Although interest rates may appear to be straightforward, they may be quoted and calculated in a number of different ways. This is why regulators have required the use of some standards, such as AER, and financial markets have evolved others (such as YTM).
The risk-free rate is important to investors as it is used for valuation.
It is often useful for investors to think in terms of real rather than nominal interest rates.
Some investments pay floating interest rates rather than fixed interest.
Central bank rates
In a public policy context, interest rates usually refers to the rates at which the central bank will buy and sell (often through repos) government bonds (gilts) in its open market operations.
If the central bank is independent, these rates will be set by the central bank. In the UK the Monetary Policy Committee of the Bank of England sets the repo rate for open market operations at a level that is in line with a target range for inflation set by the Chancellor of the Exchequer.
In the US the rate is set by the Federal Open Markets Committee, and in the euro zone by the European Central Bank.