Who Determines Interest Rates?

Most nations have central banks; interest rates are determined by the central banks.

Central Bank Monetary Policy
The proper economic policies have to be pursued by government to set the stage for stable prices and liquidity for the country. The central bank, in this case the Federal Reserve ensures it helps the government maintaining a proper balance of the supply of money within the economy, so that is neither too large (leading to price to increases) nor too small (leading to price decreases).

The Fed controls the money supply through its principal instruments, the retail banks. These financial institutions are at the forefront of exposing money to the general public. The fed can manipulate the money supply by regulating the interest rates on the money it loans to or borrows from retail banks; herein, the Fed is able to regulate the supply of money in the economy.

Manipulating Interest Rates
If the Fed chose to increase interest rates, the central bank will decrease the money supply. This would lead retail banks to reduce their borrowing of funds from the central bank and the higher interest rates will cause deposits at to increase. Conversely, if the Fed chose to decrease interest rates, the central bank will increase the money supply. The would lead to retail banks to increase borrowing of funds from the central bank and the lower interest rate will cause deposits to decline.