Consider three semi$-$annual coupon bonds with $6$ percent coupon rates, all

selling at face value. The short$-$term bond has a maturity of $3$ years, the

intermediate$-$term bond has maturity of $12$ years, and the long$-$term bond has

maturity of $20$ years. $[13$ marks$]$

$($a$)$ Calculate the price of each bond if their yields increase to $9$ percent and

discuss what happens.

$($b$)$ Calculate the price of each bond if their yields decrease to $4$ percent and

discuss what happens.

$($c$)$ What do you conclude about the relationship between time to maturity

and the sensitivity of bond prices to interest rates?