Anne Teak, the financial manager of a furniture manufacturer, is considering operating a lockbox system. She forecasts that $250$

payments a day will be made to lockboxes with an average payment size of $$3,000.$ The bank's charge for operating the lockboxes is

$$0\mathrm{.}55$ 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? $($Do not round

intermediate calculations. Round your answer to $2$ decimal places.$)$

Required time reduction

days

$($ The answer was not $185\mathrm{.}78$ days $)$