Bond A is 1-year a zero coupon bond with a par of $1,000. Bond B is a 1-year 10% coupon bond with a par of $1,000. The current yield to maturity is 10%.

a) Calculate the Macaulay duration and the modified duration for bonds A and B.

b)Suppose a bond portfolio includes one share of A and one share of B. What are the Macaulay duration and the modified duration of the bond portfolio?

c) If the required yield increases to 10.1%, what is approximate percentage change in the price of the bond portfolio based on the modified duration?