Private Information Retrieval (PIR) protocols enables fetching an arbitrary data from a server without revealing any information to the server about the data. In this paper, we construct three computational PIR (cPIR) protocols which we call P-cPIR and Recursive P-cPIR version I and II. We construct our cPIR protocols on a well known Fully Homomorphic Encryption scheme (FHE), BFVrns. For n = 220, 240, P-cPIR and Recursive P-cPIR version I provide at least ~214 × computational improvement over other prominent cPIR protocols. Recursive P-cPIR version II proposes the same query and half response cost as OnionPIR (lower communication cost in total) and less than other protocols such as SealPIR, SHECS-PIR, XPIR. It also proposes at least ~23 × less computational cost than other proposed protocols by stating the best performance in these protocols for both cases. We also provide a parameter selection method for the proposed cPIR protocols that takes the burden of parameter selection from the users and makes it more usable for real-life applications.