We present a method of computing optimal input trajectories for parameter estimation in nonlinear dynamical systems using dynamic programming. In contrast with previously published dynamic programming formulations, we avoid adding an equation for the dispersion to the system state, allowing for more efficient solutions. This method is applicable whenever the design metric is linear in the Fisher information and is applicable to a general class of noise models. We implement this algorithm in the Julia programming language, and exploit parallelism to increase computation speed. A motivating application for this investigation is the design of dynamic acquisition sequences for magnetic resonance imaging (MRI). We also benchmark the performance of our parallel implementation on a low-dimensional population dynamics model.