Annual credit sales of Nadak Company total $$324\mathrm{.}6$ million. The firm gives a $2\mathrm{.}25\%$ cash discount for payment within $10$ days of the invoice date; $75\%$ of Nadak's accounts receivable are paid within the discount period.

Required:

a$.$ What is the total amount of cash discounts allowed in a year?

b$.$ Calculate the approximate annual rate of return on investment that Nadak Company's cash discount terms represent to customers who take the discount. $($Assume a credit period of $30$ days and $360-$days year$).$