Let rt is the spot rate for a t-year maturity zero coupon bond. (i) Find an...

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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 + f[0,1]) (1 + f[1,2]) for k = 1, 2, ..., n. . (1 + f[k-1,k]) = (1+rk)* (iii) Show that d drk f[k − 1, k] > 0 and d drk-1 (iv) Show that i frk>rk-1, then f[k - 1, k] >r k• -ƒ[k − 1, k] < 0. 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 + f[0,1]) (1 + f[1,2]) for k = 1, 2, ..., n. . (1 + f[k-1,k]) = (1+rk)* (iii) Show that d drk f[k − 1, k] > 0 and d drk-1 (iv) Show that i frk>rk-1, then f[k - 1, k] >r k• -ƒ[k − 1, k] < 0.