at an exchange rate
of C$1 = A$1.0343. He spent A$2,000 in Australia before returning to Toronto. How many Canadian dollars did
he receive when he converted the remaining Australian dollars into Canadian dollars at an exchange rate of C$1 =
A$1.0200?
19. A bank in London, Ontario has a selling rate of £1 = C$1.8963. If the exchange rate is £1 = C$1.8775, calculate the
rate of commission that the bank charges.
20. A bank in London, Ontario has a buying rate of A$1 = C$0.9618. If the exchange rate is A$1 = C$0.9714, calculate
the rate of commission that the bank charges.
6.5 Index Numbers
Index Numbers
The Index Number
is used to express the
relative value of an item
compared to a base value.
The price of many items constantly fluctuates at different points in time. You may have noticed that
the cost of transportation, entertainment, education, housing, etc., have constantly been on the rise.
Index Numbers are used to quantify such economic changes over time.
An index number is a comparison of the value of an item on a selected date to the value of the same
item on a designated date, known as the base date. That is, if the index number is lower than the base
value, the value of that item has gone down since the base date; if the index number is higher than the
base value, the value of that item has gone up since the base date.
For example, the index number of 120.5 for an item on a selected date indicates that the value of that
item is 20.5% above the base period price of 100 for the same item.
The index number is calculated as follows:
Value on selected date
Index number =
× Base value
Value on base date
Example 6.5-a
Calculating the Index Number for Gasoline in 2015 Using 2002 as the Base Year
If the price of gasoline in 2002 was $0.75 per litre, and in 2015, the price had risen to $1.15 per litre,
calculate the index number for gas using 2002 as the base year with a base value of 100.
Solution
Year
Index
Price ($)
2002
100
0.75
2015
x
1.15
In fractional form,
100 0.75
=
1.15
x
Cross-multiplying and solving,
Index number =
or
Value on selected date
× Base value
Value on base date
1.15
× 100
=
= 153.333333...
0.75
=153.33
0.75x = 100 × 1.15
1.15
× 100
x=
0.75
= 153.333333...
= 153.33
Therefore, the index number for gas in 2015 is 153.33.
6.5 Index Numbers