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ONLY ANSWER #3 and #4

1. Prices of long-term bonds are more volatile than prices of short-term bonds. However, yields to maturity of short-term bonds fluctuate more than yields of long-term bonds. How do you reconcile these two empirical observations? 2. How can a perpetuity, which has an infinite maturity, have a duration as short as 10 or 20 years? 3. A 9-year bond paying coupons annually has a yield of 10% and a duration of 7.194 years. If the market yield changes by 50 basi what is the percentage change in the bond's price? 4. a. Find the duration of a 6% coupon bond making annual coupon payments if it has three years until maturity and has a yield maturity of 6%. b. What is the duration if the yield to maturity is 10%