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# Interest Rate Risk: Consider a 10-year zero coupon bond. Using the bond pricing equation, P(y), illustrate the derivation (using calculus) of this...

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 bond’s modified duration. Note: the correct answer is an equation, not a number.B. Assuming the yield-to-maturity is 7%, compute the bond’s modified duration. C. Use your answer to part B to estimate the price of the bond and the percentage price change ifinterest rates instantaneously rise to 8%. D. Use your answer to part B to estimate the price of the bond and the percentage price change ifinterest rates instantaneously decline to 6%. E. How do the estimates from C. and D. compare to the true prices using the bond pricingequation P(y) if yields change to 8% and 6%? Is the estimate more accurate for part C. or D., and why?