Prices rise over time
Inflation is the general increase in prices. As prices rise, each dollar buys less: its purchasing power falls.
A chocolate bar that cost $0.50 decades ago might cost $2 or more today.
Measuring inflation: the CPI
Statistics Canada tracks the Consumer Price Index (CPI): the cost of a fixed "basket" of goods and services (food, shelter, transportation, clothing …) compared with a base year.
Inflation rate = (CPI this year − CPI last year) ÷ CPI last year × 100
Example: CPI rises from 150 to 154.5.
(154.5 − 150)/150 = 3%
The Bank of Canada aims to keep inflation around 2% per year.
Inflation compounds
Prices grow like compound interest:
Future price = current price × (1 + r)ᵗ
Example: A $100 grocery bill with 2.5% annual inflation for 20 years:
100 × 1.025²⁰ ≈ $163.86
Purchasing power falls
What will $1 buy in 10 years at 3% inflation?
1/(1.03)¹⁰ ≈ $0.74 in today’s dollars
Money hidden under a mattress loses about a quarter of its value in 10 years at 3% inflation.
Real interest rate
If your savings earn 4% while inflation is 3%, your real gain is only about 1%.
Real interest rate ≈ nominal rate − inflation rate
A more exact formula: (1 + nominal)/(1 + inflation) − 1
Example: 6% nominal, 3% inflation → 1.06/1.03 − 1 ≈ 2.9%
If inflation is higher than your interest rate, your savings lose purchasing power.
Wages and inflation
A 2% raise when inflation is 4% means your real income fell by about 2%.
Deflation
Deflation is a general fall in prices. It sounds good but can hurt economies: people delay spending, businesses cut jobs.
Adjusting old prices
To compare prices across years, use the CPI ratio:
Price today = old price × (CPI now ÷ CPI then)
Example: A $20,000 car when the CPI was 100; now the CPI is 160. Equivalent today: 20,000 × 1.6 = $32,000.
Worked examples
Example 1: CPI goes from 140 to 147. Inflation rate? 5%.
Example 2: $50 now, 2% inflation for 5 years? 50 × 1.02⁵ ≈ $55.20.
Example 3: Savings earn 1.5%; inflation is 3%. Real rate? About −1.5% (losing purchasing power).
Common mistakes
- Adding inflation each year instead of compounding it.
- Ignoring inflation when judging returns or raises.
- Confusing the inflation rate with prices themselves.
Try it yourself
- CPI rises from 120 to 123. Inflation rate?
- $1,000 rent rising 3% a year. Rent in 5 years?
- Nominal rate 5%, inflation 2%. Approximate real rate?
- A $4 item at a CPI of 80. Equivalent cost at a CPI of 140?
Answers: 1) 2.5% 2) ≈ $1,159.27 3) about 3% 4) $7
Quick recap
- Inflation raises prices and lowers purchasing power.
- The Consumer Price Index measures it; inflation compounds.
- The real interest rate ≈ nominal rate − inflation rate.