The need to accurately estimate time and cost for effective planning of software projects is becoming crucial driven by the escalating demands of the software market. Several models proposed in the history of Software Engineering discipline to estimate time, costs associated with planning and managing software projects as Line of Code (LOC), Function Point (FP) and Constructive Cost Model (COCOMO). This paper focuses upon the COCOMO Model. It is further consisted of its two sub models called COCOMO I and COCOMO II. The primary objective of this research is to use an appropriate case study to evaluate the accuracy of the sub models COCOMO I and II and ascertain the variation of the realistic resource effort, staff and time. The findings to date show that the Application Composition Model of COCOMO II is more accurate in determining time and cost for the successful conclusion of a software project than the other two COCOMO I and II Models for a similar application for example Task Manager.