1. Interest rate movements over time are assumed to change a maximum of 0.5 percent per year. Both an increase of 0.5 percent and a decrease of 0.5 percent in interest rates are equally probable. If interest rates fall 1.0 percent below the current mortgage coupon rates, all of the mortgages in the pool will be completely prepaid. Diagram the interest rate tree and indicate the probabilities of each node in the tree.