Consider the following.

a$.$ What is the duration of a two$-$year bond that pays an annual coupon of $12$ percent and whose current yield to maturity is $14$ percent? Use $$1,000$ as the face value. $($Do not round intermediate calculations. Round your answer to $3$ decimal places. $($e$.$ge$,32\mathrm{.}161))$

b$.$ What is the expected change in the price of the bond if interest rates are expected to decrease by $0\mathrm{.}4$ percent? $($Negative amount should be indicated by a minus sign. Do not round intermediate calculations. Round your answer to $2$ decimal places. $($e$.$g$.,32\mathrm{.}16))$