> Simplified: the central bank decide on an interest rate that they want to see.

This is incorrect.

Using the US central bank example, the Fed has a target for inflation. It uses interest rates to try and hit that target. If inflation is higher than 3% the Fed will raise rates to cool the economy.

The Fed sets interest rates directly because lending money to the Fed is viewed as "risk-free" (as the US government has never defaulted on a debt). So if the Fed offers a risk-free 4%, banks will need to offer more because they are not risk-free. So banks no longer really lend savings out for loans. They borrow money and lend it out at a higher rate (eg mortgage-backed securities).

So when you could get a mortgage at 2.5%, it was because the Fed was offering 0%. When the Fed offers 5%, mortgage rates will go up to 7-8%.

There is another mechanism that the government could use to control inflation: fiscal policy, specifically taxation. A criticism of monetary policy to control inflation is that it's indiscriminate. People will go out of business and lose their houses. Taxes only target profits.

So in 2021-2022, we should've just passed a windfall profits tax of 80%. That would've cooled off inflation real quick and given the governments funds to distribute to those most adversely affected. But that will never happen because the corporations and wealthy who own both parties will never stand for wealth redistribution to the poor.

They will however demand wealth be transferred from the government to the rich.