Jays diamonds is a high end jewelry store which operates in New york. On average they have daily cash receipts of $180000.$ Its CFO is analyzing the time it takes for the collection of customers payment to clear the banking system. From the analysis, it appears many of the customers are based in the US$,$ and make payments via checks. The mail float is estimated at $2$ days and it takes an additional $2$ days for the payment to be processed before it is transferred to the bank. Then it takes another $3$ days for the bank to process the payment and make it available for jays diamonds. There are $365$ days in a year.

$8$a$.$ How much collection float $($in days$)$ does the company currently have.

$8$b$.$ The bank mentions they can reduce the float by one day if they pay an annual fee of $$18,000.$ If the company$$s opportunity cost is $8\%,$ would it be economically advisable for them to pay an annual fee of $$18,000$ to reduce the collection floor by $1$ day? Explain your answer.