Why do interest rates vary ?

This is from Business studies teaching and education resources: Biz/ed (http://www.bized.co.uk:)

The interest rate will be set by the equilibrium in the money market. As in other markets, this equilibrium depends on the levels of demand and supply. In the money market, the demand comes from people wanting to borrow and spend, while the supply of money depends on the government's monetary policy.

If either the demand or supply of money changes, then this will tend to change the equilibrium interest rate in the markets, and the government may need to act to maintain the level of interest rates.

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With respect to different borrowers at a fixed moment in time, or across time with respect to any single borrower, or across different maturities (aka the 'yield curve')?

Any one in particular you had in mind?