In this paper, we characterize an infinite-horizon mean field game of growth and capital accumulation. We present a Markov chain approximation scheme (Kushner, Numerical methods for non-zero-sum stochastic differential games: convergence of the Markov chain approximation method. In: Chow PL, Yin G, Mordukhovich B (eds) Topics in stochastic analysis and nonparametric estimation. The IMA volumes in mathematics and its applications, vol 145. Springer, New York, 2008, pp 51–84) as potentially useful for obtain the numerical (Formula Presented)-Nash equilibrium solution to the infinite-horizon mean field system of equations and highlight some of the key challenges in implementing the scheme.