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?

Please show calculations, I am having difficulties comprehending these equations...