F. Financial Literacy · Financial Decisions: Interest, Borrowing, Appreciation, Depreciation and BudgetsLearning From Past Financial Situations: Inflation and Interest Rates
F1.1 A2About 70 minutes
Learning goals- I can explain inflation and purchasing power in my own words.
- I can use the Consumer Price Index (CPI) to compare prices from different years.
- I can describe how interest rates in Canada changed in 2022 and 2023 and how that affected people who borrow and save.
- I can explain how a past financial situation can help me make better decisions now.
Words to know
inflation
A general rise in prices over time. When there is inflation, each dollar buys a little less than before.
purchasing power
How much a sum of money can actually buy.
Consumer Price Index (CPI)
A number published by Statistics Canada that tracks the cost of a typical "basket" of goods and services that households buy, compared with a base year.
percent change
(new value − old value) ÷ old value × 100%. Positive means an increase, negative means a decrease.
policy interest rate
The interest rate set by the Bank of Canada. Banks' rates for loans, lines of credit and savings tend to move up and down with it.
variable interest rate
An interest rate that can change during a loan, usually when the Bank of Canada's rate changes.
fixed interest rate
An interest rate that stays the same for a set period of time (the term).
Remember from Grade 8
In Grade 8 you made a financial plan that included income, expenses and taxes, kept budgets balanced, calculated simple interest (I = Prt) and compound interest (A = P(1 + r)ⁿ), and compared credit cards and consumer contracts. In this Grade 9 unit you will use those skills to make informed financial decisions: you will learn from real financial situations, compare the true cost of borrowing, work with appreciation and depreciation graphs, and change budgets when life changes.
Important: every price, wage and interest rate in this unit is an example in Canadian dollars. Real rates change often, so always check current numbers before making a real decision.
Hook: "Everything got more expensive!"
In 2022, many Canadian families noticed that groceries, gas and rent all cost more than the year before. They were right. Statistics Canada reported that prices rose 6.8% on average in 2022, the biggest yearly increase in about 40 years.
At the same time, the Bank of Canada raised its interest rate quickly to slow prices down. People with loans suddenly paid more interest, and savers started to earn more.
What happened then is a past financial situation. Looking at it closely, with math, helps you make better choices now. That is the big idea of this lesson.
What is inflation?
Inflation means prices in general go up over time. It does not mean every price goes up by the same amount. Some prices rise a lot, some barely move, and a few even fall.
When prices rise, the same dollar buys less. We say its purchasing power goes down.
The Bank of Canada tries to keep inflation near 2% per year. A little inflation is normal. A lot of inflation is hard on families, especially if wages do not keep up.
Measuring inflation with the CPI
Statistics Canada tracks the cost of a "basket" of things households buy: food, rent, gas, clothing, phone plans and more. The Consumer Price Index (CPI) compares the cost of that basket with a base year. In the CPI used here, the base year is 2002, so the CPI for 2002 is 100.
If the CPI is 151.2, the basket costs 151.2% of what it cost in 2002.
To move a price from one year to another, multiply by a ratio of CPIs:
price in year B = price in year A × (CPI in year B ÷ CPI in year A)
| Year | CPI (2002 = 100), about | Inflation that year |
|---|
| 2019 | 136.0 | 1.9% |
| 2020 | 137.0 | 0.7% |
| 2021 | 141.6 | 3.4% |
| 2022 | 151.2 | 6.8% |
| 2023 | 157.1 | 3.9% |
| 2024 | 160.9 | 2.4% |
Worked exampleExample 1: Bring a price forward in time
A basket of groceries cost $50.00 in 2019. About how much would the same groceries cost in 2024?
- Write the CPI ratio: CPI 2024 ÷ CPI 2019 = 160.9 ÷ 136.0 ≈ 1.1831.
- Multiply: $50.00 × 160.9 ÷ 136.0 ≈ $59.15.
- Check that it makes sense: prices went up between 2019 and 2024, so the 2024 cost should be more than $50. It is.
- Percent change: (59.15 − 50.00) ÷ 50.00 × 100% ≈ 18.3%.
About $59.15, which is about 18.3% more than in 2019.
The same basket of goods that cost $100.00 in 2019 cost about $118.31 in 2024 (using the CPI values in the table). Put the other way around, $100 in 2024 buys only about what $84.52 bought in 2019.Worked exampleExample 2: Did a raise keep up with inflation?
Sam's pay went up 3% in 2022. Prices went up 6.8% in 2022. Did Sam's purchasing power go up or down, and by about how much?
- Pay multiplier: 1 + 0.03 = 1.03. Price multiplier: 1 + 0.068 = 1.068.
- Compare them: 1.03 ÷ 1.068 ≈ 0.9644.
