Portfolio A consists of a one-year zero-coupon bond with a face value of $2,000 and a 10-year zero-coupon bond with a face value of $6,000. Portfolio B consists of a 5.95-year zero-coupon bond with a face value of $5,000. The current yield on all bonds is 10% per annum.

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?