Gates Supply is considering purchasing some new equipment at a cost of $$163,000.$ The equipment has a $3-$year life and is expected to produce cash inflows of $$46,000$ in year $1,$ $$87,000$ in year $2,$ and $$123,000$ in year $3.$ What is the payback period?

a$.2\mathrm{.}06$ years

b$.2\mathrm{.}24$ years

c$.2\mathrm{.}67$ years

d$.3\mathrm{.}11$ years