Aggregate Demand is equal to Consumption + Investment + Government Spending + (Exports - Imports).
When interest rates fall, saving becomes less profitable, as consumers will receive a smaller additional payment for depositing money into savings account. Borrowing on the other hand becomes cheaper, as the amount consumers have to pay back decreases. Higher levels of borrowing will evidently lead to more consumption of goods and services by consumers, as well as increased investment by firms of research and development for example. Both of these variables are part of the aggregate demand formula, hence AD would increase.Furthermore, this investment by firms back into their products would allow them to reach greater levels of productive efficiency, lower their costs of production and allowing them to profit maximise at a lower price level. This would make local products more price competitive compared to imports, hence the net trade component of the AD equation (X-M) would increase, also increasing aggregate demand.
We could then demonstrate this diagrammatically with a rightward shift in aggregate demand, leading to a higher level of real GDP obtained.