Michael Scott Paper, Inc. is considering a new machine that requires an initial investment of $$650,000,$ including installation costs, and has a useful life of ten years. The expected annual after$-$tax cash flows for the machine are $$90,000$ during the first two years, $$115,000$ during years three through six, and $$85,000$ during the remaining years of its useful life. What is the internal rate of return $($IRR$)?$

Group of answer choices

$8\mathrm{.}50\%$

$14\mathrm{.}97\%$

$7\mathrm{.}61\%$

$5\mathrm{.}20\%$