F. Financial Literacy · Money and Finances: Exchange Rates, Budgets, Financial Decisions and Interest

How Interest Rates Affect the Cost of Borrowing

F1.5 A1About 45 minutes

Learning goals

I can calculate the interest on a loan or credit card balance.
I can explain how the interest rate and time change the total cost of borrowing.
I can compare paying now with paying over time.
I can explain why only paying the minimum on a credit card costs more.

Words to know

loan
Money borrowed that must be paid back, usually with interest.

cost of borrowing
The extra money you pay to borrow, mostly interest and fees.

credit card balance
The amount owed on a credit card.

minimum payment
The smallest amount you must pay on a credit card each month. Paying only this leaves the rest to grow interest.

financing / payment plan
Paying for something in instalments over time instead of all at once.

mortgage
A large loan used to buy a home, paid back over many years.

The same TV, two prices

The Roy family wants a new TV. The store offers two ways to pay:

Pay now: $800.
Pay over time: 12 monthly payments of $75.

The second choice sounds easier: only $75 at a time! But 12 × 75 = $900. The extra $100 is the cost of borrowing. When you borrow, interest usually makes things cost more.

How interest rates affect borrowing

When you borrow, interest works against you. The interest you pay depends on:

How much you borrow (the principal).
The interest rate. A higher rate costs more.
How long you take to pay it back. More time usually means more interest.

Different kinds of borrowing have very different rates. Car loans and mortgages usually have lower rates. Credit cards usually have much higher rates, often around 20% a year on an unpaid balance. Rates also change over time: the Bank of Canada sets a key interest rate that influences the rates banks charge. All rates in this lesson are examples.

Worked example

Example 1: Same loan, different rates

Two people each borrow $1000 for 1 year. One gets a loan at 6%. The other puts it on a credit card at 20% and pays it all back at the end of the year. Compare the interest.

Loan: 6% of 1000 = $60. Total paid: $1060.
Credit card: 20% of 1000 = $200. Total paid: $1200.
Difference: 200 − 60 = $140.

The credit card costs $140 more for the same $1000. (Real credit cards work out interest monthly, but the idea is the same: a higher rate costs much more.)

Worked example

Example 2: When interest isn't paid off

Someone owes $500 on a credit card at 20% a year and makes no payments (in our simplified example, interest is added once a year). What is owed after 1, 2 and 3 years?

Year 1: 20% of 500 = 100. Owed: $600.
Year 2: 20% of 600 = 120. Owed: $720.
Year 3: 20% of 720 = 144. Owed: $864.

After 3 years the debt grows to $864, an extra $364. Interest on interest works against borrowers just like it works for savers. (Not paying at all also brings late fees and other problems, so real costs would be even higher.)

Unpaid credit card interest snowballs: each year's 20% is charged on a bigger balance, so the debt grows by $100, then $120, then $144.

Worked example

Example 3: Paying only a small amount each month

A credit card balance is $600. Interest is 2% a month (simplified example; that's about 24% a year). Each month, the person pays $30. Follow 3 months.

Month 1: interest 2% of 600 = $12. 600 + 12 − 30 = $582.
Month 2: interest 2% of 582 = $11.64. 582 + 11.64 − 30 = $563.64.
Month 3: interest 2% of 563.64 ≈ $11.27. 563.64 + 11.27 − 30 = $544.91.
Paid so far: 3 × 30 = $90. Balance went down by only 600 − 544.91 = $55.09.

Of the $90 paid, about $35 went to interest. That's why paying only a small amount (like the minimum) takes a long time and costs a lot.

In month 1, $12 of the $30 payment goes to interest and only $18 lowers the balance. Example numbers.

Worked example

Example 4: A rise in interest rates

A family has a $20 000 car loan. Roughly, how much interest is there in one year at 5%? At 8%?

5% of 20 000 = $1000.
8% of 20 000 = $1600.
Difference: $600 more in one year at 8%.

When interest rates go up, borrowing costs more. That's one reason families think about interest rates before buying a car or a home. (In real loans the balance goes down as payments are made, so this is a first-year estimate.)

