Two manufacturers supply MRI systems for medical imaging. St$.$ Jude's Hospital wishes to replace its current MRI equipment that was purchased $8$ years ago with the newer technology and clarity of a state$-$of$-$the$-$art system. System $K$ will have a first cost of $$1,600,000,$ an operating cost of $$70,000$ per year, and a salvage value of $$400,000$ after its $4-$year life. System $L$ will have a first cost of $$2,100,000,$ an operating cost of $$50,000$ the first year with an expected increase of $$3000$ per year thereafter, and no salvage value after its $8-$year life. Which system should be selected on the basis of a future worth analysis at an interest rate of $12\%$ per year? The following steps are required: $(1)$ Create a clean cash flow diagram for each option, $(2)$ write formula, $(3)$ determine factor values, $(4)$ complete calculation, and $(5)$ provide answer.