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F1.1 · Compare payment methods for multiple currencies and exchange rates

Learn to compare payment methods for multiple currencies and exchange rates through clear examples and targeted practice.

Ontario Grade 8 Mathematics

Financial Literacy

Use exchange rates and fees to compare what you pay and what you receive.

Imagine you are buying something while travelling. The price may be in a different currency from your own. A payment method might also charge a fee or use a different exchange rate. To compare methods fairly, use the same starting amount, check each rate and fee, and compare the final amounts. All rates and fees in this lesson are hypothetical examples, not current offers.

What you will learn

  • Explain what an exchange rate tells you.
  • Compare payment methods using the same starting amount and currency.
  • Include fees when deciding which method gives better value.

Start with the currencies and the rate

A currency is the money used in a place. CAD means Canadian dollars. USD means US dollars. EUR means euros. An exchange rate tells how much of one currency matches one unit of another currency. For example, a hypothetical rate of 1 CAD = 0.75 USD means that each Canadian dollar is exchanged for 0.75 US dollars.
The order matters. A rate that tells how many USD you receive for CAD is not the same as a rate that tells how many CAD you need for USD. Read the units beside the numbers before calculating.
To find an exchanged amount, multiply the starting amount by the rate. If the rate is given as USD for each CAD, multiplying CAD by that rate gives USD. The currency units help you check that the result makes sense.
new amount=starting amount×exchange rate\text{new amount} = \text{starting amount} \times \text{exchange rate}
  • Always identify the starting currency and the currency you want.
  • Keep the rate’s units with the number.
  • Multiply by the rate when the rate gives the new currency for each unit of the starting currency.

Include fees to make a fair comparison

A payment method is a way to pay, such as exchanging cash or paying by card. A fee is an extra amount charged for using a method. In our examples, a fee is taken from the Canadian-dollar amount before the rest is exchanged. This is an assumption for these examples, so always check how a real offer handles its fee.
Suppose you have CAD 100. One method charges CAD 4 and exchanges the remaining CAD 96. Another charges no fee and exchanges all CAD 100. If both methods use the same rate, the second method gives more foreign currency. If the rates differ, calculate both final amounts before deciding.
A comparison is fair when it uses the same starting amount, destination currency, and fee rule for every method. A larger rate number is not always enough to choose a method. A fee may reduce the amount that gets exchanged.
amount exchanged=starting amount−fee\text{amount exchanged} = \text{starting amount} - \text{fee}
  • Subtract a fee first when the stated fee is taken from the starting amount.
  • Then apply that method’s exchange rate.
  • Compare final amounts in the same currency.

Use a repeatable comparison plan

First, write down the amount you plan to spend and the currency you have. Next, record each method’s rate and fee. Work out the amount left after the fee, then convert it. Finally, compare the foreign-currency amounts. The method with the larger final amount gives you more of that currency for the stated starting amount.
You can also compare the cost of a purchase. If an item has a price in the destination currency, compare that price with the amount each method provides. If the method provides less than the price, the amount is not enough. Keep the comparison within the currencies and information given; do not assume a rate or fee that has not been stated.
The examples use rounded amounts where needed. Rounding means replacing a number with a nearby simpler number. Because different rounding choices can slightly change a result, use the same sensible precision when comparing methods.
final amount=(starting amount−fee)×exchange rate\text{final amount} = (\text{starting amount} - \text{fee}) \times \text{exchange rate}
  • Use one consistent set of starting details for every option.
  • Show the fee, amount exchanged, and final converted amount.
  • A comparison only supports a conclusion about the stated rates and fees.

Try the method yourself

Before reading the examples, try this plan with a partner: name the starting and destination currencies, list each method’s rate and fee, and predict which method may give more. Then calculate to check your prediction.
Use the diagrams as comparisons of final amounts, not as pictures of real-world rates. Their values come only from the hypothetical information stated in each example.
  • Predict first, then calculate and compare.
  • Use the diagram’s labels and units to read the result.

Worked example

Compare two ways to get USD

You have CAD 100. Method A has a hypothetical rate of 0.72 USD for each CAD and a CAD 4 fee. Method B has a hypothetical rate of 0.70 USD for each CAD and no fee. Each fee is taken from the CAD amount before exchange. Which method gives more USD?
USD received from CAD 100
USD received from CAD 100Hypothetical comparison after the stated fees.69.12 USDMethod A70 USDMethod B

Hypothetical comparison after the stated fees.

  1. Find the amount each method exchanges
    Method A takes CAD 4 from CAD 100, leaving CAD 96 to exchange. Method B has no fee, so it exchanges CAD 100.
    100−4=96100 - 4 = 96
  2. Convert each amount
    Multiply each amount in CAD by its method’s rate in USD per CAD. The units show that the results are in USD.
    96×0.72=69.12;100×0.70=7096 \times 0.72 = 69.12;\quad 100 \times 0.70 = 70
  3. Compare the results
    Method A gives USD 69.12. Method B gives USD 70. Method B gives USD 0.88 more for this starting amount and these stated terms.
    70−69.12=0.8870 - 69.12 = 0.88
Answer: Method B gives USD 70, which is USD 0.88 more than Method A.
Check: Both results are in USD, and both use the same starting amount of CAD 100.

