How do interest rate changes affect economic growth?

A cut in the base rate (rate at which the central bank lends to commercial banks) generally increases growth, and an increase in rates reduces growth. This is due to several factors:

1. Impact on consumers - a cut in I.R makes it cheaper to borrow. Houses and consumer durables (like cars) are often purchased through borrowing, so consumption increases when it becomes cheaper to borrow. Higher consumption raises growth. Note that loans to buy houses are called mortgages. A more advanced point (which you should only make if you have enough time) is that an increase in demand for housing increases house prices. This increases the wealth of home owners, so their consumption increases (known as the positive wealth effect).

2. Impact on firms - a cut in I.R makes it cheaper for firms to borrow to invest in building new factories, offices, etc. Thus investment (definition: spending on capital goods like machinery) increases and hence economic growth. 

Evaluation - lower interest rates may fail to stimulate growth when confidence in the economy is low. Consumers will not borrow to consume because they have pessimistic expectation regarding future income, employment, etc. Firms will not borrow to invest because they expect future profits to be low. This is one of the reasons why very low interest rates failed to significantly increase econmic growth following the global financial crisis of 2007/8.