In this paper, we show that the price of a premium bond and the price of a discount bond will both move toward face value at an increasing rate as the bonds approach maturity. We present a mathematical proof to show that the decline in premium and discount decline over time, to be referred to as time decay, accelerates as time passes by. We also provide numerical examples and graphical representations to illustrate the time passage effect on bond prices and discuss the implications of the findings to bond investor and asset managers in light of the quantitative easing policies taken by central banks after the 2008 financial crisis.