Halifax Manufacturing allows its customers to return merchandise for any reason up to $90$ days after delivery and receive a credit to their accounts. All of Halifax's sales are for credit $($no cash is collected at the time of sale$).$ The company began $2024$ with a refund liability of $$410,000.$ During $2024,$ Halifax sold merchandise on account for $$13,500,000.$ Halifax's merchandise costs are $65\%$ of merchandise selling price. Also during the year, customers returned $$532,000$ in sales for credit, with $$294,000$ of those being returns of merchandise sold prior to $2024,$ and the rest being merchandise sold during $2024.$ Sales returns, estimated to be $4\%$ of sales, are recorded as an adjusting entry at the end of the year.

Required:

Prepare entries to $($a$)$ record actual returns in $2024$ of merchandise that was sold prior to $2024$; $($b$)$ record actual returns in $2024$ of merchandise that was sold during $2024$; and $($c$)$ adjust the refund liability to its appropriate balance at year end.

What is the amount of the year$-$end refund liability after the adjusting entry is recorded?