On August $1,$ Batson Company issued a $60-$day note with a face amount of $$48,000$ to Jergens Company for merchandise inventory. $($Assume a $360-$day year is used for interest calculations.$)$

a$.$ Determine the proceeds of the note assuming the note carries an interest rate of $12\%.$

b$.$ Determine the proceeds of the note assuming the note is discounted at $12\%.$