In countries using a centralized banking model, interest rates are determined by the relevant Central Bank.
In order to determine interest rates, economic analysts of the government to create a policy that helps ensure stable prices and liquidity. This policy is regularly checked so that the money supply in the economy is neither too large (as a result of increase in prices) nor too small (which prices are reduced). In the US, interest rates are determined by the Federal Open market Committee, consisting of seven governors and five Federal reserve Bank presidents. The fed meets eight times a year to determine short-term direction of monetary policy and interest rates.
For more information about the functions of the Federal reserve system, see our tutorial on the fed.
Retail banks, as a rule, primarily financial institutions, to expose money into the economy, and therefore they are the main tools used by the Central Bank to manipulate the money supply. Simply put, the Central Bank can regulate money supply to the final consumer (individuals and legal entities) by adjusting the interest rates on the money it lends or borrows from the retail banks.
If manufacturers of monetary policy want to reduce the money supply, this will lead to an increase in interest rates, making it more attractive to Deposit funds and reduce borrowing from the Central Bank. Conversely, if the Central Bank wants to increase money supply they will lower the interest rate, which makes it more attractive to borrow and spend money.
For further reading on interest rates, see interest rates and investing in bonds , the forces behind interest rates and how interest rates affect the stock market.