A software company that installs systems for inventory control using RFID technology spent $$700,000$ per year for the past $3$ years in

developing their latest product. The company optimistically hopes to recover its investment in $5$ years on a single contract beginning

immediately $($year $0).$ The company is negotiating a contract that will pay $$270,000$ now and a to$-$be$-$agreed$-$upon annual increase of a

constant amount each year through year $5.$ How much must the income increase $($an arithmetic gradient$)$ each year if the company

wants to realize a return of $13\mathrm{.}00\%$ per year? $($Round the final answer to three decimal places.$)$

The income must increase by $