XYZ is a firm in the construction sector with an AAA credit rating. $2$ years ago, $xYZ$ issued a $15-$year bond. The bond makes quarterly payments, has a coupon rate of $6\mathrm{.}45\%$ and a principal of $$1,000,000.$

A$)$ Find the bond's price if the YTM is $6\%$

Assume that right after you finished valuing the bond in part A$),$ market conditions have changed and now the bond is priced at $105\%$ of par value.

B$)$ Find the bond's new YTM

C$)$ Two years ago, XYZ also issued a $30-$year bond with the same coupon frequency, coupon rate, and principal. How do you think the change in market conditions would affect the price of this new bond compared to the $15-$year bond? Explain.

D$)$ What would likely happen to the price of XYZ bonds if their credit rating were demoted to BBB$?$ Explain