A $3-$year $2\%$ $$3500$ bond has annual coupons and a redemption amount of $$3580.$ Find the modified convexity $($compounded annually$)$ and the Macaulay convexity of this bond at an annual interest rate of $4\mathrm{.}5\%.$ Round your answers to three decimal places.

$($a$)(0\mathrm{.}045,1)=$ years

$($b$)(0\mathrm{.}045,\backslash$infty $)=$ years