Interest Rate Risk: Consider a 10-year zero coupon bond. A. Using the bond pricing equation, P(y), illustrate the derivation (using calculus) of this bonds modified duration. Note: the correct answer is an equation, not a number. B. Assuming the yield-to-maturity is 7%, compute the bonds modified duration. C. Use your answer to part B to estimate the price of the bond and the percentage price change if interest rates instantaneously rise to 8%. D. Use your answer to part B to estimate the price of the bond and the percentage price change if interest rates instantaneously decline to 6%. E. How do the estimates from C. and D. compare to the true prices using the bond pricing equation P(y) if yields change to 8% and 6%? Is the estimate more accurate for part C. or D., and why