You work for the Yale Endowment in the fixed$-$income trading desk. You trade different types of fixed$-$income securities and have a $1-$year investment horizon. You are trying to choose among three bonds. All have the same degree of default risk and mature in $10$ years. The first is a zero$-$coupon bond that pays $$1,000$ at maturity and issued by the city of New Haven. The second has an $6\%$ coupon rate and pays the $$60$ coupon once per year and is issued by the Yale University Board of Trustees. The third has a $10\%$ coupon rate and pays the $$100$ coupon once per year and is issued by the state of Connecticut. Which of the three bond's prices is most sensitive to a $1\%$ increase in interest rates $($e$.$g$.,$ the YTM goes from $6\%$ to $7\%)?$