Portfolio A consists of a 2-year zero coupon bond with a face value of $1,000 and a 7-year zero coupon bond with a face value of $3,000. Portfolio B consists of a 5.3-year zero coupon bond with a face value of $7,000. The current yield on all bonds is 8.7% per annum (Continuously compounded).

A)Show that both portfolios have the same duration.

B) Show that the percentage changes in the values of the two portfolios for a 0.05% per annum increase in yields are the same.

Note: The percentage changes in the values should be computed directly from the bond yields (not from the duration relationship: =)