A currently used machine costs $$10,000$ annually to run. What is the maximum that should be paid to replace the machine with one that will last $3$ years and cost only $$4,000$ annually to run? The opportunity cost of capital is $12\%.$

Multiple Choice

a$.$ $$9,607\mathrm{.}33$

b$.$ $$10,388\mathrm{.}56$

c$.$ $$15,209\mathrm{.}84$

d$.$ $$14,410\mathrm{.}99$