This study aims to compute the aggregate claim amount distribution in one of the comprehensive motor insurance companies. One major issue that actuaries face is computing the distribution of aggregate losses, where computing the aggregate claim amount distribution requires a discrete arithmetic claim amount distribution, in some numerical techniques. This paper concerning with the discretization of continuous claims amount distribution by applying four discretization methods. Then calculate the aggregate claim amount distribution by Panjer recursive technique. Also, this paper presents how to achieve this by actuar which is a software package that provides statistical science functionality to the R statistical system. This package provides also functions to discretize & compute the continuous distributions of the overall loss distribution using a variety of techniques, including methods as recursive and simulation. Results indicate the increasing importance of comprehensive motor insurance recently according to the annual statistics book of insurance last issues. Also presents that for the four discretization methods, both unbiased and rounding seem identical.