Since the mid 1980sTaniania has been party to the macroeconomic reforms which aim at addressing socio-economic problems which have faced the country for some decades now. The key measures, which have been undertaken, include liberalizing the financial sector as well as the public sector. Among the macroeconomic achievements is the single digit inflation rate which has been achieved since mid 1990s and so far has been maintained. The study is important and may have a notable value-added in the existing literature as it attempts to dwell on the implications of low inflation rate on interest rate in Tanzania basing on different maturities of monetary instruments and using an econometric approach. Many previous studies enquired on the link between interest rate and inflation. However, this study attempts to investigate how low inflation rate can affect treasury bills interest rate. The main findings indicate that Tanzania with a low and declining inflation rate, real interest rate becomes relatively high culminating into a disequilibrium in the savings-investment markets which largely underpins the excess liquidity stance in lending institutions. This implies that it is high time that competition was enhanced in financial markets. Significantly, an attempt can be pursued to avert the disequilibrium if interest rates are made flexible as well as reducing the risk of doing business and in addition increasing the competition in the financial markets in the country. The paper is organized into six sections. Section one provides the introduction, followed by literature review in section two. Specification of the model used and regression are done in section three whereas analysis of the low bound comes in section five. Finally, conclusion comes in section six