A firm is planning to improve its infrastructure, and currently there are two projects considered for this purpose: Project $x$ and Project Y$.$ Project $x$ has an initial cost of $$69,231\mathrm{.}84$ and is expected to generate annual cash flows of $$8,000$ for the next $20$ years. Project $Y$ has an initial cost of $$39,000\mathrm{.}00$ and is expected to generate annual cash flows of $$4,700$ for the next $20$ years. What is the crossover rate?

$8\mathrm{.}41\%$

$8\mathrm{.}06\%$

$8\mathrm{.}95\%$

$9\mathrm{.}49\%$

$9\mathrm{.}13\%$