Explain how a decrease in interest rates affects real GDP and inflation. When may a decrease in the interest rate not affect real GDP?

When interest rates decrease, this decreases the cost of borrowing and reduces the reward for saving. As a result, there is a higher incentive for firms and individuals to borrow/spend and a lower incentive for them to save. This increases investment (I) and consumption (C). Since Aggregate Demand (AD) = Consumption (C) + Investment (I) + Government Spending (G) + Exports (X) - Imports (M), an increase in C and I shifts the AD curve up from AD1 to AD2. At this new equilibrium point, real GDP has increased from Y1 to Y2 and the price level has increased from PL1 to PL2. Therefore, a decrease in interest rates causes a rise in real GDP and inflation.
When the interest rate is already low (e.g. 0.5%), a decrease in the interest rate (e.g. to 0.25%) may not have the same affect on real GDP. This is because a small decrease in the interest rate may not decrease the cost of borrowing and reduce the reward for saving enough to stimulate an increase in C and I. As a result, the AD curve will not shift upwards and real GDP will not increase.