Consider a 27-year maturity US Treasury bond with a 1.25% coupon rate and a par value of $100. The coupon payment frequency is semi-annual. This bond is priced at $55.9994 with a 3.90% yield and has a duration of 20.8 and a convexity of 529. Use a Taylor series approximation to estimate the percent change in the price of this bond when:

a) the yield is increased by 100 basis points to 4.90%

b) the yield is reduced by 100 basis points to 2.90%

c) What do you observe about your results in a) and b)?

Explain your answers clearly.