1. 20 points, 10 points each part. Recall that we may relate the spot rates {r(t)} and the forward rates {f(t)} to the discount factors {d(t)} by the "simple, recursive" formulas 1+2r(t)=d(t)1;1+2f(t)=d(t)d(t.5). In this exercise we will do something similar for the par rates {c(t)}. Below we always assume 0c(t.5) if and only if f(t)c(t.5). Thus, the par curve will be increasing between t.5 and t if and only if the rate (agreed to today) for a loan starting at t.5 and maturing at t exceeds the par rate at t.5. In other words, if we determine today that the par rate at t.5 is "too low" for a six month forward loan made at t.5