Let rt is the spot rate for a t-year maturity zero coupon bond. (i) Find an expression for f k-1,k] in terms of the rt's. (ii) Show that (1 + fo,1]) (1 + f[1,2]) . . . (1 + f [k-1,k]) = (1 + rk)k for k = 1, 2, ..., n. (iii ) Show that dr k d f k - 1, k] > 0 and d drk-1 f [k - 1, k] TK-1, then fjk - 1, k) >rk