An Arbitrarily Precise Global Closed Form Approximation for the Neoclassical Growth Model

I consider a neoclassical growth model with a constant absolute risk aversion (CARA) utility function and derive a global closed form approximation that is arbitrarily precise as the discount rate $ρ$ is close to the population growth rate $n$. I use it to show that the consumption function is strictly concave and that countries can have two different paths converging to the steady-state: front-loading and back-loading.