On July $1,2024,$ Dirty Harry Company borrowed cash by issuing a $6-$month noninterest$-$bearing note with a maturity value of $$450,000$ and a discount rate of $9\%($issue value is therefore $$409,500).$ Assuming straight$-$line amortization of the discount, what is the carrying value of the note as of September $30,2024?$

Note: Round all calculations to the nearest whole dollar amount.

$$409,500$

$$429,750$

$$423,000$

$$450,000$