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 5%, 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 6%.

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 4%.

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 6% and 4%? Is the estimate more accurate for part C. or D., and why?