Anne Teak, the financial manager of a furniture manufacturer, is considering operating a lock$-$box system. She forecasts that $600$ payments a day will be made to lock boxes with an average payment size of $$2,000.$ The bank$$s charge for operating the lock boxes is $$0\mathrm{.}40$ a check. The interest rate is $0\mathrm{.}013\%$ per day.

If the lock box makes the cash available $2$ days earlier, calculate the net daily advantage of the system.

Note: Do not round intermediate calculations.

Is it worthwhile to adopt the system?

What minimum reduction in the time to collect and process each check is needed to justify use of the lock$-$box system?

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