Compare credit-card and loan options in context

Alberta Grade 11 Mathematics

Number and money

Look beyond the interest rate to compare the total cost and fit of each option.

A person may need to borrow money for an unexpected repair or a planned purchase. A credit card and a loan can both provide the money, but they may charge interest and fees in different ways. The lowest advertised rate does not always mean the lowest total cost. In this lesson, you will compare offers using the details stated in each example. All rates, fees, and prices in the examples are hypothetical, not current offers from lenders.

What you will learn

Identify the amount borrowed, interest rate, fees, payment, and repayment time in a credit offer.
Compare the cost of credit-card and loan options using the information provided.
Choose an option based on both cost and how well it fits a person’s needs.

Read the whole offer

Credit means using money now and repaying it later. The amount borrowed is the principal. Interest is the cost charged for borrowing money. A fee is another charge, such as an account or setup charge. The annual interest rate is the stated interest rate for one year. It does not, by itself, tell you the complete cost.

A credit card usually lets a person borrow up to a set limit and repay some or all of the balance. A loan often provides a set amount with an agreed repayment plan. The exact terms depend on the offer. Check how long repayment will take, whether the payment can change, and whether fees apply.

For a fair comparison, first make sure the options cover the same amount borrowed and the same need. Then find the total amount to be repaid, including interest and fees, if the offer gives it. If the total is not given, calculate only what the supplied information allows. Do not treat a one-month estimate as the full cost of borrowing.

\text{total repayment} = \text{principal} + \text{interest} + \text{fees}

Principal is the amount borrowed.
Interest and fees add to the cost of borrowing.
Compare the same amount and purpose, and check the repayment details.

Use the information supplied

A quote is information provided by a lender about a particular offer. It may state a total repayment amount, a payment schedule, an interest rate, and fees. Use the quote’s stated terms rather than assuming that every lender calculates interest in the same way.

If a problem asks for an estimate of one month’s interest and gives an annual rate, divide that rate by

12

to estimate a monthly rate. Multiply the monthly rate by the balance. This is a one-month estimate on an unchanged balance. It is not a full credit-card repayment calculation: actual interest can depend on the card’s terms and the balance over time.

A useful comparison includes more than cost. Consider whether the payment fits the borrower’s budget, how long repayment lasts, and whether the borrower can avoid adding more debt. A lower total repayment may not be the better choice if its required payment is unaffordable.

\text{estimated monthly rate} = \frac{\text{annual rate}}{12}

Use the terms actually stated in an offer.
Label estimates clearly; one month’s interest is not the total borrowing cost.
Compare payment fit and repayment time as well as total cost.

Compare in context

Start with the borrower’s situation. Ask how much money is needed, when it is needed, and what payment is manageable. Then list each option’s principal, rate, fees, repayment time, and payment amount if known.

A total repayment quote makes a direct cost comparison possible when the principal and purpose match. Subtract the principal from the total repayment to find how much is paid beyond the amount borrowed. If one offer leaves out important details, say that the comparison is incomplete. Do not guess missing fees or payment terms.

Before deciding, check units and reasonableness. Rates are percentages per year unless the offer says otherwise. Payments are amounts per payment period. A total repayment should be greater than the principal when interest or fees are charged. Keep the source of each value clear: in these examples, each offer is hypothetical.

\text{cost beyond principal} = \text{total repayment} - \text{principal}

Match the amount borrowed and purpose before comparing.
A missing term can prevent a complete comparison.
Check that rates, payment periods, and total amounts make sense together.

Worked example

Compare one month of borrowing

For a hypothetical CAD 1,000 purchase, a credit-card offer has an annual rate of 18% and no fee. A loan offer has an annual rate of 12% and a one-time fee of CAD 8. Estimate one month’s interest for each option, assuming the full balance remains unpaid for that month. Which has the lower estimated first-month cost?

First-month estimated costs

Hypothetical offers; the loan bar includes its one-time fee.

Find monthly rates
The offers state annual rates. For this estimate only, divide each annual rate by $12$ to get a monthly rate.
$18% \div 12 = 1.5%; 12% \div 12 = 1%$
Estimate interest
Multiply the CAD 1,000 balance by each monthly rate. The loan also has a one-time CAD 8 fee, so include it when comparing first-month cost.
$\text{card: CAD }1{,}000(0.015)=\text{CAD }15; \text{loan: CAD }1{,}000(0.01)+\text{CAD }8=\text{CAD }18$
Interpret the result
The card has the lower estimated first-month cost by CAD 3 under these assumptions. This does not prove it is cheaper over the full repayment period. The card’s rate is higher, and later costs depend on payments and the offer’s terms.
$\text{CAD }18-\text{CAD }15=\text{CAD }3$

Answer: The estimated first-month cost is CAD 15 for the card and CAD 18 for the loan, including the loan fee. The card is lower by CAD 3 for this one-month estimate.

Check: The monthly interest estimates are much smaller than the CAD 1,000 principal, which is reasonable for rates near 1% to 1.5% per month. This is not a total-cost comparison.

Worked example

Compare quoted total repayment

A borrower needs CAD 2,400 for the same repair. Two hypothetical offers state their total repayment: a credit card estimate totals CAD 2,760 over 18 months, while a loan quote totals CAD 2,640 over 18 months and includes its fees. Compare the cost beyond principal. What should the borrower still check?

