Why does a lower interest rate increase aggregate demand?

A lower interest rate reduces the return on saving, and as such reduces the opportunity cost of spending - for the only alternative to spending is saving. This increases the incentive for consumers and institutions to consume/invest. Aggregate demand consists of the following elements: government spending, investment, consumption and net exports. Institutional spending (investment) and consumer spending (consumption) increase due to the added incentive to spend, thus increasing aggregate demand ceteris paribus.