How can a fall in interest rates affect the Aggregate Demand of an economy

AD=C+I+G+(X-M) Interest rates (i) determine the return of saving money in a bank and the cost of borrowing money from a bank. Therefore, a fall in i means that the cost of borrowing falls and the return on savings fall, therefore reducing the opportunity cost of not saving money in the bank. Therefore this makes it less worthwhile to save money and more attractive for consumers to borrow money for spending and for investors to borrow money to fund investment. Therefore a fall in i leads to an increase in C and I, boosting AD. Changes in i can also affect the strength of the currency and hence the trade balance. As lower i reduce the incentive to save money in the bank, this means that fewer people, whether they are domestic or abroad, will want to save money at UK banks. Therefore as the return on savings fall in UK banks, people who have money saved there will exchange this money into a currency which belongs to a country where there is a higher i, as there they will receive a greater return on their savings. For example, if the i is 0.25% in the UK and 1.25% in the US, then someone who has £s saved in the UK bank may decide to exchange these to $s in order to save the money in a bank in the US, leading to a greater return. Therefore there will be hot money flows out of the UK, as the demand for £s falls, therefore weakening the £. This means that following a depreciation in the £, the demand for UK exports will increase as they are cheaper and more competitive, causing X to increase. Whereas, M into the UK will become more expensive, and therefore less attractive to domestic consumers, causing M to decrease. Therefore, this increases the net balance in trade (X-M), boosting AD. The overall impact of a fall in i will be an increase in AD.