Portfolio A consist of a one-year zero-coupon bond with a face value of $2000 and a 10-year zero-coupon with a face value of $6,000. Portfolio B consist of a 5.95-year zero-coupon bond with a face value of $5000. The current yield on all bonds is 10% 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 0.1% per annum increase in yields are the same

c What are the percentage changes in the values of the two portfolios for a 5% per annum increase in yields?