- 0.9644 is less than 1, so Sam can buy less than before: 1 − 0.9644 = 0.0356, or about 3.6% less.
Sam's purchasing power went down by about 3.6%, even though Sam got a raise. A raise only helps if it is bigger than inflation.
Don't just subtract
It is tempting to say "3% − 6.8% = −3.8%". That is close, but not exact. To compare a pay change with a price change, divide the multipliers: 1.03 ÷ 1.068. The same idea works for savings: money earning 1.5% interest while prices rise 3.9% loses purchasing power because 1.015 ÷ 1.039 < 1.
A second past situation: interest rates jump
From March 2020 until March 2022, the Bank of Canada's policy rate was very low: 0.25%. Borrowing was cheap. Then, to fight inflation, the Bank raised the rate ten times. By July 2023 it was 5.00%. In 2024 it began to lower the rate again, and after four more cuts in 2025 it was 2.25%, where it stayed into 2026.
Banks' interest rates move with the policy rate. People with variable-rate loans, lines of credit or mortgages saw their interest costs rise quickly. People with fixed rates were protected until their term ended, but then many had to renew at a much higher rate.
Worked exampleExample 3: The cost of a rate increase
A family has a $10 000 line of credit with a variable rate. In early 2022 the rate was 2.70% per year. By mid-2023 it was 7.20% per year. About how much interest builds up each month at each rate? (Use simple interest for one month: I = P × r × t, with t = 1/12 of a year.)
- At 2.70%: I = 10 000 × 0.027 × 1/12 = $22.50 per month.
- At 7.20%: I = 10 000 × 0.072 × 1/12 = $60.00 per month.
- Difference: $60.00 − $22.50 = $37.50 more per month, or 37.50 × 12 = $450 more per year, on the same debt.
About $22.50 a month before and $60.00 a month after: $450 more per year for the same $10 000.
How the past informs decisions
A past situation is useful when you ask: What happened? Why? What does the math show? What would I do differently? For the 2022 to 2023 situation, many people concluded:
- Rates can change fast. Before taking a variable-rate loan, check what the payment would be if the rate rose by 2 or 3 percentage points.
- Savings protect you. An emergency fund helped families pay higher costs without new debt.
- Inflation eats savings that earn little interest. Compare the interest rate on savings with inflation.
- Wages may lag behind prices. A budget needs room for prices to rise.
This is the context of the situation. Context plus math gives you a better decision than either one alone.
Hands-on activityThen-and-now price hunt
You need: a grown-up to interview, a current store flyer or website, a calculator, paper.
- Ask a grown-up to name something they remember buying, and roughly what it cost in a certain year (for example, a litre of milk, a bus fare or a movie ticket). An old receipt also works.
- Find what that item costs today.
- Calculate the percent change. Then divide by the number of years to get a rough average per year.
- If the year is between 2019 and 2024, use the CPI table to predict today's price, and compare your prediction with the real price.
- Ask the grown-up: "Did prices rising ever change a decision you made?"
Model answer: a movie ticket cost $13.00 in 2019 and $16.00 now. Percent change = 3 ÷ 13 × 100% ≈ 23%. The CPI prediction for 2024 is 13 × 160.9 ÷ 136.0 ≈ $15.38, so this price rose a bit faster than prices overall.
Just for funInflation is like a sweater that shrinks in the wash. The dollar bill looks exactly the same size as last year, but somehow it covers less.
Your turn
1The CPI was 141.6 in 2021 and 151.2 in 2022. Find the percent change.
About 6.8%. (151.2 − 141.6) ÷ 141.6 × 100% = 9.6 ÷ 141.6 × 100% ≈ 6.78%.
2A movie ticket cost $13.00 in 2019. Use the CPI table to estimate its cost in 2024.
About $15.38. 13 × 160.9 ÷ 136.0 ≈ 15.38.
3Prices rose 3.9% in 2023. Something cost $200 at the start of the year. Estimate its cost a year later.
$207.80. 200 × 1.039 = 207.80.
4In 2023, a worker's pay rose 5% and prices rose 3.9%. Did the worker's purchasing power go up or down?
Up, by about 1.1%. 1.05 ÷ 1.039 ≈ 1.0106, which is greater than 1.
5Find one month of simple interest on $5 000 at 3% per year and at 8% per year.
At 3%: 5000 × 0.03 ÷ 12 = $12.50. At 8%: 5000 × 0.08 ÷ 12 ≈ $33.33.
6What inflation rate does the Bank of Canada aim for? Was 2022 above or below it?
The target is 2%. 2022 (6.8%) was far above the target.
7Give one lesson a family could learn from the 2022 to 2023 rate increases, and explain it.
Sample answer: Keep an emergency fund, because when interest costs rose by hundreds of dollars a year, families with savings could pay without borrowing more. Other good answers: test what a loan payment would be at a higher rate before borrowing; choose a fixed rate if you cannot afford a payment increase.
