HMK Enterprises would like to raise $$10\mathrm{.}0$ million to invest in capital expenditures. The company plans to issue $5-$year bonds with a face value of $$1,000$ and a coupon rate of $6\mathrm{.}51\%($annual payments$).$ The following table summarizes the yield to maturity for $5-$year $($annual$-$payment$)$ coupon corporate bonds of various ratings:

a$.$ Assuming the bonds will be rated $AA,$ what will be the price of the bonds?

b$.$ How much of the total principal amount of these bonds must HMK issue to raise $$10\mathrm{.}0$ million today, assuming the bonds are AA rated? $($Because HMK cannot issue a fraction of a bond, assume that all fractions are rounded to the nearest whole number.$)$

c$.$ What must be the rating of the bonds for them to sell at par?

d$.$ Suppose that when the bonds are issued, the price of each bond is $$956\mathrm{.}80.$ What is the likely rating of the bonds? Are they junk bonds?

a$.$ Assuming the bonds will be rated $AA,$ what will be the price of the bonds?

The price of the bonds will be $$,($Round to the nearest cent$)$

Data table

$($Click on the following icon $$ in order to copy its contents into a spreadsheet.$)$

$\backslash$table$[[$Rating$,$AAA,AA$,$A$,$BBB$,$BB$],[$YTM$,6\mathrm{.}15\%,6\mathrm{.}36\%,6\mathrm{.}51\%,6\mathrm{.}92\%,7\mathrm{.}58\%$