Worked example

Compare methods when the rate and fee both matter

You have CAD 160 and want EUR. Method C has a hypothetical rate of 0.65 EUR for each CAD and a CAD 2 fee. Method D has a hypothetical rate of 0.64 EUR for each CAD and a CAD 1 fee. Fees are taken from the CAD amount before exchange. Which method gives more EUR?
EUR received from CAD 160
EUR received from CAD 160Hypothetical comparison after subtracting each fee.102.7 EURMethod C101.76 EURMethod D

Hypothetical comparison after subtracting each fee.

  1. Subtract each fee
    Method C exchanges CAD 158 after its fee. Method D exchanges CAD 159 after its fee.
    160−2=158;160−1=159160 - 2 = 158;\quad 160 - 1 = 159
  2. Apply each exchange rate
    Multiply each amount left in CAD by its rate in EUR per CAD. The answers are amounts in EUR.
    158×0.65=102.70;159×0.64=101.76158 \times 0.65 = 102.70;\quad 159 \times 0.64 = 101.76
  3. Decide using the final amounts
    Method C gives EUR 102.70, while Method D gives EUR 101.76. Although Method D has a smaller fee, Method C gives EUR 0.94 more because its rate is higher.
    102.70−101.76=0.94102.70 - 101.76 = 0.94
Answer: Method C gives more: EUR 102.70, which is EUR 0.94 more than Method D.
Check: The lower-fee method does not automatically give the most foreign currency. Compare the final amounts.

Worked example

Check whether a method provides enough for a purchase

A purchase costs 80 units of a hypothetical destination currency. You have CAD 120. Method E has a hypothetical rate of 0.68 destination-currency units for each CAD and a CAD 3 fee. Method F has a hypothetical rate of 0.67 units for each CAD and a CAD 1 fee. Fees are taken from the CAD amount before exchange. Which method provides enough, and which gives more?
Destination currency available
Destination currency availableHypothetical amounts compared with the purchase price of 80 units.79.56 destination-currencyMethod E79.73 destination-currencyMethod F80 destination-currencyPurchase price

Hypothetical amounts compared with the purchase price of 80 units.

  1. Find the amounts exchanged
    Subtract each fee from CAD 120. Method E exchanges CAD 117, and Method F exchanges CAD 119.
    120−3=117;120−1=119120 - 3 = 117;\quad 120 - 1 = 119
  2. Convert to the destination currency
    Use each method’s rate to find the amount available for the purchase.
    117×0.68=79.56;119×0.67=79.73117 \times 0.68 = 79.56;\quad 119 \times 0.67 = 79.73
  3. Compare with the purchase price
    The purchase costs 80 units. Both methods provide less than 80, so neither provides enough. Method F gives more than Method E, but it is still short of the purchase price.
    80−79.73=0.2780 - 79.73 = 0.27
Answer: Neither method provides enough. Method F gives more, but it is 0.27 destination-currency units short.
Check: Being the better of two methods does not mean the amount is enough to pay the stated price.

Common mistakes and how to avoid them

Choosing the method with the highest rate without considering its fee.
Correction: Subtract the fee as stated, calculate the final converted amount, and compare the results.
Comparing amounts in different currencies as if they were the same.
Correction: Convert both options to the same destination currency before comparing.
Using a rate in the wrong direction.
Correction: Read the units. Check which currency is received for each unit of the currency you start with.
Assuming the best method must provide enough for the purchase.
Correction: Compare the final amount with the stated price as a separate step.

Lesson summary

  • An exchange rate connects a starting currency to a destination currency.
  • For the fee rule used here, subtract the fee before applying the rate.
  • Compare final amounts in the same currency and use the same starting amount.
  • Check separately whether the amount received is enough for the purchase.

Check your understanding

Question 1

You have CAD 50. A hypothetical method charges a CAD 2 fee and gives 0.80 units of another currency for each CAD. How many destination-currency units do you receive?
  1. 40
  2. 38.4
  3. 41.6
  4. 48
Show answer and explanation
38.4
The fee leaves CAD 48 to exchange. Then 48 multiplied by 0.80 gives 38.4 destination-currency units.

Question 2

Two hypothetical methods start with the same CAD amount and use the same exchange rate. Method A has no fee. Method B has a fee taken from the CAD amount. Which gives more destination currency?
  1. Method A
  2. Method B
  3. They give the same amount
  4. There is not enough information to compare
Show answer and explanation
Method A
With the same starting amount and rate, Method A exchanges more CAD because it has no fee.

Question 3

A purchase costs 60 units of a destination currency. One method gives 59.70 units, and another gives 59.90 units. What is true?
  1. The first method gives enough.
  2. The second method gives enough.
  3. Neither method gives enough, though the second gives more.
  4. Both methods give the same amount.
Show answer and explanation
Neither method gives enough, though the second gives more.
Both amounts are less than 60. The second amount is larger, but it is still 0.10 units short.

Key terms

Currency
The kind of money used in a place, such as CAD, USD, or EUR.
Exchange rate
A number that tells how much of one currency is exchanged for a unit of another currency.
Payment method
A way to pay or exchange money, such as using cash or a card.
Fee
An extra amount charged for using a payment or exchange method.

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Published by DoAssignment. This reviewed lesson follows Ontario Grade 8 Mathematics, expectation F1.1. It is a study resource, not an official curriculum publication.

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