$[$Ch $9]$ Barrone Sanitation is considering project that will require an initial outlay of cash today of $$11,107,000.$ The project is expected to generate $$725,000$ of free cash flows per year for the next $20$ years. Barrone's opportunity cost of capital is $10\mathrm{.}8\%$ per year, compounded annually. What is the payback period for the project?

$($to nearest $0\mathrm{.}0001$ year$)$