In the recent past, there has been a tremendous growth of the solution of differential equations using algorithmic methods. This work deploys Newton’s interpolation polynomial method (NIPM) and Lagrange interpolation polynomial method (LIPM) to create cubic polynomials for solving initial value problems of the first order. The results obtained show greater accuracy for the investigated method when compared with some known methods in literature. Illustrative examples are presented to demonstrate the validity and applicability of the technique.