Please show the formular and the work for each question, thank you.
ABC Corp has a 5% coupon bond making annual payments that matures in 4 years.
a) Find the duration of the bond if it has a yield to maturity of 3%.
b) Using the modified duration relationship, find the price of the bond if the yield goes down 75bps.
c) Compared to a zero-coupon bond that has a maturity of 4 years, which bond would change most to a rate change? Explain without using calculations.