Cost beyond principal

Hypothetical quoted totals, with principal removed; loan fees are included.

Find the card’s cost
Subtract the amount borrowed from the stated total repayment. The result is the amount paid beyond the principal, based on this hypothetical estimate.
$\text{CAD }2{,}760-\text{CAD }2{,}400=\text{CAD }360$
Find the loan’s cost
Use the same subtraction for the loan. Its stated total already includes fees, so do not add a fee again.
$\text{CAD }2{,}640-\text{CAD }2{,}400=\text{CAD }240$
Compare and decide what is missing
The loan’s stated cost beyond principal is CAD 120 lower. Before choosing, check whether the required payments fit the borrower’s budget and whether the quoted terms match the actual repayment plan.
$\text{CAD }360-\text{CAD }240=\text{CAD }120$

Answer: The card costs CAD 360 beyond principal; the loan costs CAD 240. The loan is CAD 120 lower on the stated totals. The borrower should still check payment amounts, repayment conditions, and that all relevant charges are included.

Check: Both stated totals exceed CAD 2,400, as expected when interest or fees are charged. The comparison is useful because both offers cover the same principal and 18-month period.

Worked example

Compare payment fit

A hypothetical borrower has CAD 600 left on a card. The offer information gives an annual rate of 24%, with no new purchases or payments during the month. A hypothetical loan offer for the same CAD 600 states that its monthly payment is CAD 55 and that the remaining total repayment, including fees, is CAD 660. Estimate the card’s interest for one month, then compare the information available for each option.

Known amounts are not the same measure

Hypothetical values shown for reference; card is one-month interest, loan is total cost beyond principal, so the bars should not be treated as a direct cost comparison.

Estimate card interest
For a one-month estimate on an unchanged balance, divide the stated annual rate by $12$ and multiply by the balance.
$24% \div 12=2%; \text{CAD }600(0.02)=\text{CAD }12$
Read the loan information
The loan’s remaining total repayment is stated as CAD 660, including fees. Compared with CAD 600 borrowed, that is CAD 60 beyond principal. The monthly payment is also stated as CAD 55.
$\text{CAD }660-\text{CAD }600=\text{CAD }60$
Make a careful comparison
The card’s estimated interest for one month is CAD 12, but that is not its full repayment cost. The loan provides a total and monthly payment, while the card’s total and repayment time are not given. The borrower cannot decide which has the lower total cost from these details alone.

Answer: The card’s estimated interest for one month is CAD 12. The loan’s stated cost beyond principal is CAD 60, with a monthly payment of CAD 55. There is not enough information to compare full repayment costs; the card’s payment plan and total repayment are needed.

Check: The CAD 12 estimate is 2% of CAD 600. Do not compare it directly with the loan’s CAD 60 total cost because the time periods are different.

Common mistakes and how to avoid them

Choosing the offer with the lower annual rate without checking fees or repayment terms.

Correction: Compare total repayment and payment conditions when those details are available. A fee or a longer repayment period can affect the cost.

Treating one month’s estimated interest as the total cost of a credit card.

Correction: A one-month estimate covers only one month under stated assumptions. The full cost depends on the balance and repayment over time.

Comparing a monthly amount from one offer with a total repayment from another.

Correction: Make sure the amounts describe the same time period and measure. If they do not, state what information is missing.

Lesson summary

Compare offers for the same amount and purpose.
Include interest and fees when finding cost beyond principal.
Use stated terms; label any estimate and its assumptions.
Check affordability, repayment time, and whether the comparison is complete.

Check your understanding

Question 1

A hypothetical offer has a principal of CAD 800 and a total repayment of CAD 920, including fees. How much is paid beyond principal?

CAD 120
CAD 920
CAD 800
CAD 80

Show answer and explanation

CAD 120

Subtract principal from total repayment: CAD 920 minus CAD 800 is CAD 120.

Question 2

A hypothetical card rate is 12% per year. Using the one-month estimate method, what monthly rate is used?

1%
12%
0.12%
144%

Show answer and explanation

1%

Divide 12% by 12 months to get 1% per month for this estimate.

Question 3

One offer gives a one-month interest estimate. Another gives a total repayment over a year. What is the best next step?

Get matching time-period information before comparing full costs.
Assume the one-month amount is the full cost.
Choose the offer with the smaller number.
Ignore the repayment period.

Show answer and explanation

Get matching time-period information before comparing full costs.

The values describe different time periods and cannot be compared as full costs without more information.

Key terms

Credit: Using money now and agreeing to repay it later.
Principal: The amount of money borrowed.
Interest: The cost charged for borrowing money.
Fee: An additional charge connected to an offer.
Annual interest rate: The stated interest rate for one year.
Total repayment: The full amount paid back, including principal, interest, and any included fees.

Continue through Math 20-3

View the complete Math 20-3 Alberta Grade 11 Mathematics curriculum and lessons

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About this lesson and its review

Published by DoAssignment. This reviewed lesson follows Alberta Grade 11 Mathematics (Math 20-3), expectation N5. It is a study resource, not an official curriculum publication.

Before publication, content is checked for structure, mathematical or chemical notation, calculations, course boundaries, and readability. Errors can still occur, so corrections are welcomed.

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