Bond A maturing in October 2029, with a face value of $1,000 and a coupon rate of 5.25% and Bond B maturing in October 2027, with a face value of $1,250 and a coupon rate of 6.15%. (a) Calculate duration and modified duration for the two bonds, assuming for Bond A a YTM of 5%, and for Bond B a YTM of 6%, and both bonds priced at par. How does the duration change for each bond, when YTM increases by 1 percentage point? What is the percentage change in the price of bond due to 1 percentage point change in yield for each bond? (b) Now, suppose the quoted price of the bond is $990 for Bond A and $1,240 for Bond B. How do your answers to (a) change? (c) Assuming expected inflation in 2028 and 2029 of 2.1% and 1.9%, respectively, which bond is a better investment at quoted prices in (b)? Why? Show your work (preferred submission via Excel).