a$.$ Find the duration of a $8\%$ coupon bond making annual coupon payments if it has three years until maturity and a yield to maturity of $6\mathrm{.}9\%.($Do not round intermediate calculations. Round your answers to $4$ decimal places.$)$

b$.$ What is the duration if the yield to maturity is $10\mathrm{.}9\%?($Do not round intermediate calculations. Round your answers to $4$ decimal places.$)$