The latest inflation figures released by the Australian Bureau of Statistics look, at first glance, like good news. The headline rate for May rose 4.0% over the past year, down from 4.2% in April.

After a long run of high inflation numbers and interest rate hikes, mortgage holders could be forgiven for hoping rate relief is on the way.

But don’t hold your breath. Look under the bonnet and the picture is far less comforting. The fall was largely driven by one thing — petrol — and the part of inflation the Reserve Bank of Australia (RBA) actually cares about hasn’t budged.

Why inflation matters

Inflation is measured by the consumer price index (CPI), which tracks the price of a typical basket of things Australian households buy.

The RBA has one main job here: keep inflation low and steady at around 2.5% on an annual basis. Its main tool is the cash rate, the official interest rate that flows through to your mortgage and your savings account. When inflation runs hot, the bank lifts that rate to cool spending down.

Fuel is the great troublemaker in these figures. Back in March, petrol prices jumped almost 33% in a single month after the Iran war squeezed global oil supplies.

Since then, two things have pushed oil prices down sharply:........

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