Consider a short rate binomial lattice where the risk-free rate at \(t=0\) is \(10 \%\). At \(t=1\) the rate is either \(10 \%\) (for the upper node) or \(0 \%\) (for the lower node). Trace out the growth of \(\$ 1\) invested risk free at \(t=0\) and rolled over at \(t=1\) for one more period. The values obtained at \(t=1\) and \(t=2\) correspond to \(R_{01}\) and \(R_{02}\). Show that these factors cannot be represented on a binomial lattice, but rather a full tree is required. Draw the tree.