On August $1,$ Batson Company issued a $60-$day note with a face amount of $$90,000$ to Jergens Company for merchandise inventory. $($Assume a $360-$day year is used for interest computations.$)$

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

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