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A3.9 · Compare extra costs for different transaction types

Learn to compare extra costs for different transaction types through clear examples and targeted practice.

Ontario Grade 11 Mathematics

Earning and Purchasing

Use a fee list, a calculator, or a spreadsheet to find which way of paying costs less.

A transaction is an exchange, such as paying a store or sending money. The amount shown on a price tag may not be the only cost. A payment method can add a fee, and different methods can add different fees. For example, a business might pay one fee for each debit purchase and a different fee for each credit purchase. To compare fairly, use the same purchase amount and the same fee information for each option. The examples in this lesson use made-up fee schedules for practice. Actual fees depend on the service, account, and agreement, so check the current fee information before making a real decision.

What you will learn

Identify extra costs attached to different transaction types.
Calculate and compare the total extra cost using a sample fee list.
Choose a lower-cost option while explaining what the comparison does and does not include.

1. Find the extra cost in the fee information

An extra cost is an amount added to the basic amount paid or received. A transaction type is the way the exchange is carried out. For example, a customer may pay by debit card, credit card, cash, or electronic transfer. A business may be charged a fee for accepting some of these methods.

A fee list may show a fixed fee for each transaction, a percentage of the purchase, or both. A fixed fee stays the same for each transaction. A percentage fee depends on the amount. A sample list might say that debit costs CAD 0.10 per purchase and credit costs 2% of the purchase amount. Those are different kinds of fees, so the purchase amount matters when comparing them.

Read the fee details carefully. Check which method the fee applies to, whether it is charged once or for each transaction, and whether the fee is a fixed amount or a percentage. Do not assume a fee applies if the fee list does not say so. In this lesson, compare only the extra costs shown in the sample information.

Use the fee list rather than guessing.
A fixed fee is the same amount each time; a percentage fee changes with the purchase amount.
Keep the basic purchase amount separate from the extra cost.

2. Calculate and compare on the same basis

First, identify the purchase amount and the fee for each transaction type. For a percentage fee, change the percent to a decimal by dividing by 100. Then multiply the purchase amount by that decimal. For example, 2% is the same as 0.02. For a fixed fee, use the stated amount.

Next, add any fees that apply to get the total extra cost for that option. If a business makes several transactions, calculate the fee for one transaction and multiply by the number of transactions when the fee is charged each time. Compare totals for the same number of transactions. This avoids comparing one debit purchase with a whole week of credit purchases.

A calculator is useful for checking multiplication and addition. A spreadsheet can also help when there are many purchases. One column can list each transaction type, another can show the fee for one purchase, and another can show the number of purchases. The total fee for each type can then be compared. Check that the spreadsheet uses the right fee and number of transactions.

The lowest extra cost is not automatically the best choice in every situation. This comparison tells you which option has the lower cost based on the information provided. Convenience, payment rules, or other costs may matter too, but include them only when reliable information is available.

\text{total extra cost}

= fee per transaction × number of transactions

Calculate each option using the same purchase amount and number of transactions.
For a percentage fee, multiply the amount by the percent written as a decimal.
State the basis of your decision: the listed extra costs.

3. Make a clear decision

After calculating, compare the extra costs directly. A difference can be found by subtracting the smaller cost from the larger one. This tells how much more the higher-cost option adds. Keep the wording clear: say which transaction type costs less and name the fee information used.

A useful comparison includes the purchase amount, the transaction types, and the extra cost for each. If the amounts change, the result may change too, especially when one fee is a percentage. Avoid saying that one method is always cheaper based on only one example.

When working with a real bill or workplace agreement, check for other listed charges and make sure the fee information is current. If a fee is unclear, ask the service provider rather than filling in a guess.

Compare the final extra costs, not just the fee rates.
A percentage fee can have a different effect on a small purchase and a large purchase.
Explain the decision using the information actually provided.

Example 2: total fees for 25 payments

Transaction type	Fee for one CAD 30 payment	Number of payments	Total extra cost
Electronic transfer	CAD 0.25	25	CAD 6.25
Card	CAD 0.40	25	CAD 10.00

Worked example

A small shop compares card fees

A shop accepts debit and credit. Its sample fee list says debit costs CAD 0.12 per purchase. Credit costs 1.8% of the purchase amount. For a CAD 40 purchase, compare the extra costs and say which method costs the shop less.

