An inflation rate is the percentage change in a price index between two periods. The index itself only shows the price level compared with a base year.
This lesson belongs to economic indicators. The next lesson, comparing nominal and real changes, uses the same index to adjust incomes.
What is the difference between the index and the rate?
The index answers “how high are prices now compared with the base year?”. The base year is set at 100, so an index of 110 means prices are 10% higher than in the base year.
The rate answers “how fast did prices rise over the period?”. It needs two index values and always divides by the earlier one.
Worked example: a fictional price index
A fictional country publishes a consumer price index with Year 1 as the base year.
| Year | Price index | Annual inflation rate | Change since Year 1 |
|---|---|---|---|
| Year 1 | 100 | not given | 0% |
| Year 2 | 105 | 5% | 5% |
| Year 3 | 113.4 | 8% | 13.4% |
Year 2 rate. (105 − 100) ÷ 100 × 100 = 5%.
Year 3 rate. (113.4 − 105) ÷ 105 × 100 = 8.4 ÷ 105 × 100 = 8%. The earlier year is Year 2, so Year 2’s index of 105 is the divisor.
Change since Year 1. (113.4 − 100) ÷ 100 × 100 = 13.4%. This is the total rise over two years, not the rate for Year 3.
What does it mean for a household?
Suppose a basket of goods cost RM200 in Year 1. In Year 3 the same basket costs 200 × 113.4 ÷ 100 = RM226.80. The household needs RM26.80 more to buy the same goods.
If the household’s income did not change, its purchasing power fell. The money is the same, but it buys less.
The mistake that costs marks
The usual slip is to read the Year 3 index of 113.4 and write “inflation was 13.4%”. The figure is correct as the change since the base year, yet the question asked for the annual rate.
| Step | Wrong | Right |
|---|---|---|
| Earlier value used | 100 (base year) | 105 (Year 2) |
| Working | (113.4 − 100) ÷ 100 | (113.4 − 105) ÷ 105 |
| Answer | 13.4% | 8% |
Before calculating, underline the two years in the question and write which one is earlier. That tells you the divisor.
Check yourself
The fictional index is 100 in Year 1, 110 in Year 2 and 115.5 in Year 3. Find (a) the inflation rate in Year 2, (b) the inflation rate in Year 3, (c) the change since Year 1 at Year 3 and (d) the Year 3 cost of a basket that cost RM200 in Year 1.
Answer
(a) (110 − 100) ÷ 100 × 100 = 10%.
(b) (115.5 − 110) ÷ 110 × 100 = 5.5 ÷ 110 × 100 = 5%.
(c) (115.5 − 100) ÷ 100 × 100 = 15.5%.
(d) 200 × 115.5 ÷ 100 = RM231.
Notice that the rate fell from 10% to 5%, yet the index still rose. Prices were still increasing, only more slowly.
What to study next
Go on to comparing nominal and real changes, or widen your reading with distinguishing unemployment concepts. The graph evidence and fair-comparison lab helps you compare figures on the same basis.
For a teacher to check your base choice on live questions, see online one-to-one Economics tuition.