We present a novel approach for computing biomolecular interaction binding affinities based on a simple path integral solution of the Fokker-Planck equation. Computing the free energy of protein-ligand interactions can expedite structure-based drug design. Traditionally, the problem is seen through the lens of statistical thermodynamics. The computations can become, however, prohibitively long for the change in the free energy upon binding to be determined accurately. In this work, we present a different approach based on a stochastic kinetic formalism. Inspired by Feynman's path integral formulation, we extend the theory to classical interacting systems. The ligand is modeled as a Brownian particle subjected to the effective nonbonding interaction potential of the receptor. This allows the calculation of the relative binding affinities of interacting biomolecules in water to be computed as a function of the ligand's diffusivity and the curvature of the potential surface in the vicinity of the binding minimum. The calculation is thus exceedingly rapid. In test cases, the correlation coefficient between actual and computed free energies is >0.93 for accurate data sets.