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In this paper Modified Heun’s algorithm of Heun’s algorithm is presented with different formulations which are applied on exponential Population growth rate problems. In Heun’s algorithm the average of two formulations is considered as A.M mean, where as in Modified Heun’s algorithm G.M and Modified Heun’s algorithm H.M are also considered as averages which are also applied on exponential population growth rate problems respectively. Comparison between numerical results of both Modified Heun’s algorithm and existing Heun’s algorithm shows that Modified Heun’s algorithm of Heun’s algorithm is more convergent then Heun’s algorithm. Both algorithms will be analyzed by different errors for the convergent purpose.