On January $1,$ Applied Technologies Corporation $($ATC$)$ issued $$500,000$ in bonds that mature in $10$ years. The bonds have a stated interest rate of $10$ percent. When the bonds were issued, the market interest rate was $10$ percent. The bonds pay interest once per year on December $31.$

Required:

$1.$ Determine the price at which the bonds were issued and the amount that ATC received at issuance.

$2.$&$3.$ Prepare the required journal entries to record the bond issuance and the first interest payment on December $31$ assuming no interest has been accrued earlier in the year.