Selected information for Morgan Inc for a recent fiscal year $($year ending $6/30/2023)$ is presented below $($dollar amounts in millions$)$:

Note $($Maturity Date$)$ Reported Book Value, $6/30/2023$ Reported Book Value, $6/30/2024$ Stated Interest Rate Effective Interest Rate

@ date notes were issued

October $1,20251,0001,0003\mathrm{.}00\%3\mathrm{.}14\%$

May $1,20289991,0002\mathrm{.}38\%2\mathrm{.}47\%$

December $6,20332,0441,9933\mathrm{.}13\%3\mathrm{.}22\%$

Required:

$(1)$ Are the October $1,2025$ notes issued at par, at a discount, or at a premium? Why?

$(2)$ Are the May $1,2028$ notes recorded at a discount or a premium? Why?

$(3)($a$)$ Are the December $6,2033$ notes recorded at a discount or a premium? Why? $($b$)$ What explains the decrease in the notes from the beginning to the end of the fiscal year?

$(4)$ Assume that Moody's reports that the October $1,2025$ notes were originally rated as Aaa. $($a$)$ If Moody's lowers the rating to Aa$1($which signals an increase in risk$),$ what is the effect on the effective interest rate? Would it be higher, lower or the same? $($b$)$ If the notes had been secured by collateral, would the effective interest rate have been higher, lower, or the same?