An energy conservation option has a first cost of $$50,000.$ It requires $$4,000$ per year maintenance and saves $$10,000$ per year in utilities. Calculate the life$-$cycle costs for the two cases $(2\%$ decrease in productivity pay back $10\mathrm{.}42$ years, $2\%$ increase in productivity payback $6\mathrm{.}94$ years$)$ for a $5\%$ discount rate and a $15\%$ discount rate?