Interior Designs has an inventory period of $84\mathrm{.}6$ days, an accounts payable period of $43\mathrm{.}2$ days, and an accounts receivable period of $41\mathrm{.}7$ days. Management is considering an offer from their suppliers to pay within $10$ days and receive a discount of $2$ percent. If the new discount is taken, the accounts payable period is expected to decline by $30\mathrm{.}4$ days. What will be the new operating cycle given the change in the payables period?