Monthly term structures are fit to US Treasury inflation-indexed securities using a QN (Quadratic-Natural) spline, developed in this paper, and also to conventional nominal securities of comparable maturities. The ratio of the real to nominal discount functions is an implicit forward CPI function. The difference between the nominal and real forward interest rate curves is an implicit marginal inflation premium. It is demonstrated that under consumption risk-neutrality per Stanley Fischer (1975), this inflation premium does not equal expected future inflation per Irving Fisher (1896,1930), but rather incorporates a weighted average of expectations about the future course of inflation, that tends to give greater weight to low inflation scenarios than to high. The method is applied to 29 dates since the introduction of the 30-year indexed bond in April 1998. Nominal interest rate volatility is 2-2.5 times greater (in terms of standard deviation) than real interest rate volatility, nominal rate shocks are highly correlated with shocks to the inflation premium,
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