Suppose Drake Pile Co$.$ is considering a project to invest in a racehorse over the next $12$ years. They anticipate that the project will cost $$130,000$ to be paid immediately and will yield revenue of $$431,500$ in one lump sum $12$ years from today. Find the internal rate of return $($IRR$)$ on the project if interest is compounded semiannually.

Should Drake Pile Co$.$ accept the project if their cost of capital is $11\mathrm{.}69\%?$