Interest rate delta of annuities The interest rate delta of a derivative contract is defined as the partial derivative, 
its value, and measures sensitivity of the price to interest rate movements. Assume again that Z (0, j) = 
(a) Using your results from Questions 4 and 5, calculate the interest rate delta of
(i) a spot-starting annual libor stream (α = 1) until time T = n.
(ii) a spot-starting fixed rate annuity paying c each year until time T = n.
(b) Show that the deltas are equal in magnitude (but opposite in sign) when
(This formula is sometimes referred to as the Third Wrangler result.) Verify that when r = c = 0.06, the delta of the floating rate annuity is equal in magnitude (but opposite in sign) to that of the fixed rate annuity when n = 20.734 years.
(c) Calculate the interest rate delta of (i) an infinite libor stream and (ii) an infinite fixed annuity. Explain your answers.