Inflation

Video coming soon3 worked examples

Theory

Inflation is a general rise in prices over time, which is measured as a percentage. Here in the UK, the Bank of England is responsible for keeping inflation low and stable, with a government target of 2%.

1. The Purchasing Power of Money

Inflation results in a decrease in the "purchasing power" of money over time.

This means that as prices rise, fewer goods or services can be bought for the exact same amount of money than in previous years.

2. Measuring Inflation (The CPI & RPI)

Inflation is measured based on the change in value of an inflation index, most commonly the Consumer Price Index (CPI) or the Retail Price Index (RPI).

To calculate this index, the government tracks the prices of a "basket" containing around 300 commonly purchased goods and services.
To ensure the index is accurate, items are added and removed from the basket each year to keep up with current consumer trends. For example, recent additions have included meat-free sausages and anti-bac wipes, while items like coal and reference books have been removed.

3. Base Years and Calculating Rates

To track the index over time, a specific year is chosen as the "base year" and its index value is set to exactly 100. For example, the current base year for the CPI is 2005.
The rate of inflation is simply the percentage change in the price index from one year to another.

Exam Strategy:

You can treat annual inflation rates exactly like successive interest rates. If you have different inflation rates over several years, you can use a chain of multipliers to find the overall percentage change.

Worked examples

Example 1

Example 1: Calculating the Rate of Inflation

The UK Consumer Price Index (CPI) was recorded at 108.6 in August 2019. By August 2023, the CPI had risen to 132.5.

Calculate the rate of inflation between these two time periods, giving your answer as a percentage to one decimal place.

To find the rate of inflation, we calculate the percentage change between the two index values.

Find the difference: $132.5 - 108.6 = 23.9$ .
Divide by the original value and multiply by 100:
$(23.9 \div 108.6) \times 100 = 22.007...\%$
Round to 1 decimal place: 22.0%.

Example 2

Example 2: Purchasing Power and Reversing Inflation

In April 2015, the CPI was set to a baseline of 100. By April 2022, the CPI had increased to 119.0. A family paid £14,875 for a new kitchen installation in April 2022.

Assuming the cost of the kitchen installation rose exactly in line with the CPI, calculate how much the exact same kitchen would have cost in April 2015.

The 2022 index of 119.0 means prices were 119% of their 2015 value. We must work backwards to find the original 100% value.

Find the multiplier: 119% → 1.19.
Divide to reverse the inflation:
$2015 \text{ Price} = \text{\pounds}14,875 \div 1.19 = \text{\pounds}12,500$ .

Example 3

Example 3: Successive Inflation Rates (Chain Multipliers)

The average price of domestic electricity changed at the following annual effective rates:

2021 to 2022: 5.4% increase
2022 to 2023: 12.1% increase
2023 to 2024: 3.5% decrease

(a) Calculate the overall percentage change in the price of electricity between 2021 and 2024.

(b) The average annual electricity bill for a household in 2024 was £1,350. Calculate the average bill for a household in 2021.

Solution (a):

Overall Percentage Change:

Find the multipliers: 1.054, 1.121, and 0.965.
Multiply them together:
$1.054 \times 1.121 \times 0.965 = 1.14018...$
Convert back to a percentage:
$(1.14018... - 1) \times 100 = 14.02\%$ (an overall increase).

Solution (b):

Working Backwards: Because we know the 2024 price and the overall multiplier connecting the two years, we can divide to find the 2021 price.

2021 \text{ Bill} = \text{\pounds}1350 \div 1.14018... = \text{\pounds}1,184.02

Ready to practise?

5 Inflation questions with answers and video solutions