Determine the payback period in years for a project that costs $$42,000$ and would yield after$-$tax cash flows of $$7,000$ the first year, $$9,000$ the second year, $$12,000$ the third year, $$14,000$ the fourth year, $$18,000$ the fifth year, and $$24,000$ the sixth year.

Question $7$ options:

$3\mathrm{.}24$

$3\mathrm{.}38$

$3\mathrm{.}77$

$4\mathrm{.}00$

$4\mathrm{.}21$