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Heidi Company is considering the acquisition of a machine that costs $$485,000.$ The machine is expected to have a useful life of $6$ years, a negligible residual value, an annual net cash inflow of $$111,000,$ and annual operating income of $$84,937.$ The estimated cash payback period for the machine is $($round to one decimal point$)?$

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

b$.4\mathrm{.}4$ years

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

d$.5\mathrm{.}7$ years