Numerical Methods: Euler to Runge–Kutta · Challenge problem

For the test equation $y' = \lambda y$, one RK4 step multiplies $y_n$ by $R(z) = 1 + z + \dfrac{z^2}{2} + \dfrac{z^3}{6} + \dfrac{z^4}{24}$, where $z = \lambda h$. For $\lambda = -20$, find the largest step size $h$ with $|R(z)| \le 1$. Round to the nearest thousandth.