In the existing literature of inventory modeling under the conditions of permissible delay in payments, researchers have assumed that the retailers have to settle their accounts at the end of credit period i.e. supplier accept only full amount at the end of the credit period. However in reality, supplier may either accept the partial amount at the end of the credit period and unpaid balance subsequently or the full amount at a fix point of time after the expiry of the credit period, if the retailer finances the inventory from the supplier itself. Further, in the classical deteriorating inventory models, the common unrealistic assumption is that all the items start to deteriorate as soon as they arrive in the system. However, in realistic environment, it is observed that there are several non-instantaneous deteriorating items that have a shelf life and start to deteriorate after a time lag, like dry fruits, potatoes, yams and even some fruits and vegetables etc. Considering the importance of above mentioned facts, the present study formulates a fuzzy inventory model for non-instantaneous deteriorating items under conditions of permissible delay in payments. The paper discusses all the possible cases which may arise and yet not considered in the previous inventory models under permissible delay in payments. Further, this paper also considers price-dependent demand and the possibility of higher interest earn rate than interest payable rate. The objective of this study is to determine the optimal decision policies for the retailer which maximizes the total profit. Finally, the numerical examples are solved by using the proposed algorithm to show the validity of the model followed by the sensitivity analysis.