Consider three bonds with $14\mathrm{.}66\%$ coupon rates, all selling at face value. The short$-$term bond has a maturity of $4$ years, the intermediate$-$term bond has maturity $8$ years, and the long$-$term bond has maturity $30$ years. $$

a$.$ What will be the price of each bond if their yields increase to $16\mathrm{.}1\%?$

b$.$ What will be the price of each bond if their yields decrease to $11\mathrm{.}7\%?$