On January $1,2023,$ Targaryen Corp. issued $$750,000$ of $8\%,10-$year bonds, with annual interest payments on December $31.$ The bonds were issued for $$657,831$ yielding an effective$-$interest rate of $10\%.$ Targaryen Corp. uses the effective$-$interest method of amortization.

$1.$ Prepare the necessary journal entries to record the issuance of the bonds and the first interest payment.

$2.$ Determine the carrying value of the bonds on December $31,2023.$