Understand how the CPI is used to measure inflation and how to calculate the inflation rate from CPI values.
The Consumer Prices Index (CPI) is a statistical measure that shows how the price of a fixed basket of goods and services changes over time. Think of it as a “price tag” on a favourite snack that keeps rising as the cost of ingredients goes up.
The CPI for a given year is calculated as:
\$\text{CPI} = \frac{\text{Cost of basket in current year}}{\text{Cost of basket in base year}} \times 100\$
• Base year is the year chosen as the reference (usually 100).
• Current year is the year you are measuring.
The inflation rate between two consecutive years is:
\$\text{Inflation Rate (\%)} = \frac{\text{CPI}{\text{current}} - \text{CPI}{\text{previous}}}{\text{CPI}_{\text{previous}}} \times 100\$
It tells you how much prices have increased (or decreased) in percentage terms.
Suppose the government uses a basket of 5 items. Prices in the base year (2015) and current year (2020) are:
| Item | Base Year (2015) Price (£) | Current Year (2020) Price (£) |
|---|---|---|
| Bread (500g) | 0.80 | 1.00 |
| Milk (1L) | 0.60 | 0.75 |
| Eggs (12) | 1.20 | 1.50 |
| Rice (1kg) | 0.70 | 0.90 |
| Cereal (500g) | 1.00 | 1.30 |
Total cost in 2015: £4.30
Total cost in 2020: £5.45
Now calculate CPI for 2020 (base year 2015 = 100):
\$\text{CPI}_{2020} = \frac{5.45}{4.30} \times 100 \approx 126.74\$
Inflation rate from 2015 to 2020:
\$\text{Inflation} = \frac{126.74 - 100}{100} \times 100 \approx 26.74\%\$
So, on average, prices rose by about 27% over those five years.
If the CPI in 2021 is 130, what is the inflation rate from 2020 (126.74) to 2021?
Answer: \$\frac{130 - 126.74}{126.74} \times 100 \approx 2.57\%\$