Carol and Darrell purchase different bonds for the same price $P.$ Carol purchases a zero$-$

coupon bond with a redemption value of $$3000,$ a duration of $6$ years, and an effective annual

yield rate of $5\%.$ Darrell purchases a $10-$year bond with a face value $$800,$ an effective annual

coupon rate of $r,$ and a redemption value of $$2500,$ that is priced to earn an effective annual

yield rate of $4\%.$ Calculate $r.$