Consider the following bond:

Coupon rate $=11\%$

Maturity $=18$ years

Par value $=$ $$1,000$

First par call in $13$ years

Only put date in five years and puttable at par value

Suppose that the market price for this bond $$1,169.$

$($a$)$ Show that the yield to maturity for this bond is $9\mathrm{.}077\%$ by using the formula.

$($b$)$ Show that the yield to first par call is $8\mathrm{.}793\%.$

$($c$)$ Show that the yield to put is $6\mathrm{.}942\%.$

$($d$)$ Suppose that the call schedule for this bond is as follows:

Can be called in eight years at $$1,055$

Can be called in $13$ years at $$1,000$

And suppose this bond can only be put in five years and assume that the yield to eight years$$call is $8\mathrm{.}535\%.$ What is the yield to worst for this bond?