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Abstract This paper examined and compared the Islamic banks’ time series rates of return to depositors, 1-month, 3-month, 6-month, 9-month, and 12-month as well as the rate of return on Islamic Bank's Mudharabah saving and with the conventional banks’ similar time series deposit interest rates during 2001-2015. Non-cointegration of monthly and quarterly series of deposit interest rates, established by Johansen Cointegration test, led to the VAR Granger causality test which showed unidirectional causality running from the conventional banks’ deposit interest rates to the Islamic banks’ rate of returns. The establishment of cointegration for the conventional bank and the Islamic bank series of 6-month, 9-month, and 12-month as well as saving deposit rates series by Johansen Cointegration test led to the VEC model which establishes the short term dynamics and the stability of long run equilibrium between the rates of return of Islamic banks and interest rates of the conventional banks. The Vector Error correction results showed the speed of convergence varied from 18 percent to 24 percent. The results of the VEC Granger causality /Wald test (F-test) found unidirectional causality i.e. the direction causality running from conventional banks’ interest rate to the Islamic bank’s rate of return in all series, 6-month, 9-month, 12-month, and the saving deposit.

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