Chevron Phillips has put into place new laboratory equipment for the production of chemicals; the initial cost is $$1,800,000$ installed. Chevron Phillips borrows $45\%$ of all capital needed, and the borrowing rate is $12\mathrm{.}5\%$ over $4$ years. The throughput rate for in$-$process test samples has increased the capacity of the lab, with a net savings of $$$ per year. Depreciation follows MACRSGDS, MARR is $11\%,$ and the planning horizon is $6$ years with a salvage value of $$250,000$ at that time. Use Goal Seek or Solver in Excel $$ to determine the value of X such that MARR is exactly achieved, no more and no less, if:

a$.$ The loan is paid back using Method $1($interest only at the end of each year of the loan, plus principal at the end of the last year$).$

b$.$ The loan is paid back using Method $2($equal annual principal payments plus interest on the unpaid loan balance$).$

c$.$ The loan is paid back using Method $3($equal annual principal plus interest payments during each year of the loan$).$

d$.$ The loan is paid back using Method $4($principal plus interest is paid at the end of the loan period$).$

An important step in this problem is determining the principal and interest payments on the loan for the laboratory equipment. Method $1$ has interest only at the end of each year of the loan plus principal at the end of the last year. Method $2$ has equal principal payments plus interest on the unpaid loan balance. Method $3$ has equal annual principal plus interest payments during each year of the loan. Method $4$ has principal plus interest is paid at the end of the loan period. They financed $45\%$ of the $$1,800,000$ at $12\mathrm{.}5\%$ per year over $4$ years and keep it for $6$ years. Based on this information, fill in the following chart:

$\backslash$table$[[$EOY$,$Method $1,,$Method $2,$Method $3,,$Method $4,],[,$Principal,Interest,Principal,Interest,Principal,Interest,Principal$]]$