Consider an investment with an initial cost of $$24,000$ and is expected to last for $6$ years. The expected cash flow in years $1$ and $2$ are $$5,500,$ in years $3$ and $4$ are $$7,500$ and in years $5$ and $6$ are $$8,500.$ Compute the payback period in years.

A$.$

$2\mathrm{.}27$ years

B$.$

$3\mathrm{.}73$ years

C$.$

$2\mathrm{.}97$ years

D$.$

$4\mathrm{.}08$ years

E$.$

$3\mathrm{.}20$ years