Consider the following “equation of exchange” (where each variable refers to a growth rate):
The power of this equation is that it rests on a tautology, which is that the total spending across the entire economy must be equal to total receipts. That being the case, we can break down total spending into two components: the amount of money that is available to spend (M), and people’s desire to spend the money already in circulation (V). Spending rises when more money gets created, or if people choose to spend more of what they already have. Central banks therefore stimulate the economy either by Quantitative Easing (more M) or reducing interest rates (more V). This “total spending” is sometimes referred to as aggregate demand, but notice that it is equal to the combined rate of inflation (P) and real GDP growth (Y). It is through their ability to determine the amount of aggregate demand that central banks will directly affect nominal GDP (P+Y). And since one person’s expenditure is another’s income, another term for NGDP is nominal income.
For more on using this equation as a foundation for understanding macroeconomic policy objectives and performance, see here.