Heidi Company is considering the acquisition of a machine that costs $$509,000.$ The machine is expected to have a useful life of $6$ years, a negligible residual value, an annual net cash inflow of $$119,000,$ and annual operating income of $$82,541.$ The estimated cash payback period for the machine is $($round to one decimal point$)$

a$.6\mathrm{.}2$ years

b$.6\mathrm{.}5$ years

c$.5\mathrm{.}0$ years

d$.4\mathrm{.}3$ years