on a one-year CD is 8%, and you expect inflation to be 5% over the coming year, then using the approximation formula, you expect the real rate to be r 8% - 5% 3%. Using the exact formula, the real rate is r .08 .05 .0286, or 1 .05 2.86%. Therefore, the approximation rule overstates the expected real rate by only .14% (14 basis points). The approximation rule is more exact for small inflation rates and is per- fectly exact for continuously compounded rates. We discuss further details in the appendix to this chapter. Before the decision to invest, you should realize that conventional certificates of deposit offer a guaranteed nominal rate of interest. Thus you can only infer the expected real rate on these investments by subtracting your expectation of the rate of inflation. It is always possible to calculate the real rate after the fact. The inflation rate is pub- lished by the Bureau of Labor Statistics (BLS). The future real rate, however, is unknown, and one has to rely on expectations. In other words, because future inflation is risky, the real rate of return is risky even when the nominal rate is risk-free.     The Equilibrium Real Rate of Interest   Three basic factors-supply, demand, and government actions-determine the real inter- est rate. The nominal interest rate, which is the rate we actually observe, is the real rate plus the expected rate of inflation. So a fourth factor affecting the interest rate is the expected rate of inflation. Although there are many different interest rates economywide (as many as there are types of securities), economists frequently talk as if there were a single representative rate. We can use this abstraction to gain some insights into determining the real rate of interest if we consider the supply and demand curves for funds. Figure 5.1 shows a downward-sloping demand curve and an upward-sloping supply curve. On the horizontal axis, we measure the quantity of funds, and on the vertical axis, we measure the real rate of interest. The supply curve slopes up from left to right because the higher the real interest rate, the greater the supply of household savings. The assumption is that at higher real interest rates households will choose to postpone some current consumption and set aside or invest more of their disposable income for future use.1 The demand curve slopes down from left to right because the lower the real interest rate, the more businesses will want to invest in physical capital. Assuming that businesses rank projects by the expected real return on invested capital, firms will undertake more projects the lower the real interest rate on the funds needed to finance those projects. Equilibrium is at the point of intersection of the supply and demand curves, point E in Figure 5.1.