a$.$ What is the duration of a two$-$year bond that pays an annual coupon of $10\mathrm{.}9$ percent and has a current yield to maturity of $13\mathrm{.}5$

percent? Use $$1,000$ as the face value. $($Do not round intermediate calculations. Round your answer to $4$ decimal places. $($e$.$g$.,$

$32\mathrm{.}1616))$

b$.$ What is the duration of a two$-$year zero$-$coupon bond that is yielding $11\mathrm{.}5$ percent? Use $$1,000$ as the face value.