This paper investigates the long run relationship between the interest rates of Bangladesh and the United Sates (US). Using time series quarterly data for the period 1972- 2019, the study finds that the nominal rate of the US positively influences the nominal rate of Bangladesh and they do maintain a long run relationship. Similar result is obtained by examining the real rates of both countries. However, in the latter case the study period covers from the third quarter of 1993 to the third quarter of 2019. Estimation of the error correction model signifies that in both cases policy rate of Bangladesh significantly responds to the error, which is the measure of deviation from long run equilibrium. Although interest rates of Bangladesh respond to the error in both cases, the speed of adjustment is much higher in case of the real rates. Empirical findings reveal that around 6% error is corrected in every quarter if it is nominal rate whereas in the event of real rate the rate of error correction is almost 77%. These findings indicate that small economy Bangladesh plans its policy rate taking account of the dynamics of the large economy the US, and such policy dependence is more apparent for real rate of interest.