A currently used machine costs $$11,000$ annually to run. What is the maximum that should be paid to replace the machine with one that will $3$ years and

will cost only $$2,000$ annually to run? The opportunity cost of capital is $9\%.$

The maximum amount that should be paid is:

$

$($please round your final result to $2$ decimals, but keep as many decimals as possible during calculation$)$