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F1.6 · Compare credit-card rates, fees, and rewards

Learn to compare credit-card rates, fees, and rewards through clear examples and targeted practice.

Ontario Grade 8 Mathematics

Financial Literacy

A Grade 8 guide to comparing hypothetical offers fairly

A credit card lets a person pay for a purchase and repay the card company later. A card offer may include a rate, a fee, and rewards. The rate describes interest charged on an unpaid amount. A fee is a charge for using or holding the card. A reward is a benefit earned from purchases that meet the offer’s rules. To compare offers fairly, imagine the same person using each card in the same way. All numbers and terms in this lesson are hypothetical examples, not current offers.

What you will learn

  • Identify the rate, fee, and reward in a credit-card offer.
  • Compare hypothetical offers using the same balance, spending, and time assumptions.
  • Explain why the lowest rate does not always lead to the lowest estimated cost.

Read the three parts of an offer

A rate is a percentage used to describe interest charged on money that remains unpaid. Interest is the extra amount charged for borrowing. For a simple classroom estimate, a hypothetical rate of 18% means CAD 18 for each CAD 100 over one year, if the balance is treated as unchanged. This is a comparison model, not an exact prediction of a real card bill.
A fee is a stated charge. An annual fee is charged once each year. A reward is a benefit for eligible purchases. An eligible purchase is one that counts under the card’s reward rules. Check which purchases qualify and how the reward can be used. Do not assume that every purchase earns a reward or that points have a particular value.
Before comparing offers, choose the situation. Decide whether the person carries an unpaid balance, how much they spend on eligible purchases, and what time period they compare. Use the same assumptions for both cards. That way, you compare the offers rather than two different situations.
For example, 18% of CAD 100 is CAD 18 in the simple estimate. A percentage means “out of 100,” so this is a useful way to make a small estimate from a stated rate.
  • A rate matters to the interest estimate when there is an unpaid amount.
  • A fee adds a charge; a reward can reduce the estimated cost.
  • Use only reward rules and values stated for the comparison.

Build a simple comparison

For a simple one-year estimate, write the rate as a decimal and multiply it by the unchanged balance. A decimal is another way to write a number: 18% is 0.18. This gives an estimated interest amount for comparing offers. It does not account for every detail that may affect a real card bill.
Next, add the fee and subtract the stated value of rewards earned in the example situation. Keep each part visible so you can check the calculation. If one estimated cost is smaller, that offer has the lower estimated cost for those assumptions.
The model can be written as one short rule. The reward value is subtracted because it is a benefit in this comparison. If the reward value is not known, do not invent it. You can compare the stated rates and fees, and explain that the full cost comparison is not possible without the reward value.
A bar chart can compare amounts in CAD. Each bar should use the same unit and represent the same time period and situation. Bars for interest, fees, rewards, or final estimated costs can help show which amounts are larger. A chart cannot make an unfair comparison fair if the assumptions differ.
Estimated cost=estimated interest+fee−reward value\text{Estimated cost}=\text{estimated interest}+\text{fee}-\text{reward value}
  • Use the same balance, spending, and time period for each offer.
  • Estimate interest, add fees, and subtract reward value.
  • A result applies only to the assumptions used.

Match the comparison to the person’s habits

If someone pays the full amount owed by the due date, this simple model has no unpaid balance on which to estimate interest. In that situation, fees and rewards may make a bigger difference. The rate is still part of the offer, but it may not affect this particular estimate.
If someone carries an unpaid balance, the rate can affect the estimated interest. A lower rate may give a smaller interest estimate, but a higher fee or smaller reward can change which offer has the lower total estimated cost.
A reward is not automatically the same as cash in hand. Check the offer’s rules and use a value only when the value is stated or supplied for the example. If you do not know the value, say so. A careful comparison is more useful than a made-up number.
A comparison is not a universal ranking of cards. It answers a specific question: which offer has the lower estimated cost for this balance, spending, time period, and reward assumption? If those details change, the result may change too.
  • There is not one best offer for every person and situation.
  • State the assumptions before comparing.
  • Do not treat an unknown reward value as known.

A quick comparison checklist

FeatureQuestion to ask
RateWhat rate applies, and is there an unpaid amount in this situation?
FeeWhat fee is charged, and how often?
RewardWhich purchases qualify, and what stated value can be used?
AssumptionsAre spending, balance, and time period the same for both cards?

Worked example

Compare two rates

Two hypothetical offers have rates of 18% and 15%. Estimate the interest for an unchanged CAD 1,000 balance over one year using the simple model. Which estimate is lower?
Estimated interest for one year
Estimated interest for one yearHypothetical simple estimates on the same CAD 1,000 balance. Both bars use CAD.180 CAD18% rate150 CAD15% rate

Hypothetical simple estimates on the same CAD 1,000 balance. Both bars use CAD.

  1. Use the same balance
    Compare both offers using the same CAD 1,000 balance and one-year period. This keeps the comparison fair.
  2. Estimate each amount
    Write each percentage as a decimal and multiply by CAD 1,000. The 15% rate gives the smaller estimate.
    1,000×0.18=180;1,000×0.15=1501{,}000\times0.18=180;\quad1{,}000\times0.15=150
Answer: The 18% offer gives a simple estimate of CAD 180, and the 15% offer gives CAD 150. The 15% estimate is lower by CAD 30.
Check: These are simple one-year estimates for an unchanged balance, not exact billing predictions.