Before you borrow, ask

Do I need it now, or can I save and buy it later?
What is the interest rate, and are there fees?
What is the total I'll pay altogether?
Can I afford the payments every month, even if something unexpected happens?

Borrowing can be a useful tool for big, important things, like a home or education. The goal is to borrow wisely.

"0% financing" and "buy now, pay later"

Some stores offer 0% interest for a while. That can be a good deal if every payment is made on time. But read the rules: there may be fees, and missing a payment can mean a high interest rate starts. Grown-ups should read the agreement carefully.

Just for fun

Why is an unpaid credit card balance never lonely?

Interest keeps dropping by to visit, every single month!

Hands-on activity

Borrowing cost detective

You need: a store flyer or website (with a grown-up), paper, a pencil and a calculator.

Find an item that's offered with a payment plan, like "$X a month for 12 months" (or use the TV example).
Calculate the total of all payments and compare it with the pay now price. What is the cost of borrowing?
Now imagine the same price put on a credit card at 20% a year and paid off after one year. What would the interest be?
Then imagine saving for the item instead. If you saved the monthly payment amount each month, how many months until you could pay cash?
Write your recommendation: pay now, pay over time, or save first? Give two reasons.

What to look for: correct totals, comparing the same item three ways, and a recommendation with reasons that mention interest and time.

Your turn

Borrow $500 for 1 year at 8%. How much interest? Total paid?

A bike costs $450 now, or 6 payments of $85. What is the cost of borrowing?

$1500 borrowed for 1 year at 4% vs 19%. How much more interest at 19%?

$300 on a credit card at 20% a year, no payments, interest added yearly. What is owed after 2 years?

A balance of $400 at 2% a month. You pay $50. What is the balance after month 1?

Why does paying only a small amount on a credit card cost more over time?

More practice: warm-up

When you borrow, is a higher interest rate good or bad for you?

10% of $700 = ?

Borrow $200 at 5% for 1 year. Interest?

12 payments of $50 = ?

What is a mortgage?

More practice: on your own

A laptop costs $900 cash, or 24 payments of $42. What is the cost of borrowing? What percent of the cash price is that?

A balance of $1000 at 2% a month, paying $100 a month. Find the balance after 2 months.

A family's $300 000 mortgage: about how much interest in the first year at 4%? At 5%? What's the difference?

Owen can buy a $240 game system now with a credit card at 20% and pay it off in a year, or save $40 a month and buy it in 6 months. How much does waiting save?

A store offers 0% for 12 months on a $600 couch, but if any payment is late, 25% a year interest is charged. Why should a buyer be careful?

Challenge

Continue Example 3 (balance $544.91, 2% a month, $30 payment) for one more month. What is the new balance? About how much of the 4 payments went to interest in total?

Mila borrows $2000 at 10% a year. Plan A: pay back everything after 1 year. Plan B: wait 2 years (interest on interest). How much more does Plan B cost?

Explain how the same interest rate can help one person and cost another. Use savings and borrowing in your answer.

Check your understanding

Quiz

Borrow $800 for 1 year at 5%. What is the total paid back?

A $600 phone, or 12 payments of $55. What is the cost of borrowing?

Which usually has the highest interest rate?

$400 owed at 20% a year, no payments, interest added yearly. What is owed after 2 years?

If interest rates rise, what happens for a person with a variable-rate loan?

A $600 balance at 2% a month with a $30 payment. How much of the first payment goes to interest?

For parents and teachers

Big idea: This lesson completes F1.5 by showing how interest rates affect the cost of borrowing to pay for goods and services over time: loans, payment plans, credit cards and mortgages. Students see that the rate, the amount and the time all matter.

Common difficulties:

Seeing only the monthly payment. Always multiply to find the total and compare it with the cash price.
Monthly vs yearly rates. Our credit card examples are simplified (a yearly rate added once a year, or 2% a month). Real cards calculate interest daily or monthly; the big idea is the same.
Forgetting that unpaid interest also earns interest.

How to help: If you're comfortable, show your child the interest rate on a credit card statement or loan (hide account numbers). Talk about a time borrowing made sense for your family and why. All rates here are examples, not advice. This lesson builds A1 skills: thinking critically and making connections between math and real life.