The prices of two bonds with $10-$year maturities are $81\mathrm{.}62\%($for a $2\%$ pa coupon rate$)$ respectively $133\mathrm{.}42\%($for a $8\%$ pa coupon rate$).$ These annual coupons are paid annually.

$($a$)$ Calculate the yields to maturity and durations of each of these bonds.

$($b$)$ Which bond o$$ers the higher vs$.$ lower yield to maturity? Which one has the longest and shortest duration?