Worked example

Include a fee and rewards

Two hypothetical cards have no interest cost in this example because the person pays the full amount owed. Card A has no annual fee and gives 1% back on eligible purchases. Card B has a CAD 60 annual fee and gives 2% back. The person makes CAD 3,000 in eligible purchases. Which has the lower estimated cost after rewards?
Fees and reward values
Fees and reward valuesHypothetical amounts in CAD for the same eligible purchases. The chart compares the nonnegative fee and reward amounts; Card A’s reward exceeds its fee by CAD 30.0 CADCard A fee30 CADCard A reward60 CADCard B fee60 CADCard B reward

Hypothetical amounts in CAD for the same eligible purchases. The chart compares the nonnegative fee and reward amounts; Card A’s reward exceeds its fee by CAD 30.

  1. Find each reward value
    Apply each reward rate to the same CAD 3,000 of eligible purchases. Card A earns CAD 30 and Card B earns CAD 60 under these hypothetical terms.
    3,000×0.01=30;3,000×0.02=603{,}000\times0.01=30;\quad3{,}000\times0.02=60
  2. Include each fee
    There is no interest cost in this situation. Card A’s estimated cost after rewards is CAD 30 below zero. Card B’s CAD 60 fee and CAD 60 reward balance to zero. Card A is lower by CAD 30 in this comparison.
    0−30=−30;60−60=00-30=-30;\quad60-60=0
Answer: Card A has the lower estimated cost by CAD 30 for these assumptions. The negative result means the stated reward value exceeds the fee; it does not guarantee a cash profit.
Check: This comparison depends on all CAD 3,000 being eligible and on the stated reward values being usable as described.

Worked example

Compare the whole situation

Two hypothetical offers are being compared for a person who carries an unchanged CAD 500 balance for one year and makes CAD 2,000 in eligible purchases. Card C has a 12% rate, a CAD 20 annual fee, and a hypothetical reward value of CAD 10. Card D has a 10% rate, a CAD 50 annual fee, and a hypothetical reward value of CAD 20. Use the simple model to compare estimated costs.
Estimated total costs
Estimated total costsHypothetical one-year comparison using the stated balance, fees, and reward values. Both bars use CAD.70 CADCard C80 CADCard D

Hypothetical one-year comparison using the stated balance, fees, and reward values. Both bars use CAD.

  1. Estimate interest
    Use the same CAD 500 balance for both offers. Card C’s estimate is CAD 60, and Card D’s estimate is CAD 50.
    500×0.12=60;500×0.10=50500\times0.12=60;\quad500\times0.10=50
  2. Add fees and subtract rewards
    For Card C, add the CAD 20 fee and subtract the CAD 10 reward value. For Card D, add CAD 50 and subtract CAD 20. Card C has the lower estimated cost in this situation.
    60+20−10=70;50+50−20=8060+20-10=70;\quad50+50-20=80
Answer: Card C has an estimated cost of CAD 70, compared with CAD 80 for Card D. Card C is lower by CAD 10 under the stated assumptions, even though Card D has the lower rate.
Check: This example shows why the rate, fee, and reward all matter. The result may change with different borrowing or spending habits.

Common mistakes and how to avoid them

Choosing an offer only because it has the lowest rate.
Correction: Compare the rate, fee, and reward for the stated situation.
Subtracting rewards before finding how much is earned.
Correction: Use the stated reward rate or value and eligible purchases to find the reward amount first.
Comparing cards with different spending or balance assumptions.
Correction: Use the same balance, spending, and time period for each offer.
Treating a classroom interest estimate as an exact card bill.
Correction: Call it a simple estimate. Actual charges depend on the card terms and account details.

Lesson summary

  • A rate describes interest on an unpaid amount; a fee is a charge; a reward is a benefit for eligible purchases.
  • Compare offers using the same situation and time period.
  • Estimate interest, add fees, and subtract stated reward values.
  • The lower estimated cost depends on the assumptions and the person’s habits.

Check your understanding

Question 1

For the same unchanged CAD 400 balance over one year, which simple estimate is lower: 14% or 11%?
  1. 14%, because a larger rate gives a smaller amount
  2. 11%, because a smaller rate gives a smaller amount
  3. They are equal because the balance is the same
  4. There is no way to compare the rates
Show answer and explanation
11%, because a smaller rate gives a smaller amount
The balance and time period match, so the lower rate gives the lower simple estimate.

Question 2

A card has a CAD 25 fee and a stated reward value of CAD 40 for the example situation. What is the estimated cost after rewards if there is no interest cost?
  1. CAD 65
  2. CAD 40
  3. CAD 15 below zero
  4. CAD 25
Show answer and explanation
CAD 15 below zero
Subtract the CAD 40 reward value from the CAD 25 fee. The result is CAD 15 below zero.

Question 3

Why should two card offers be compared using the same spending and balance assumptions?
  1. So the comparison is fair and differences come from the offers
  2. So both cards have the same rate
  3. So rewards do not need to be checked
  4. So fees can be ignored
Show answer and explanation
So the comparison is fair and differences come from the offers
Matching assumptions lets you compare the offers rather than different situations.

Key terms

Rate
A percentage used to describe interest charged on an unpaid amount.
Interest
An extra amount charged for borrowing money.
Fee
An amount charged for a service or account.
Reward
A benefit earned for purchases that meet the offer’s rules.
Eligible purchase
A purchase that counts under the card’s reward rules.
Simple estimate
A basic calculation used to compare amounts, not an exact prediction of a real bill.

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Published by DoAssignment. This reviewed lesson follows Ontario Grade 8 Mathematics, expectation F1.6. It is a study resource, not an official curriculum publication.

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