Hayden Company is considering the acquisition of a machine that costs $$447,000.$ The machine is expected to have a useful life of $6$ years, a negligible residual value, an annual net cash inflow of $$99,000,$ and annual operating income of $$84,150.$ The estimated cash payback period for the machine is $($round to one decimal place$)$

a$.1\mathrm{.}2$ years

b$.4\mathrm{.}5$ years

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

d$.5\mathrm{.}3$ years