### Show that both portfolios have the same duration

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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 discount 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?

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