This paper investigates whether the occurrences of business cycles have caused the fluctuations of real interest rates in the US. Based on a standard consumption-based asset pricing model, the model incorporates a new feature that investors have to learn about the unobservable alternations between expansions and recessions. The model captures the qualitative property that real interest rates increase with expected future consumption growth. The simulation technique of the Gibbs Sampling is used to estimate and calibrate the model. It is discovered that the conditional variances of consumption growth are too small to be modeled as a time-vary volatility process. This finding casts doubt on Weitzman (2007). Furthermore, the model largely duplicates the dynamics of real interest rates prior to Year 1980. However, it fails to yield the drastic increase in the real interest rates during the 1981-1982 Recession, which was mainly caused by the quick tightening of monetary policy by the Federal Reserve. It is concluded that the consumption-based asset pricing models without a monetary perspective are difficult to fully capture the dynamics of real interest rates in the US data.