equation predicts a close connection between inflation and the rate of return on T-bills. This is apparent in Figure 5.2, which plots both time series on the same set of axes. Both series tend to move together, which is consistent with our previous statement that ex- pected inflation is a significant force determining the nominal rate of interest. For a holding period of 30 days, the difference between actual and expected inflation is not large. The 30-day bill rate will adjust rapidly to changes in expected inflation induced by observed changes in actual inflation. It is not surprising that we see nominal rates on bills move roughly in tandem with inflation over time.     Taxes and the Real Rate of Interest   Tax liabilities are based on nominal income and the tax rate determined by the investors tax bracket. Congress recognized the resultant "bracket creep" (when nominal income grows due to inflation and pushes taxpayers into higher brackets) and mandated index- linked tax brackets in the Tax Reform Act of 1986. Index-linked tax brackets do not provide relief from the effect of inflation on the taxa- tion of savings, however. Given a tax rate (t) and a nominal interest rate (R), the after-tax I. Introduction 5. History of Interest Rates and Risk Premiums The McGraw−Hill Companies, 2001           136 PART I Introduction     interest rate is R(1 t). The real after-tax rate is approximately the after-tax nominal rate minus the inflation rate:   R(1 t) i (r i)(1 t) - i r(1 t) it   Thus the after-tax real rate of return falls as the inflation rate rises. Investors suffer an inflation penalty equal to the tax rate times the inflation rate. If, for example, you are in a 30% tax bracket and your investments yield 12%, while inflation runs at the rate of 8%, then your before-tax real rate is 4%, and you should, in an inflation-protected tax system, net after taxes a real return of 4%(1 .3) 2.8%. But the tax code does not recognize that the first 8% of your return is no more than compensation for inflation-not real income- and hence your after-tax return is reduced by 8% .3 2.4%, so that your after-tax real interest rate, at .4%, is