Anne Teak, the financial manager of a furniture manufacturer, is considering operating a lockbox system. She forecasts that $350$ payments a day will be made to lockboxes with an average payment size of $$2,000.$ The bank$$s charge for operating the lockboxes is $$0\mathrm{.}45$ a check. Assume an interest rate of $9\%$ and a $365-$day year.

What reduction in the time to collect and process each check is needed to justify use of the lockbox system?

Note: Do not round intermediate calculations. Round your answer to $2$ decimal places.