Problem $13\mathrm{.}033-$ Calculate the payback period considering the time$-$value of money

Accusoft Systems is offering small business owners a software package that keeps track of many accounting functions from bank transactions to sales invoices. The site license will cost $$60,000$ to install and will require a fee of $$5,000$ every $3$ months. If your company can save $$13,500$ every quarter and have the security of managing its books in$-$house, how long will it take for you to recover the investment at an interest rate of $10\mathrm{.}00\%$ per quarter? $($Round the final answer to three decimal places.$)$

The time taken to recover the investment is determined to be $$ quarters.