Problem $6.$ A construction company has made a nonrefundable deposit of the first month's rent

$($equal to $$10,000)$ on a $6-$month bulldozer lease. The next day the company finds a different

bulldozer that is suitable for their current project as well, but its monthly rent is only $$9,000.$

They plan to use the bulldozer only $6$ months. Should they switch to the new bulldozer? What if

they plan to use $1$ year? Assume a nominal interest rate of $6\%$ per year, compounded monthly.

$($Hint: This problem is about comparing options$/$alternatives$.$ The concepts are similar to

Problem $9$ in the "Mathematics of Money" worksheet$).$