a$.$ Find the duration of a $6\mathrm{.}6\%$ coupon bond making annual coupon payments if it has three years until maturity and has a yield to maturity of $6\mathrm{.}6\%.$ Note: The face value of the bond is $$1,000.($Do not round intermediate calculations. Round your answer to $3$ decimal places.$)$

$6\mathrm{.}6\%YTM$

years

b$.$ What is the duration if the yield to maturity is $9\%?$ Note: The face value of the bond is $$1,000.($Do not round intermediate calculations. Round your answer to $3$ decimal places.$)$

$9\%$ YTM years