Find the debit fee
The list gives a fixed fee for each debit purchase. Since there is one purchase, the extra cost is the listed fee.
$\text{Debit fee} = \text{CAD }0.12$
Find the credit fee
Convert 1.8% to 0.018 by dividing by 100. Multiply the purchase amount by 0.018 to find 1.8% of CAD 40.
$40 \times 0.018 = 0.72$
Compare the fees
The credit fee is CAD 0.72, while the debit fee is CAD 0.12. Subtracting shows that the credit fee is CAD 0.60 higher for this purchase.
$0.72 - 0.12 = 0.60$

Answer: The debit transaction has the lower extra cost: CAD 0.12 compared with CAD 0.72 for credit. Based only on these listed fees, debit costs the shop CAD 0.60 less for this CAD 40 purchase.

Check: The credit fee is less than CAD 1 because 1.8% is less than 2%, and 2% of CAD 40 is CAD 0.80. CAD 0.72 is reasonable. It is also greater than the debit fee of CAD 0.12.

Worked example

A worker compares fees for a week of payments

A small service business expects 25 customer payments. Its sample fee list says electronic transfer costs CAD 0.25 per payment. Card payment costs CAD 0.10 per payment plus 1% of each payment amount. If each customer pays CAD 30, compare the total extra costs for the 25 payments.

Calculate the transfer total
Each electronic transfer costs CAD 0.25. Multiply by 25 because the fee is charged for every payment.
$25 \times 0.25 = 6.25$
Calculate the percentage part of one card fee
One percent is 0.01. Multiply the CAD 30 payment by 0.01 to find the percentage part of the card fee for one customer.
$30 \times 0.01 = 0.30$
Find the full card fee per payment
The card fee has both a fixed part and a percentage part. Add CAD 0.10 and CAD 0.30 to get the fee for one payment.
$0.10 + 0.30 = 0.40$
Calculate and compare the card total
Multiply the CAD 0.40 fee by 25 payments. Then compare the result with the transfer total.
$25 \times 0.40 = 10.00$

Answer: Electronic transfers have the lower extra cost: CAD 6.25 compared with CAD 10.00 for card payments. For these 25 payments, the card fees are CAD 3.75 higher.

Check: For 25 payments, the card's fixed part alone is CAD 2.50, and its percentage part is CAD 7.50. Together they make CAD 10.00. Both parts are included in the comparison.

Common mistakes and how to avoid them

Comparing the credit percentage directly with a fixed debit fee.

Correction: Calculate the actual fee for the given purchase amount before comparing.

Forgetting the fixed part of a fee that has both a fixed amount and a percentage.

Correction: Calculate each part, add them for one transaction, and then multiply by the transaction count.

Multiplying a per-transaction fee by the purchase amount.

Correction: A per-transaction fee is multiplied by the number of transactions, not the purchase amount.

Claiming one transaction type is always cheaper based on one situation.

Correction: Limit the conclusion to the purchase amounts, transaction counts, and fees that were compared.

Lesson summary

Read the fee information and identify every extra cost that applies.
Calculate percentage fees from the purchase amount and include fixed fees where listed.
For repeated transactions, multiply the fee per transaction by the number of transactions.
Compare totals on the same basis and explain the decision using the listed costs.

Check your understanding

Question 1

A payment service charges CAD 0.20 for each transfer. What is the extra cost for 8 transfers?

CAD 0.20
CAD 1.60
CAD 8.20
CAD 40.00

Show answer and explanation

CAD 1.60

The fee is charged for each of the 8 transfers, so multiply CAD 0.20 by 8. The total is CAD 1.60.

Question 2

A card fee is 2% of a CAD 50 purchase. What is the extra cost?

CAD 0.10
CAD 1.00
CAD 2.00
CAD 10.00

Show answer and explanation

CAD 2.00

Write 2% as 0.02 and multiply by 50. The fee is CAD 1.00? Check: 50 times 0.02 equals 1. Therefore the correct option is CAD 1.00.

Question 3

A business compares two payment methods for the same number of customer payments. What should it compare?

Only the percentage rates
The total extra cost for each method
The purchase amount for one method and the fee for the other
The fee for one transaction in one method and the total for all transactions in the other

Show answer and explanation

The total extra cost for each method

Comparing total extra costs for the same number of payments gives a fair comparison. Rates alone may not show the actual amount charged.

Key terms

Transaction: An exchange, such as paying a business or sending money.
Transaction type: The method used to carry out an exchange, such as debit, credit, or electronic transfer.
Extra cost: An amount added to the basic amount because of a fee or charge.
Fixed fee: A fee that stays the same for each transaction.
Percentage fee: A fee calculated as a percent of the payment amount.

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View the complete Ontario Grade 11 Mathematics learning path

About this lesson

Published by DoAssignment. This AI-assisted lesson follows Ontario Grade 11 Mathematics (MEL3E), expectation A3.9. It is a study resource, not an official curriculum publication.

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