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 bonds with a face value of $5,000 in maturity, all of which currently yield 10% a year (compounded continuously).

(1) Prove that the two combinations have the same duration.

(2) Prove that if the yield increases by 0.1%, the change in the value of the two portfolios will be the same as the percentage change in the interest rate.

(3) How can the yield rise by 5%? What percentage of the change in the value of the two portfolios is the change in interest rates.