This is the highest the cash rate has been since December 2011 to April 2012 where it was 4.25%.
RBA Governor Dr Philip Lowe said inflation has peaked but is still too high.
However, he said the RBA's path to its inflation target while maintaining full employment is a narrow one.
"A significant source of uncertainty continues to be the outlook for household consumption. The combination of higher interest rates and cost-of-living pressures is leading to a substantial slowing in household spending," Dr Lowe said.
"Housing prices are rising again and some households have substantial savings buffers, although others are experiencing a painful squeeze on their finances. There are also uncertainties regarding the global economy, which is expected to grow at a below-average rate over the next couple of years."
Could be 4.80% and for an extended period
An 11 May Freedom of Information request to the RBA revealed that internal economic modelling from March showed the cash rate would need to be 4.80% to see the central bank's underlying inflation target reached by 2025.
The modelling used the Taylor Rule, a formula to determine the correct cash rate for economic stability, as well as a NAIRU unemployment rate of 4.5%.
NAIRU stands for Non-Accelerating Inflation Rate of Unemployment, and at 4.5% implies the current rate of 3.7% is too inflationary.
A cash rate of 4.80% implies three more hikes to 4.85% after June's monetary policy increase.
However the notes also said this is about a percentage point higher than the 'neutral' rate, placing the rate slightly in a zone of economic contraction.
A 'steady climb' would see the cash rate peak at 4.80% in August 2023 and remain there until the end of the year at least.
It did not anticipate an RBA cash rate pause in April, suggesting a disconnect between bank economists and the monetary policy board.
Internal emails also suggest the RBA is looking firmly at central banks from similar economies in the Bank of Canada and the Reserve Bank of New Zealand, with modelled scenarios based on these central banks' movements.
The Bank of Canada's rate is currently 4.50%, while New Zealand's is 5.25%.
Calls for a more aggressive stance to avoid cynicism among public
Peter Tulip, an ex-RBA economist and now chief economist at the Centre for Independent studies, said the RBA should have increased the rate by 50 basis points in June.
This would minimise risk of de-anchoring public expectations of cash rate rises, unemployment rates rising, and accelerating inflation.
"The RBA's preferred path seems to reflect to aversion to action; it would prefer to make errors of omission than errors of commission because it gets publicly blamed for the latter," Mr Tulip wrote on Twitter.