Cow Chips, Inc., a large fertilizer distributor based in California, is planning to use a lockbox system to speed up collections from its customers located on the East Coast. A Philadelphia$-$area bank will provide this service for an annual fee of $$15,000$ paid at the end of the year plus $10$ cents per transaction. The estimated reduction in collection and processing time is one day. Treasury bills are currently yielding $5$ percent per year.

If the average customer payment in this region is $$5,200,$ how many customers are needed, on average, each day to make the system profitable for the company? $($Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$