Portfolio A consists of a two-year zero-coupon bond with a face value of $3,000 and a 10-year zero-coupon bond with a face value of $7,000. Portfolio B consists of a 6.88-year zero-coupon bond with a face value of $10,000. The current yield on all bonds is 5% 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 to 0.01%.

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