$2.$ Interpolating Yields.

Suppose that the $5$ year Treasury note has a par yield of $2\mathrm{.}75\%,$ while the $10$ year T$-$Bond

has a par yield of $4\mathrm{.}25\%.$ What are the yields of hypothetical treasury securities that have

the following maturities? Also, what would their yield be at the time they are issued

$($knowing that Treasury bonds are priced at par$)?$

$($a$)6$ years

$($b$)7$ years

$($c$)8$ years

$($d$)9$ year