We study numerical (i.e. approximate) and analytical (i.e. exact) solutions to the system of Riccati ordinary differential equations (RODE) used in estimating the class of Gaussian affine term structure models (ATSM). We base our study on accuracy and convergence time, and find that usage of the approximate solution and exact solution to the RODE yield similar accuracy. Our results are consistent with the no-arbitrage condition specified in ATSM. We also show that exact solutions, when available, lead to faster convergence times than approximate solutions.