Assume that the 3.95% US Treasury bond that matures on 15 August 2041 is priced to yield 5.14% for settlement on 15 November 2014. Coupons are paid semiannually on 15 February and 15 August. The yield-to-maturity is stated on a street-convention semiannual bond basis.

(a) Using the formula showing all calculations, calculate the full price of the US Treasury if the yield is 5.14%?

(b) ComputetheapproximatemodifieddurationandtheapproximateMacaulay duration for this Treasury bond assuming a 5 bp change in the yield-to-maturity. Show all the necessary calculations using appropriate formulas.

Show your work step by step please,