More practice: warm-up
1In one sentence, what is inflation?
A general rise in prices over time, so each dollar buys less.
2A price went from $4.00 to $4.20. What is the percent increase?
5%. 0.20 ÷ 4.00 × 100% = 5%.
3Inflation is 2% this year. Goods cost $100 at the start of the year. What do they cost at the end?
4True or false: when inflation is high, the same amount of money buys less.
True. Purchasing power falls when prices rise.
5The CPI rose from 137.0 (2020) to 141.6 (2021). Find the percent change to one decimal place.
About 3.4%. 4.6 ÷ 137.0 × 100% ≈ 3.36%.
More practice: on your own
1A phone bill was $80 in 2019. Use the CPI to estimate the equivalent bill in 2023.
About $92.41. 80 × 157.1 ÷ 136.0 ≈ 92.41. This shows what the bill would be if it rose at the same rate as prices overall.
2In an example town, gas was $1.20/L in 2019 and $1.80/L in 2022. Compare that change with the CPI change from 2019 to 2022.
Gas rose (1.80 − 1.20) ÷ 1.20 = 50%. The CPI rose 151.2 ÷ 136.0 − 1 ≈ 11.2%. Gas rose much faster than prices in general, so a household that drives a lot was hit harder than the average.
3A savings account earns 1.5% per year while prices rise 3.9%. Does the money gain or lose purchasing power, and by about how much?
It loses about 2.3%. 1.015 ÷ 1.039 ≈ 0.9769, and 1 − 0.9769 ≈ 0.023.
4A $15 000 variable-rate loan has interest-only payments. The rate rises from 3% to 7% per year. How much more interest is charged per month? Per year?
Monthly interest goes from 15 000 × 0.03 ÷ 12 = $37.50 to 15 000 × 0.07 ÷ 12 = $87.50. That is $50 more per month, or $600 more per year.
5A salary of $50 000 in 2024 has the same purchasing power as what salary in 2019?
About $42 262. 50 000 × 136.0 ÷ 160.9 ≈ 42 262.27. Prices were lower in 2019, so a smaller salary bought the same things.
Challenge
1Prices rose 6.8% in 2022 and 3.9% in 2023. A student says the total increase over the two years was 6.8% + 3.9% = 10.7%. Is that right?
Not quite: it is about 11.0%. The 2023 increase applies to the already-higher 2022 prices: 1.068 × 1.039 ≈ 1.1097, so prices rose about 11.0%. You can check with the CPI: 157.1 ÷ 141.6 ≈ 1.109.
2A worker earned $20.00 per hour in 2021. What hourly wage in 2023 would give the same purchasing power?
About $22.19. 20.00 × 157.1 ÷ 141.6 ≈ 22.19. Any wage below this means the worker can buy less than in 2021.
3Use the Rule of 72 (from Grade 8) to estimate how many years it takes prices to double at 2% inflation and at 6.8% inflation. Check the first one with a calculator.
At 2%: 72 ÷ 2 = 36 years. Check: 1.02³⁶ ≈ 2.04, so it is close. At 6.8%: 72 ÷ 6.8 ≈ 10.6 years. Higher inflation makes prices double much faster, which is why the Bank of Canada works to keep it low.
Quiz
1. Which statement best describes inflation?
2. The CPI was 136.0 in 2019 and 160.9 in 2024. An item cost $10.00 in 2019. About what would it cost in 2024 if it kept up with the CPI?
3. Your pay rises 2% in a year when prices rise 5%. What happened to your purchasing power?
4. What inflation rate does the Bank of Canada aim to keep?
5. You have a variable-rate loan and the Bank of Canada raises its rate. What usually happens?
6. Prices rise 10% one year and 10% the next. What is the total increase over both years?
Big idea: expectation F1.1 asks students to identify a past or current financial situation and explain how it can inform financial decisions, using both the context and the math. This lesson uses a real recent example: high inflation in 2022 and the Bank of Canada's rate increases of 2022 and 2023. The CPI values are rounded yearly averages based on Statistics Canada data; interest-rate examples are simplified.
Common difficulties:
- Dividing the CPIs the wrong way. Ask: "Should the later price be bigger or smaller?" If prices rose, the later price must be bigger.
- Subtracting percents instead of comparing multipliers (raise vs. inflation). Show that 1.03 ÷ 1.068 gives the real change.
- Adding yearly percents. Two increases of 10% make 21%, not 20%.
How to help: Share a real memory of a price change or an interest-rate change in your household, if you are comfortable doing so. Students learn a lot from hearing how adults made decisions. You do not need to share private numbers: rounded or made-up amounts work just as well. This also builds the A2 expectation of connecting math to lived experience.