Please show all work and explain. Especially explain how finding N works I am confused on that and list equations. If you dont know how to answer please just dont I really need it to be correct. Answers given. Thanks.

On $3/9/2013$ a $30-$year corporate bond was issued with a coupon of $3\mathrm{.}5\%.$

a$.$ What would be the bond$$s quoted price on $9/9/2016$ if the YTM is $3\mathrm{.}5\%?$ If the YTM is

$3\mathrm{.}0\%?$ If the YTM is $4\mathrm{.}0\%?100\mathrm{.}000$; $109\mathrm{.}096$; $91\mathrm{.}876$

b$.$ What would be the bond$$s quoted price on $9/9/2022$ if the YTM is $3\mathrm{.}8\%?$ If the YTM is

$4\mathrm{.}2\%?95\mathrm{.}974$; $90\mathrm{.}442$

c$.$ What would be the bond$$s price on $3/9/2024$ if the YTM is $3\mathrm{.}2\%?$ If the YTM is $4\mathrm{.}1\%?$

$$1,042\mathrm{.}46$; $$921\mathrm{.}34$